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APPLETONS' CYCLOPAEDIA 
OF TECHNICAL DRAWING 



EMBRACING THE PRINCIPLES OF CONSTRUC- 
TION AS APPLIED TO PRACTICAL DESIGN 



IVITH NUMEROUS ILLUSTRATIONS OF TOPOGRAPHICAL, 

MECHANICAL, ENGINEERING, ARCHITECTURAL, 

PERSPECTIVE, AND FREE-HAND DRAWING 



EDITED BY 

W. E. WORTHEN, C. E. 





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NEW YORK 
D. APPLETON AND COMPANY 



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Copyright, 1885, 1896, 
By D. APPLETON AND COMPANY. 



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PREFACE 



'' At the suggestion of the publishers, this work was undertaken to form 
one of their series of dictionaries and cyclopaedias. In this view, it has 
been the intention to make it a complete course of instruction and book of 
reference to the mechanic, architect, and engineer. It has not, therefore, 
been confined to the explanation and illustration of the methods of projec- 
tion, and the delineation of objects which might serve as copies to the 
draughtsman, matters of essential importance for the correct and intelligible 
representation of every form ; but it contains the means of determining the 
amount and direction of strains to which different parts of a machine or 
structure may be subjected, and the rules for disposing and proportioning 
of the material employed, to the safe and permanent resistance of those 
strains, with practical applications of the same. Thus, while it supplies 
numerous illustrations in every department for the mere copyist, it also 
affords suggestions and aids to the mechanic in the execution of new 
designs. And, although the arranging and properly proportioning alone 
of material in a suitable direction, and adequately to the resistance of the 
strains to which it might be exposed, would produce a structure sufficient 
in point of strength for the purposes for which it is intended, yef, as in 
many cases the disposition of the material may be applied not only practi- 
cally, but also artistically. . . . 1857." 

" There are no changes in the principles of projection as applied to 
drawing, and no marked improvement in drawing-instruments ; but in the 
present practice finished drawings in shade and colour are exceptional. It 
is sufficient, for almost every purpose, for the draughtsman to make accu- 
rate projections with pencil on paper, and trace them afterward on cloth. 
The pencil-drawings can be readily altered or amended, and, where there 
are many repetitions of the same parts, but a single one may be drawn. 
On the tracing they are made complete, and these are preserved as originals 
in the office, while sun-prints of them are used for details of construction 
in the shop, or distributed as circulars among customers. 

" Of late years the science of ' graphics ' has become of great impor- 
tance, and is here fully illustrated in its varied applications, showing not 
only this method of recording the facts of the statistician, and affording 
comparisons of circumstances and times, the growth of population, the 

iii 



iv PREFACE. 

quantities and cost of agricultural and meclianical production, and of their 
transport, movements of trade, fluctuations of value, the atmospheric con- 
ditions, death-rates, etc., but also in its application to the plotting of 
formulae for their ready solution, by the draughtsman and designer. For 
many of the rules in this work the results of the formulae of various 
authors have been plotted graphically, and the rule given one deemed of 
the greatest weight, not always by average, but most consistent with our 
own experience. 

" In astronomical calculations every decimal may have its importance. 
It is not so in those of the mechanical or architectural designer ; solutions by 
graphics are sufficient for their purpose, and, simpler than mathematical 
calculations, they are thus less liable to error ; it is a very good practice to 
use one as a .check on the other. It is to be remarked that inaccuracy in 
facts, and carelessness in observation, are not eliminated from an equation 
by closeness of calculation, and when factors are not established within the 
limits of units it is useless to extend the results to many places of decimals. 
It is of the utmost importance to know at first well the object and pur- 
poses of the design, the stresses to which its parts are to be subjected, and 
the strength and endurance of the materials of ^ which it is to be composed. 
In establishing rules for ourselves, be sure of the facts, and that there are 
enough of them for a general application. Kules are necessary, but their 
application and usefulness depend largely on the experience of the user, 
and hfe must be a record of applications and effects. It is comparatively 
easy to make a work strong enough ; but to unite economy with propor- 
tion is difficult. . . . 1886." 

The first edition of this work was suggested by '' The Engineer and 
Machinist's Drawing Book" of Messrs. Blackie & Son, 1855, from which, 
with the consent of the publishers, much of the text and illustrations were 
taken. Since then, in the many editions, it has been the aim to keep up 
with mechanical progress, and matter has been drawn from all sources. 
Credit, as far as possible, has been given to mechanics for their designs and 
to experimenters for their results. 

Geometrical problems and examples of orthographic projection of the 
first work are largely retained, but examples of mechanical and archi- 
tectural construction are brought up to the present age of steel, with the 
latest illustrations of the applications, of steam, and some of electricity. 
Isometry is retained, perspective has been more fully illustrated, and free- 
hand drawing now includes the recent processes by which, through pho- 
tography, the mechanical labour of sketching is diminished, adding to the 
correctness of detail and improving the effectiveness on paper. This may 
be called an age of illustration, and the processes have enabled a work like 
the present drawing book to give better and more illustrations, less text, 
more comprehensiveness, and greater certainty of detail. 

Mr. Eobert E. Hawley,' brought up in my office, has had charge of the 
new drawings and has acted as co-editor. W. 



CONTENTS 



PAGES. 

Construction of Geometrical Problems 1-82 

Drawing of lines — straight, curved, perpendicular, and parallel : angles, arcs, 
and circles, 18. Triangles, polygons and circles, inscribed and described ; 
polygonal angles ; use of protractor, 21. Use of the triangle and square ; areas 
of figures ; scales, 25. Similar triangles, squares of proportionate sizes, 30. El- 
lipse, parabola, hyperbola, spiral, 35. Drawing-board, table ; straight-edges ; 
T-squares ; parallel rulers ; curves, variable and adjustable ; splines and weights ; 
thumbtacks; drawing pens; dotting instrument; compasses; dividers; plot- 
ting scales; protractors; sector; pantographs, 51. Drawing paper; tracing 
paper ; tracing cloth ; heliographic paper ; damp stretching and mounting, 55. 
Use of instruments ; representation of surfaces ; enlarging and reduction of 
drawings; designs in lines, 62. Lettering; profile and cross-section paper, 77. 
Ornamental designs in straight and curved lines, 82. 

Plotting 83-94 

Scales ; plotting for surveys, plans and maps : plotting by protractor, by lati- 
tudes and departures, by triangles, by offsets ; United States division of public 
lands, 94. 

Topographical Drawing 95-120 

Conventional signs ; representation of hills; chart from United States Sur- 
vey, 102. Railway, 103. Hydrometrical chart, geological and section, 109. 
Transferring field notes, 110. Map projections, 116. Colored topography;" 
pen and brush work, 119. Meridians and borders, 120. 

Orthographic Projection 121-146 

Point ; straight line ; solid ; simple bodies ; pyramid ; prism, 127. Conic 
sections, 130. Intersection of solids, 139. The helix, 141. Development of 
surfaces, 144. Shade lines, 146. 

Shades and Shadows 147-166 

Shadow of a point, of a straight line, of a solid, of a pyramid, of a cylinder, 
of a hollow hemisphere; niche, 154. Lines of shade on sphere ; ring; grooved 
pulley; screw, 159. Manipulation shades, surfaces in light, in shade by flat 
tints, by softened tints. Examples in plates. Conventional tints, 166. 

Materials * 167-185 

Earth and rocks ; woods, 170. Masonry, technical terms for ; stones, gra- 
nitic, argillaceous, sand, lime, 174. Artificial building material ; brick, sizes of ; 
fire; enamelled tile; terra cotta, 175. Mortars; concrete; plastering; weight 
of masonry, 177. Metals, conventional signs of, properties of; alloys, strength 
of, graphic representation by Prof. Thurston ; sulphur ; glass ; rubber ; paints ; 
coal ; flame, 185. 

V 



vi CONTENTS. 



Mechanics 186-228 

Force ; centres of gravity ; mechanical powers ; parallelogram of forces ; 
toggle joint ; hydraulic press ; statics ; dynamics ; velocity of falling bodies, 
196. Friction, 201. Mechanical work ; unit of force ; the force of animals, 
water, steam, and their application ; the steam-pressure indicator and cards, 
211. Motion, example of the path of ; parts of machines ; of the crank ; the 
Stanhope lever ; Whitworth's quick return ; parallel motion ; car coupler, 218 ; 
valve diagram ; Corliss cut off : link motion ; valve gear, 228. 

Machine Design and Mechanical Construction 229-414 

Stress ; strain ; dead load ; factor of safety ; safe load of columns, cast and 
wrought iron : shearing, torsional and transverse stress ; graphic diagrams, 
239. Table of safe load on yellow-pine beams, on cast iron, on wrought iron, 
on steel ; box girders ; composite, 250. Bolts and nuts ;" screws ; washers, 257. 
Shafts and axles, cast and wrought iron, 262. Pillow blocks ; standards ; 
hangers ; steps ; suspension and thrust bearings,' 273. Couplings ; clutches, 
282. Pulleys, wooden and iron plates ; cone, 287. Belts, plain, twist, and 
cross. Strength of rope driving, 299 ; chain driving ; leather links, 301. 
Gearing, spur, rack, and pinion ; bevel. Form of teeth ; cycloid ; hypocycloid ; 
involute, 310. Diagram of stress on teeth ; diameter of pitch circle. Adcock's 
table of arcs for gear teeth ; mortise wheels, 316. Projections of a spur, bevel, 
and worm wheels ; screws, 330. Frictional and wedge^gearing, 383. Blocks for 
running rigging ; chains ; chain couplings ; wire rope ; sockets ; hooks ; 337. 
Levers, cranks, 342. Eccentrics; wiper; stamp mill, 347. Connections, cot- 
ters, pins, rods, 348. Eccentrics and straps ; crossheads, 354. Working beam ; 
guide bars, 358. Steam cylinders ; pistons of pumps. Water pumps, 362. Wood 
and cup packing, 364. Steam jacket ; air chamber ; Thames Ditton pump ; 
Reidler ; Worthington, 366. The injector, 368. Clearances ; piston rods ; stuff- 
ing boxes, 370. Steam ports ; Valves, cylindrical, balanced, automatic, 
disk, rubber, ball, poppet, flap, 376. Valves controlled by hand, cocks, 
plug. Valves : compression, air, globe, gate, damper rotary, safety, 382. Hy- 
drants, 383. Hiveted joints, 389. Boilers: tubular, marine ; water tube ; ilue : 
locomotive, vertical, 398. Connections of steam and water pipes ; wrought- 
iron pipes ; couplings ; unions ; coils ; joints for submerged pipes, 406. Gov- 
ernor ; fly-wheels ; air chambers ; accumulators ; hydraulic press ; jack screw ; 
housings. 

Engineering Drawing 415-547 

Foundations ; concrete base ; crib work ; New York dock ; Thames embank- 
ment ; breakwater ; screw piles ; masonry curbs ; steel caissons ; Poughkeepsie 
bridge pier ; pneumatic piles ; caissons and air lock ; freezing process, 435. 
Retaining walls, 436. Dams : earth, crib, masonry, 444. Gates : head, waste, 
451. Canals, navigation, power. Locks of canals ; flumes and conduits, 459. 
Reservoirs ; sheet-iron pipe ; water tanks, 462. Water mains for city service ; 
specials ; inspection, 466. Sewers : brick, vitrified pipe, circular, egg-shaped, 
concrete, man-holes, 471. Gas supply, 472. Roads and highways ; street pave- 
ments : granite, asphalt, wooden, block, 479. Railroads ; road bed ; rails ; elec- 
tric conduit, 483. Roofs and bridges ; principle of bracing ; frames, wooden, 
iron ; trestles, 498 ; truss bridges : wooden, iron, combination, 510. Turn ta- 
bles ; ferry-landing bridge ; high wrought-iron trestles ; masonry piers ; arch 
bridge, 522. Boiler setting, horizontal, tubular, 526 ; chimneys, 530. Loca- 
tion of machines ; foundation, 535. Tunnels ; principles of timbering ; Hoo- 
sac ; bar timbering, 539. Railway rolling stock ; box car ; standard passenger ; 
locomotive frame, 545. Wave-line principle of ship construction, 547. 



CONTENTS. vii 

PAGES 

Architectural Construction 548-693 

Plans and elevations, 553 ; details of construction ; timber frames and 
floors, 561. Examples of fire-proofing, old, recent ; skeleton frames, fire-re- 
tarding construction of mills, 571 ; windows ; stairs ; doors. Fireplaces ; 
flues ; roofs ; gutters ; cornices, 587. Plastering ; mouldings, 590. Sizes of 
rooms ; water appliances and accessories ; Ferguson's rules of proportion ; de- 
signing of house ; illustration and details ; country and city, 609. Apartment 
houses ; store and warehouses ; machine-shop ; school-houses ; churches ; 
theatres ; lecture rooms ; music and legislative halls ; waves of sound ; effect 
of air currents ; space for seats; ancient and modern churches; organs; 628. 
Theatres, dimensions of some, 630. Legislative halls, acoustic principles; 
hospitals ; stables ; cowhouses ; greenhouses, 634. Ventilation and warming ; 
stoves ; hot-air furnaces ; steam and hot water circulation, 647. Kadiators ; 
laying out of pipes, 649. Plumbing ; soil pipe ; fixtures for kitchens ; baths ; 
water-closets ; traps and bends, 656. Lighting : gas, electric, wiring. Orders 
of architecture : Greek and Roman, Romanesque, Byzantine, Gothic, the Re- 
riaissance. Arches ; domes and vaults ; buttresses ; towers ; bell cots ; spires, 
674. Windows, lancet, traceried ; doorways, 679. Mouldings ; arch and 
architrave ; capitals ; bases ; string courses and cornices, 682. Ornaments, 693. 

isometrical drawing 694-705 

Perspective 706-725 

Points and planes of perspective ; parallel and angular perspective of cubes 
and other solids, of buildings, of an arched bridge, of an interior, of a staircase, 
of reflection of objects in water, of shadows ; perspective as illustration of ad- 
vertisements. 

Free-hand Drawing 726-764 

Materials : paper, pencils, lithographic chalk, pens, ink. Proportions of Hu- 
man Frame, Geometrical drawings of, " Dictionnaire Raisone par Viollet le 
Due " and Dr. Rimmer's " Elements of Design." Half tones of photographs of 
plaster models, " ecorche " of wash drawing of flowers, etc., P. de Longpre, Pen 
and ink reproduction of photographs on plain salted paper, models " ecorche," 
Sandow, manikins, Venus de Milo, and Dumas. Pumping Station after Emer- - 
son in toothpick and splatter work. Drawings on stipple paper or clayboard, Sal- 
vini and Venetian fete on the Seine. Pen and ink drawing, hands, feet, heads, 
Electioneer, Cow, Donkey from Landseer, hoofs, paws, muzzles, Espanola y 
Americana, Erik Werenskiold and design by Fortuny, Alexandrian pilot. Head 
of Sheik, Water Bearer, Donkey's Head, Deer, Ducks, Landscapes, Oak Trees, 
Morning, Cattle going Plome, Lady of the Woods, Elm, Cedar, Sketch in 
chalk, Suez Canal and sea sketch. 

Appendix 765-861 

Patent office. Requirements for drawings and Registration of prints and labels. 
Mensuration, areas of surfaces, contents of solids ; measures, lineal, of surface ; 
of capacity; liquid: dry. Weights, apothecaries', Troy, avoirdupois, compari- 
son of; Dynamic Table; cubic measure; shipping measure; register; ship- 
ping ; carpenter's rule. Table of inches and parts in decimals of a foot ; elec- 
trical units ; units of heat. Table of fifth powers of numbers ; weight of cast- 
iron balls, of cast-iron pipe, weights of rolled iron, 773 ; weight of wrought. 
Tables of dimensions and weight of wrought iron welded tubes ; nominal and 
actual diameters of boiler tubes. Heavy pipe for driven wells ; spiral riveted 
tubes, heavy and light ; weight of copper and brass rods ; rivets ; wrought spikes ; 
cut nails and spikes ; wire nails, weight of. Galvanized telegraph wire ; 
weights; resistance in ohms ; sizes used. Standard Beams and Channels of Asso- 



viii CONTENTS. 



ciation of American Steel Manufacturers ; grades of steel ; weights of lead pipe. 
Weight of a cubic foot of water at different temperatures. Flow of water, 
781-791, over weirs, through pipes and conduits ; graphic diagrams of Kutter 
formulae. Table of equalizing the diameter of pipes ; flow of air ; comparison 
of flow of water by the Kutter diagrams, with that of air ; with that of gas, 
and the products of combustion in chimneys. The Babcock and Wilcox boiler ; 
the Green economizer ; the Heine boiler. Table of saturated steam, 798 ; ex- 
pansive working of steam. Table of factors of evaporation. Electric Light 
and Power Station, Twenty-eighth Street, New York city, 805. Diagram of 
electric wiring ; lamp socket switch and Lundell motor ; Table of the density 
of gases. Specific gravity of liquids, of earths, of woods, of metals, solders ; 
alloys' Table of the circumferences and areas of circles, 819. Tables of 
squares, cubes, and roots, 826 ; of reciprocals ; Latitudes and Departures, 835. 
Natural sines and cosines, 845. Logarithms, 861. 

Scraps 862-912 

Compound steel cylinders ; manholes and covers ; compressed-air locomo- 
tive ; cranks ; rudder frame ; boiler flues ; screw propeller ; spherical bearing ; 
conventional signs of riveting ; mechanical stokers. Boilers : Stirling and 
Abendroth and Hoot. Engines — Corliss stationary: Deane steam pump; 
Reidler valve ; Locomotives ; car springs ; elevated railroad ; cable grip ; der- 
rick. Dams : canvas, earth, masonry, movable ; l^uilder's hardware ; hinges ; 
construction of safes. Mantels and fireplaces ; doors ; marquetry ; pediment ; 
brackets ; railing ; summer house ; windows ; doorways ; porches ; house fronts ; 
dormers and towers ; skeleton construction ; Broad Street Station, Philadel- 
phia. Church spires; churches; perspective; buildings of Centennial Exhi- 
bition ; of World's Fair ; Coney Island. 



DESCRIPTION OF PLATES. 



I. Shading of prism and cylinder by fiat tints. Page IGO. 
II. Shading of cylinder and segment of hexagonal pyramid. Page 161. 
Ill, lY. Finished shading and shadows of different solids. Page 163. 
V. Shades and shadows on screws. Page 164. 

YI. Example of topographical drawing, done entirely with the pen. 
Page 101. 
YII. The same, with the brush, in black. Page 117. 
YIII. The same, with the brush, in colour. Page 118. 
IX. Contoured map of Staten Island, shaded by superimposed washes, 
the washes increasing in intensity or strength as required to pro- 
duce the effect. Page 117. 
X. Geological map of part of 'New Jersey, coloured to show the different 
formations. Page 106. 
XI, XII. Topographical maps of parts of Massachusetts. 
XIII. Plan and ceiling in colour. Page 548. 

XI Y. Perspective view of Gothic church, finished in colour. (Frontispiece.) 
XY. Front elevation of a building, in colour. 
XYI. Finished perspective drawing, with shades and shadows, of a large 

bevel- wheel and two pinions, with shifting clutches. Page 160. 
XYII. Plan, elevation, and section of bevel-wheel, pinion, and clutches, 
shown in perspective Plate XYI. Page 160. 



ERRATA. 

Page 160, 19th line, omit Plate XI, and for Plates XII and XV, 

substitute Plates XVI and XVII. 



i 



APPLETONS' 



CYCLOPAEDIA OF DRAWING 



CONSTRUCTION OF GEOMETRICAL PROBLEMS. 




Most persons, at some time, have made use of the simple drawing instru- 
ments, as pencils, straight edges or rulers, dividers and compasses with change- 
able points, and many suppose that there can be no skill in their use ; but to 
one critical in these matters there are great differences, even in common draw- 
ings, in the straightness and uniformity of the lines and in the care of the 
surface of the paper. 

Pencils are marked according to their hardness : H (hard), H H, H H H, 

to 8 H ; or H, V (very) H, V V H, M (me- 
dium), H M, M B (black), S (soft), M S, V S, 
V V S ; or by numerals, 1, 2, 3, to 8. 
^ Select for the geometrical problems and 

for usual drawings a No. 3 or H H H pencil. 
It should be sharpened to a cone-point (Fig. 
1). Where a pencil is used for drawing lines 
only, some draughtsmen sharpen the pencil 
to a wide edge, like a chisel. 
In drawing a straight line, hold the ruler firmly with the left hand ; with 
the right hand hold the pencil lightly but without slackness, and a little 
inclined in the direction of the line to be drawn, keeping the pencil against 
the edge of the ruler, and in the same relative position to the edge during the 
whole operation of drawing the line. 

2 (1) 




Fig. 1. 



CONSTRUCTION OF GEOMETRICAL PROBLEMS. 



To draw a clean line and preserve the point of the pencil, the part of the 
cone a little above the point of the pencil should bear against the edge of the 
ruler, and the pencil should be carried steadily while drawing. Any oscilla- 
tion will throw the point farther from or nearer the ruler, and the line will not 
be straight (Fig. 2). 




Fig. 2 



In the use of the compasses do not make a hole through the paper with 
the needle or sharp point, but only into the paper sufficient to maintain the 
position. 

Keep the paper clean, and use rubber as little as possible. 

A geometrical point, which is position only, is indicated in drawing by the 
prick-mark of a needle or sharp point, or the dot of a pencil ; sometimes it is 
inclosed o, sometimes designated by the intersection of two short lines X >. 
A line, which is extension in length only, is indicated by a visible mark of 
pencil or pen traced upon the paper. 

Geometrically lines have but one dimension, lengthy and the direction of a 
line is the direction from point to point of the points of which the line is com- 
posed : in drawing, lines are visible marks of pencil or pen upon paper. 

A straight line is such as can be drawn along the edge of the ruler, and is 
one in which the direction is the same throughout. In drawing a straight line 
through two given points, place the edge of the ruler very near to and at equal 
distances from the points, as the point of the pencil or pen should not be in 
contact with the edge of the ruler (Fig. 3). 



A 


B 


G) 


(T) 





Fig. 3. 

Lines in geometry and drawing are generally of limited extent. A given 
or known line is one established on paper or fixed by dimensions. Lines of 
the same length are equal. 

Curved Lines. — For the pencil-points of compasses, whittle down the- 
stumps of pencils to suit. Insert the pencil-point in the compasses. With 
the needle or sharp point resting on the paper describe a line with the pencil 
around this point ; the line thus described is usually called a circle — more 



CONSTRUCTION OF GEOMETRICAL PROBLEMS. 3 

strictly it is the circumference of a circle — the circle being the space inclosed. 
A portion of a circumference is an arc. The point around which the circum- 
ference is described is the centre of the circle (Fig. 4). 

The line embraced between the two points of the compasses is called the 
radius of the circle, and by mechanics a sweep; a line passing through the 
centre and terminating at each end in the circum- 
ference is a diameter^ and is equal in length to 
two radii ; any line not passing through the cen- 
tre and limited by the circumference is less than 
a diameter and is a chord. The space embraced 
between a chord and its lesser arc is a segment. 
The space embraced between two radii and its arc 
is a sector; if the arc is the quarter of the cir- 
cumference, the sector is distinguished as a quad- 
rant. 

It will be observed that arcs are lines which 
are continually changing the directions, and are 
called curved lines, but there are other curved lines than those described by 
compasses, of which the construction will be explained hereafter. 

Lines which can neither be drawn by rulers or compasses, representing the 
directions of brooks and rivers, the margins of lakes and seas, points in which 
are established by surveys, defined on paper, and connected by hand-drawing, 
are irregular or crooked lines. 

Where it is necessary to distinguish lines by names, we place at their 

extremities letters or figures, as A B, 1 2 ; the line A B, or 1 2. 

But in lines other than straight, or of considerable extent, it is often necessary 
to introduce intermediate letters and figures, as a a a. 




Fig. 4. 




In the following problems, unless otherwise implied or designated, where 
lines are mentioned, straight lines are intended. 

If a straight line moves sideways in a single direction, it will sweep over a 
surface which is called a plane. All drawings are projecHons on planes of 
paper or board. 

Two lines drawn on paper, and having the same direction, can never come 
any nearer each other, and must always be at the same distance apart, however 
far extended. Such lines are called parallel lines. 

To draw a line parallel to a given line^ and at a given distance from it 
(Fig. 5). 

Draw the line A B for the given line, and take in the compasses the 
distance A — the distance at which the other line is to be drawn. On A, 
as a centre, describe an arc, and on B, as a centre, a similar arc ; draw the 
line' C D just touching these two arcs, which will be the parallel line re- 
quired. 



4 CONSTRUCTION OF GEOMETRICAL PROBLEMS. 

To draw a line parallel to a given line through a given point outside this 
line (Fig. 6). 

Draw the given line A B, and. mark the given point C. With C as a centre, 
find an arc that shall only just touch A B ; and with B as a centre, and the 





Fig. 5. 



Fig. 6. 



same radius, describe an arc D. Draw through the point a line just touching 
this last arc, and the line C D will be the parallel line required. 

Two lines in the same plane, not parallel to each other, will come together 
if extended sufficiently far. The inclination or intersection of two lines is 
called an angle (Fig. 7). 

If but two lines come together, the angle may be designated by a single 
letter at the vertex^ as the angle E. 

But, if three or more lines have a common vertex, the angles are designated 
by the lines of which they are composed, as the angle D B C of the lines D B 
and B ; the angle A B C of A B and B ; the angle A B D of A B and 1^ D. 
The letter at the vertex must always be the central letter. 

Describe a circle (Fig. 8). Draw the diameter A B. From A and B as 
centres, with any opening of the compasses greater than the radius, describe 
two arcs cutting each other as at D. Through the intersection of these arcs 
and the centre C, draw the line D E. 
D E makes, with the diameter A B, four 
angles, viz., A D, D C B, B E, and 
E C A. Angles are equal whose lines 



E c 

FiQ. 7. 



B 




have equal inclination to each other, and whose lines, if placed one on tjie 
other, would coincide. By construction, the points and D have, respectively, 
equal distances from A and B ; the line D C can not, therefore, be inclined 
more to one side than to the other, and the angle A D must be equal to the 
angle BCD. Such angles are called inght afigles. The four angles, formed 
by the intersection of D E with A B, are equal, and are right angles. 

The angles A C D and D B, on the same side of A B, are called adjacent 
angles ; as also D C B and B C E, on the same side of D E. 



CONSTRUCTION OF GEOMETRICAL PROBLEMS. 



If the lase line be parallel with the surface of still water, it is called an 
horizontal line, and the line perpendicular to it is called a vertical line. 

Draw the line C F. It will be observed that the angle F C B is less than 
a right angle, and it is called an acute angle; 
the angle F C A is greater than a right angle, 
and it is called an oUiise angle. It will be 
observed that, no matter how many lines be 
drawn to the centre, the sum of all the angles 
on the one side of A B can only be equal to 
two right angles, and, on both sides of A B, 
can only be equal to four right angles. It will 
be observed that the angles at the centre in- 
clude greater or less arcs between their sides, 
according to the greater or less inclination of 
their sides to each other ; that the right angles 
intercept equal arcs, and that, no matter how 
large the circle, the proportion of the circle 
intercepted by the sides of an angle is always 
the same, and that the arcs can therefore be 
taken as the measures of angles. For this 
purpose the whole circumference is supposed 
to be divided into three hundred and sixty de- 
grees (360°), each degree subdivided into sixty minutes (60'), and each minute 
into sixty seconds (60"). Each right angle has for its measure one quarter of 
the whole circumference (— f— ), or 90°, and is called a quadrant. 

To construct an angle equal to 
a given angle (Fig. 9). ^ 

Draw any angle, as C A B, for 
the given angle, and the line a h 




A B E- 

Fig. 10. 




Fig. 11. 



as the base of the required angle. From A, with any suitable radius, describe 
the arc B C, and from «, with the same radius, describe the arc h c. With 
the compasses take the length of the chord B C, and, from h as centre, describe 
an arc cutting the arc ^ c at c, and draw the 'line a c; cab is the required 
angle. 

To construct an angle of sixty degrees (Fig. 10). 

Lay off any base line, and from A, with any radius, describe an arc, and 
from B, with the same radius, describe another arc cutting the first, as at C. 
Draw the line C A, and the angle CAB will be an angle of sixty degrees. 



6 



CONSTRUCTION OF GEOMETRICAL PROBLEMS/ 



For if, on the circumference of any circle, chords equal to the radius are 
stepped off successively, six will exactly complete the circle, making 360°. 

To draw a 'perpendiciilar to a line from a point without the line 
(Fig. 11). 

Draw a line, and mark the given point A. From A as a centre, with a 



:X2> 



\ 



E 








/ 


\ 






\ 




'''^% 


/ 


A 


\ 




D 



A 
Fig. 12. 



C\ 



Fig. 13. 



suitable radius, describe an arc cutting the line at G and F. From G and 
F, as centres, describe arcs cutting each other. The line drawn through 
the point A, and the point of intersection E, will be perpendicular to the 
line G F. 

The radial line A E divides the chord G F and the arc G E F into two 
equal parts ; and, conversely, the line perpendicular to the middle point of a 
chord of a circle is radial — passes through the centre of that circle. 

To draiu a perpendicular to a line from a point luithin that li7ie (Fig. 12). 
1st Method. — Draw a line, and take the point A in the line. From A, as 
a centre, describe arcs cutting the line on each side at B and C. From B and 
0, as centres, describe intersecting arcs at D. Draw a line through D and A, 
and it will be perpendicular to the line B C at A. 

2d Method (Fig. 13). — Draw the line, and mark the point A as before. 
From any centre F, without the line, and not directly over A, with a radius 
equal to F A, describe more than a half-circle cutting the line, as at D. From 

D, through the centre F, draw a 
^^^/ line cutting the arc at E. Draw 

A E, and it will be the perpendicu- 
lar to the line A D. 

The line D E is the diameter 
of a circle, and the angle DAE, 
,jg with its vertex at A in the circum- 
ference, embraces with its sides half 
a circle. It has beeu shown that 
angles at the centre of a circle have 
for their measure the arc embraced 
by their sides. Angles with their 
vertices in the circumference have 
for their measure half the arc em- 
braced by their sides ; and, consequently, angles embracing half a circumfer- 
ence are right angles. 

To draw a perpendicular to the middle point of a li?ie (Fig. 14). 



Ji 



Fig. 14. 



• CONSTRUCTION OF GEOMETRICAL PROBLEMS. 7 

From the extremities A and B of the line, as centres, describe similar inter- 
secting arcs above and below the line. Through these intersections draw the 
line D. It will be perpendicular to the line A B, and bisect or divide it into 
two equal parts. 

If the line A B be considered the chord of a circle, its centre would lie in 
the line C D. 

This construction is sometimes used merely to divide a line into two equal 
parts, or bisect it; it can be more readily done with dividers (Fig. 15). 

Place one point of the dividers on one end of the line, and open the 
■dividers to a space as near as may be half the line. Turn the dividers on the 




Fig. 15. 

'Central point ; if the other point then falls exactly on the opposite extremity 
of the line, it is properly divided ; but, if the point falls either within or with- 
out the extremity of the line, divide the deficit or excess by the eye, in 
halves, and contract or extend the dividers by this measure. Then apply the 
dividers as before, and divide deficit or excess till a revolution exactly covers the 
length of the line. By accustoming one's self to this process, the eye is made 
accurate, and one estimate is sufficient for a correct division of any deficit or 
excess. By a similar process it is evident that a line can be divided into any 
number of equal parts, by assuming an opening of the dividers as nearly as 
possible to that required by the division, and, after spacing the line, dividing 
the deficit or excess by the required number of parts, contracting or expanding 
the dividers by one of these parts, and spacing the line again, and so on till it 
is accurately divided. 

To bisect a given angle (Fig. 16). 

Construct an angle, and from its vertex A, as a centre, describe an arc 
outting the two sides of the angle at B and C. From B and C, as centres, de- 




FiG. 16. 



Fig. 17. 



scribe intersecting arcs. Draw a line through A and the point of intersection 
D, and this line will bisect the angle. 

To lisect an angle luhen the vertex is not on tlie paper (Fig. 17). - 



8 



CONSTRUCTION OF GEOMETRICAL PROBLEMS.. 



Let A B and E C be two lines inclined to each other ; at equal distances 
and parallel to the above lines draw a i and a c, intersecting lines ; bisect the 
angle lac. A line a d drawn through the vertex and the point of bisection is 
the required line. 

Through two given points to descrihe mi arc of a circle with a given radius 
(Fig. 18). 

From B and C, the two given points, with an opening of the dividers equal 
to the given radius, describe two arcs intersecting at A. From A, as a centre, 
with the same radius, describe an arc, and it will be the one required. 



^^>. 




Fig. J8. 




To find the centre of a given circle^ or of an arc of a circle. 

Of a circle (Fig. 19). — Draw the chord A B. Bisect it by the perpen- 
dicular D, whose extremities lie in the circumference, and bisect CD. Gr, 
the point of bisection, will be the centre of the circle. 

To find the centre of an arc (Fig. 20). — Select the points A, B, and C in 
the arc, well apart. From A and B as centres, and then from B and as 
centres, describe arcs of equal radii cutting each other ; draw the two lines D E 
and F G through their intersections. The point 0, where these lines meet, is 
the centre required. 

To descrihe a circle passing through three given points (Fig. 20). 

Proceed, as in the last problem, to find the point 0. From 0, as a centre, 
with a radius A, describe a circle, and it will be the one required. 



V / 



\ r. 





Fig. 20. 



Fig. 21. 



To describe an arc of a circle passing through three given points^ luhere the 
centre is not available (Fig. 21). 



CONSTRUCTION OF GEOMETRICAL PROBLEMS. 9 

From the extreme given points A and B describe arcs A E and B D ; 
through the third given point draw lines from A and B, intersecting the arcs 
at and ; from and cut the arcs in either direction by equal divisions, 
1, 2, 3, and 1', 2' ; draw lines A 1, A 2 ; A 1', A 2' ; B 1, B 2 ; B 1', 
B 2'. The successive intersections of A 1 by B 1, A 2 by B 2, A 1' by B 1' are 
points in the required arc by the connection of which the problem will be 
complete. 

To describe this arc mechanically (Fig. 22). 

Lay off on a piece of cardboard the three points A, C, B, and connect them 
by lines extended beyond the points A and B ; and then cut out the cardboard 




Fig. 22. 

along these lines. Insert pins at the points A and B on the drawing, arid 
placing the cardboard templet against these pins, and the angle against the 
point C, slide the templet each way, dotting in the drawing the angle C in its 
different positions. These dots will be points in the curve, which are to be con- 
nected. By extending the bisecting line in different positions of the templet 
to the drawing, radial lines are given which will be useful in laying off voussoir 
joints on segmental arches of large radius. Radial lines are also necessary in 
perspective drawing, for 
which an instrument 
called the centrolinead 
(Fig. 23) is used. The 
principle is similar to 
that of the cardboard 
templet. 

To draw a tangent to 
a circle from a given 
point in the circumfer- 
ence. 

1st Method (Fig. 24). 
— Through the given 
point A draw the radial 
line A 0. The perpen- 
dicular F Gr to that line 
will be the 
quired. 

2d Method (Fig. 25). 
— From the given point A set off equal arcs, A B and A D. Join B and D. 
Through A draw A E parallel to B D, and it will be the tangent required. 
This method is useful when the centre is inaccessible. 



tangent re- 



FiG. 23. 



10 



COIs^STRUCTION OF GEOMETRICAL PROBLEMS. 



To draw tangents to a circle from a point witliout it (Fig. 26). 
From the given point A draw A to the centre of the circle. Bisect A C 
to find the point D. From D, as a centre, describe an arc with a radius D C, 





Fig. 24. 



Fig. 25. 



cutting the circle at E and F. Draw A E and A F, and they will be the tan- 
gents required. 

To construct within the sides of an angle a circle tangent to these sides at a 
given distance from the vertex (Fig. 27). 





By- 



Fig. 27. 



Let a and I be the given points equally distant from the vertex A. Draw 
a perpendicular to A C at a, and to A B at h. The intersection of these per- 
pendiculars will be the centre of the required circle. 

In the same figure, to find the cent^^e^-jthe^ radius being given, and the 
points a and b not known. Draw lines parallel to A C and A B, at a distance 
equal to the given radius, and their intersection will be the centre required. 

To describe a circle from a given point to touch a giv^n^^cle (Figs. 28 
^md 29). 





Fig. 28. 



Fig. 29. 



D E being the given circle, and B the given point, draw a line from B to 
the centre C, and produce it, if the point B is within the circle, until it cuts 
the circle at A. From B, as a centre, with a radius equal to B A, describe the 
circle F G, touching the given circle, and it will be the circle required. 



CONSTRUCTION OF GEOMETRICAL PROBLEMS. 



11 



In all cases of circles tangent to each other, their centres and their points 
of contact must lie in the same straight line. 

To draw tangents to two given circles (Fig. 30). 

Draw a straight line through the centres of the two given circles. From 
the centres A and B draw parallel radii, A D and B E, in the same direction. 



C--- 




FiG. 30. 

Draw a line from D to E, and produce iti^o meet the centre line at C ; and 
from C draw tangents to one of the circles by Fig. 26. Those tangents will 
touch lotli circles as required. 

To construct a circle through a given point tangent to a second circle at a 
given point (Fig. 31). 

Let A be the given point of a circle A D C, B the point through which the 
required circle is to be drawn. Connect A and B, extend A O, bisect A B by 
a perpendicular. The intersection of this perpendicular with A extended 
will be the centre of the required circle. The same method of construction 
would apply if the point B were inside the circle ADC. 

Between two inclined lines to draiu a series of circles touching these lines 
and touching each other (Fig. 32). 





Fig. 31. 



Fig. 32. 



Bisect the inclination of the given lines A B and C D by the line N ; this 
is the centre line of the circles to be inscribed. From a point, P, in this line, 
draw P B perpendicular to the line A B ; and from P describe the circle B D, 
touching the given lines, and cutting the centre line at E. From E draw E F 
perpendicular to the centre line, cutting A B at F ; from F describe an arc, 
with a radius F E, cutting A B at G ; draw Gr H parallel to B P, giving H the 
centre of the second touching circle, described with the radius H E or H G. 
By a similar process the third circle, I N", is described. And so on. 

Inversely, the largest circle may be described first, and the smaller ones in 
succession. 



12 



CONSTRUCTION OF GEOMETRICAL PROBLEMS. 



Note. — This problem is of frequent use in scroll-work. 

Between tico inclined lines to draiv a circular arc to fill up the angle 
(Fig. 33). 

Let A B and D E be the inclined lines. Bisect the inclination by the line 
F C, and draw the perpendicular A F D to define the limit within which the 
circle is to be drawn. Bisect the angles A and D by lines cutting at C, 





Fig. 34. 



and from C, with radius C F, draw the arc H F G, which will be the arc 
required. 

To fill up the angle of a straight line and a circle^ luith a circular arc of a 
given radius (Fig. 34). 

On the centre C, of the given circle A D, with a radius E equal to that 
of the given circle plus that of the required arc, describe the arc E F. Draw 
G F parallel to the given line H I, at the distance G H, equal to the radius 
of the required arc, cutting the arc E F at F. Then F is the required centre. 
Draw the perpendicular F I, and the line F C, cutting the circle at A ; and, with 
the radius F A or F I, describe the arc A I, which will be the arc required. 

To fill up the angle of a straight lifi?^~andL a circle., loith a circular arc to 
join the circle at a given point (Fig. 35). 

In the given circle B A draw the 
radius to A, and extend it. At A 





Fig. 36. 



draw a tangent, meeting the given line at D. Bisect the angle A D E, so 
formed, with a line cutting the radius, as extended at F ; and, on the cen- 
tre F, with radius F A, describe the arc A E, which will be the arc required. 



CONSTRUCTION OF GEOMETRICAL PROBLEMS. 



13 



To describe a circular arc joining two circles, and to touch one of them at a 
given point (Fig. 3G). 

Let A B and F G be the given circles to be joined by an arc touching one 
of them at F. 



Fig. 37. 





Draw the radius E F, and produce it both ways ; set off F H equal to the 
radius, A 0, of the other circle ; join C to H, and bisect it with the perpen- 
dicular L I, cutting E F at I. On the centre I, with radius I F, describe the 
arc F A, which will be the arc required. 

To find the arc which shall he tangent to a given point on a straight line, 
and pass through a given point outside the line (Fig. 37). 

Erect at A, the given point on the giv- 
en line, a perpendicular to the line. From 
C, the given point outside the line, draw 
C A, and bisect it with a perpendicular. 
The intersection of the two perpendiculars 
at a will be the centre of the required arc. 
To connect tiuo parallel lines hy a re- 
versed curve composed of two arcs of equal 
radii, and tangent to the lines at given 
points (Fig. 38). 

Join the two given points A and B, and divide the line A B into two equal 
parts at ; bisect C A and C B by perpendiculars ; at A and B erect perpen- 
diculars to the given 
lines, and the intersec- 
tions a and h will be 
the centres of the arcs 
composing the required 
curve. 

To join two given 
points in ttvo given 
parallel lines hy a re- 
versed curve of two 
eq7ial arcs, ivhose cen- 
tres lie in the p)araUels 
(Fig. 39). 

Join the two given 
points A and B, and divide the line A B in equal parts at C. Bisect A C and 
B by perpendiculars ; the intersections a and h of the parallel lines, by these 
perpendiculars, will be the centres of the required arcs. 




14 



CONSTRUCTIOX OF GEOMETRICAL PROBLEMS. 



On a given line, to construct a compouiid curve of three arcs of circles, the 
radii of the t'wo side ones deing equal and of a given length, and their centres 
in the given line ; the central arc to pass through a given point on the perpen- 
dicular, bisecting the given line, and to he tangent to the other two arcs 
(Fig. 40). 

Let A B be the given line, and the given point. Draw C D perpen- 
dicular to A B ; lay off A (2, B h, and C c, each equal to the given radius of the 
side arcs ; draw a c, and bisect it by a perpendicular ; the intersection of this 
line with the perpendicular C D will be the required centre of the central arc 
e C e'. Through a and d draw the lines D e and D e' ; from a and i, with the 
given radius equal to <2 A or J B, describe the arcs A e and B e'. From D, as 
a centre, with a radius equal to C D, and, consequently, by construction, equal 
to D e and D e', describe the arc e C e'. The entire curve A e C e' B is the 
compound curve required. 

PEOBLEMS OK POLYGONS AND CIRCLES. 

Three lines inclosing a space form a triangle (Fig. 41). If two of the sides 
are of equal length, it is an isosceles triangle (Fig. 42) ; if all three are of equal 




Fig. 41. 




length, it is an equilateral triangle (Fig. 43). If one of the angles is a right 
angle, it is a right-angled triangle (Fig. 44), and if no two of the sides are of 
equal length, and not one of "^e angles a right angle, it is a scalene triangle. 

To construct an isosceles triangle (Fig. 42). 

Draw any line as a base, and, from /" 

each extremity as a centre, with equal 
radius, describe intersecting arcs. Draw 





Fig. 43. 



Fig, 44. 



a line from each extremity of the base to this point of intersection, and the 
figure is an isosceles triangle. 

To construct an equilateral triangle (Fig. 43). 

Draw a base line, and from each extremity as a centre, with a radius equal 



CONSTRUCTION OF GEOMETRICxiL PROBLEMS, 



15 



to the base line, describe intersecting arcs. Draw lines from the extremi- 
ties of the base to this point of intersection, and the figure is an equilateral 
triangle. 

To construct a riglit-angled triangle (Fig. 44). 

Construct a right angle by any one of the methods before described. 
Draw a line from the extremity of the one side to the extremity of the other 
side, and the figure is a right-angled triangle. 

It will be evident, in looking at any right-angled triangle, that the side 
opposite the right angle is longer than either of the other or adjacent sides ; 
this side is called the liypotlienuse. 

To construct a triangle equal to a given triangle ABC (Fig. 45). 

1st Method (Fig. 46). — Draw a base line, and lay off its length equal to 
A B; from one of its extremities, as a centre, with a radius equal to A C, 
describe an arc; and, from its other extremity, with a radius equal to B C, 
describe an arc intersecting the first. Draw lines from the extremities to the 
point of intersection, and the triangle equal to A B C is complete. 





Fig. 45. 



Fig. 46. 



2d Method (Fig. 47). — Draw a base line, as before, equal to A B. At one 
extremity construct an angle equal to C A B, and at the other an angle equal 
to B A. The sides of these angles will intersect, and form the required 
triangle. 

Sd Method (Fig. 48). — Construct an angle of the triangle equal to any angle 
of A B C, say the angle A C B. On one of its sides measure a line equal to 
C A, and on the other side one equal to C B ; connect the two extremities by a 
line, and the triangle equal to A B C is complete. 





Fig. 47. 



Fig. 48. 



From the above constructions it will be seen that, if the three sides of a 
triangle, or two sides and the included angle, or bne side and the two adjacent 
angles are known, the triangle can be constructed. 

Construct a triangle, ABC (Fig. 49). Extend the base to E, and draw 
B D parallel to A C. As A C has the same inclination to C B that B D has, 
the angle C B D is equal to the angle A C B. As A C has the same inclina- 
tion to A E that B D has, the angle D B E is equal to C A B. That is, the 



16 



CONSTRUCTION OF GEOMETRICAL PROBLEMS. 



two angles formed outside the triangle are equal to the two inside at A and C ; 
and the three angles at B are equal to the three angles of the triangle, and 
their sum is equal to two right angles. Therefore, the sum of the three angles 
of a triangle is equal to two right angles. 

On one side of a triangle (Fig. 50) construct a triangle equal to the first. 
The exterior lines of the two triangles form a four-sided or quadrilateral 
^ figure, of which the opposite sides are 

equal and parallel, and the opposite an- 





FiG. 49. 



Fig. 50. 



gles equal. This figure is called a parallelogram^ and the line C B, extend- 
ing between opposite angles, is a diagonal. 

On the hypothenuse of a right-angled triangle (Fig. 51) construct another 
equal to it, and the exterior lines form a parallelogram, which, as all the angles 
are right angles, is called a rectangle. If the four sides are all equal, it is called 
a square. 

A parallelogram in which all the sides are equal, but the angles not right 
angles, is called a rliomhus (Fig. 52) ; if only the opposite sides are equal, it is 






Fig. 51. 



Fig. 52. 



called a rliomloid (Fig. 50) ; if only two sides are parallel, the figure is a trape- 
zoid (Fig. 53). 

Take any figure (Fig. 54) bounded by straight lines and from any interior 
point draw lines to all the angles. There will be as many triangles as sides, and 
the sum of the angles of the figure will be equal to as many times two right 




Fig. 53. 



Fig. 54. 



angles as sides less the four right angles at the centre, the sum of the angles 
of any triangle being equal to two right angles. If a line be drawn from the 



CONSTRUCTION OF GEOMETRICAL PROBLEMS. 



17 



interior point to one side, another triangle is added to the collection and two 
right angles to the sum of the angles. 

Polygons are figures of many angles, which if equal and of equal sides are 




Fig. 55. 



Fig. 56. 



Fig. 57. 



Fig. 58. 



called regular polygons, and are designated by the number of their sides, as 
pentagons, hexagons, octagons, nonagons, decagons, etc. 

To describe a circle about a triangle (Fig. 59). 

Bisect two of the sides A B, A 0, of the triangle at E, F ; from these points 
draw perpendiculars cutting at K. From the centre K, with K A as radius, 
describe the circle A B 0, as required. 

To inscribe a circle in a triangle (Fig. 60). 

Bisect two of the angles A, C, of the triangle 
ABC, by lines cutting at D ; from D draw a 
perpendicular D E to any side, as A C ; and 
with D E as radius, from the centre D, describe 
the circle required. 

When the triangle is equilateral, the centre 
of the circle is more easily found by bisecting 
two of the sides, and drawing perpendiculars. 
Or, draw a perpendicular from one of the sides 
to the opposite angle, and from the side set off 
one third of the length of the perpendicular. 

To inscribe a square in a circle; and to describe a circle about a square 
(Fig. 61). 

To inscribe the square. Draw two diameters, A B, C D, at right angles, 
and join the points A, C, B, D, to form the square as required. 




Fig. 59. 




,4 


/ 


\ 


r> 


f 


\ 


^ 


\ 


1 




'"■■?■•■'' 




\ 


/ 




1 
/ 


D 


\ 


J 


B 



Fig. 60. 



Fig. 61. 



To describe the circle. Draw the diagonals A B, C D, of the given square, 
cutting at E ; on E as a centre, with E A as radius, describe the circle as required. 



18 



CONSTRUCTION QF GEOMETRICAL PROBLEMS. 



In the same way, a circle may be described about a rectangle. 
• To inscribe a circle in a square; and to describe a square about a circle 
(Fig. 62). 

To inscribe the circle. Draw the diagonals A B, C D, of the given square, 
cutting at E ; draw the perpendicular E F to one of the sides, and with the 
radius E F, on the centre E, describe the circle. 

To describe the square. Draw two diameters A B, C D, at right angles. 



I) 





G 








^^- — ; "~- 


-v^^ 












/ 


\ 


^ 


\ 


/ 






\ 
























\ 




y^^ 






\ 


/ \ '^ 




/ 


\ 


y' 1 


^^ 


/ 










\ 


1 i 


^, 


/ 


/ 


\^^ : ^ 


^ 





F 

Fig. 62. 




and produce them ; bisect the angle D E B at the centre by the diameter F G-, 
and through F and Gr draw perpendiculars A 0; B D, and join the points A, D^ 
B, 0, where they cut the diagonals, to complete the square. 

To inscribe a pentagon in a circle (Fig. 63). 

Draw two diameters, A C, B D, at right angles ; bisect A at E, and from 
E, with radius E B, cut A C at F ; from B, with radius B F, cut the circum- 
ference at G and H, and with the same radius step round the circle to I and K ; 
join the points so found to form the pentagon. 

To construct a regular hexagon upon a given straight line (Fig. 64). 

From A and B, with a radius equal to the given line, describe arcs cutting 
at g ; from ^, with the radius g A, describe a circle ; with the same radius set 




Fig. 64. 





Fig. 65. 



off from A the arcs A G, G F, and from B the arcs B D, D E. Join the 
points so found to form the hexagon. 

To inscribe a regular hexagon in a circle (Fig. ^h). 

Draw a diameter, A B ; from A and B as centres, with the radius of the 
circle A C, cut the circumference at D, E, F, G ; draw straight lines A D, 
D E, etc., to form the hexagon. 

To describe a regular hexagon about a circle (Fig. ^^). 



CONSTRUCTION OF GEOMETRICAL PROBLEMS. 



19 



Draw a diameter, A B, of the given circle. With a radius A D from A as a 
centre, cut the circumference at ; join A C, and bisect it with the radius 
D E ; through E draw F G parallel to A C, and with the radius D F describe 

F 




Fig. 66. 




the circle F H. Within this circle describe a regular hexagon by the preceding 
problem ; the figure will touch the given circle as required. 

To construct a regular octagon upon a given straight line (Fig. 67). 

Produce the given line A B both ways, and draw perpendiculars A E, B F ; 





Fig. 68. 

bisect the external angles at A and B by the lines A H, B 0, each equal to 
A B ; draw D and H G parallel to A E and equal to A B ; and from the 
centers G, D, with a radius equal to A B, cut the 
perpendiculars at E, F, and draw E F to complete 
the octagon. 

To make a regular octagon from a square 
(Fig. 68). 

Draw the diagonals of the square intersecting 
at e ; from the corners A, B, C, D, with A e as 
radius, describe arcs cutting the sides at g li^ etc. ; 
join the points so found to complete the octagon. ^ 

To inscribe a regular octagon in a circle (Fig. 
69). 

Draw two diameters, AC, B D, at right an- 
gles; bisect the arcs A B, B C, etc., at e,/, etc. ; and join A e, e B, etc., for the 
inscribed figure. 

To describe a regular octagon about a circle (Fig. 70). 



// 



/ '^N.^ / \ 


\ / \ '\^ 



/? 



Fig. 70. 



20 



CONSTRUCTION OF GEOMETRICAL PROBLEMS. 



Describe a square about the given circle A B ; draw perpendiculars h k^ etc., 
to the diagonals, touching the circle. 

Or, to find the points A, ^, etc., cut the sides from the corners of the square, 
as in Fig. 68. 

To inscribe a circle within a regular polygon. 

When the polygon has an even number of sides, as in Fig. 71, bisect two 





Fig. 71. 



Fig. 72. 



opposite sides at A and B, draw A B, and bisect it at C by D E drawn between 
opposite angles ; with the radius A describe the circle as required. 

When the number of sides is odd, as in Fig. 72, bisect two of the sides at A 
and B, and draw lines A E, B D, to the opposite angles, intersecting at ; 
from C, with C A as radius, describe the circle as required. 

To describe a circle about a regular polygon. 

When the number of 
sides is even, draw two 
diagonals from opposite 
angles, like D E (Fig. 
71), to intersect at C ; 
and from 0, with C D as 
radius, describe the cir- 
cle required. 

When the number of 
sides is odd, find the cen- 
tre C (Fig. 72) as in last 
problem, and, with C D 
as radius, describe the 
circle. 

For the construction 
of the regular polygons 
Fig. 73 will be found 
useful. 

Divide the interior 
circle into the number 
of degrees corresponding 
to the proportion of the 

sides of the polygon to the entire circle, e. g., ^^ = 72°. With a radius of unity 
describe an exterior circle and extend radii through the divisions of the in- 




FlG 



CONSTRUCTION OF GEOMETRICAL PROBLEMS. 



21 



terior circle. The chords of the arcs intersected correspond to the sides of the 
different polygons. 

The figure gives the polygons such as are usually found in practice, but a 
similar figure can be constructed increasing the number of sides as far as may 
be required. 

msm 




For the laying out of angles the protractor is used. In its simplest form it 
consists of a semicircle of metal or horn of which the edge is divided into 180 
degrees. 

To lay off a given angle — say 47° (Fig. 74) — place the edge of the protractor, 
a b, along the given line and make the centre of the protractor coincide with 
the vertex c of the angle to be laid off ; mark off on 
the edge the division 47°, remove the protractor, and 
through this mark and the vertex c draw a line ; 
the angle a c d will be equal to 47°, and h c d to 
133°. These two are supplements of each other, or 
what each requires to make up the sum of 180°. 

Fig. 75 represents the terms used in defining 
angles, and of which tables are given in the Appen- 
dix by which angles may be constructed without the 
use of the protractor. 

Considering BCD the angle, the perpendicular 
D H dropped from the radius at D and intersecting 

the diameter at II is the sine^ the line B A perpendicular to B C and inter- 
secting the extended radius at A is the tangent^ the extension of the radius C D 
to the intersection of the tangent at A the secant ; the versed sine is the line 
B H extending from the sine to the tangent. The cosine^ cotangent^ cosecant^ 
and coversed sine are respectively the sine, tangent, secant, and versed sine 
of the angle D C F, the complement of B C D, having the number of degrees 
necessary to complete the quadrant of 90 degrees. 




Fig. 



22 



CONSTRUCTION OF GEOMETRICAL PROBLEMS. 




Use of Tkiangle and Square. 

Right-angled triangles constructed of wood, hard rubber, celluloid, or metal 
are very useful in connection with a straight-edge, or ruler, in drawing lines 
parallel or perpendicular to other lines. 

To draw lines parallel to each other, place any edge of the triangle in close 
contact with the edge of the ruler. Hold the ruler (Fig. 76) firmly with the 




Fig. 76 



thumb and little finger of the left hand, and the triangle with the other three 
fingers ; with a pencil or pen in the right hand, draw a line along one of the 
free edges of the triangle ; withdraw the pressure of the three fingers upon the 
triangle, and slide it along the edge of the ruler, keeping the edges in close 
contact ; a line drawn along the same edge of the triangle, as before, will be 
parallel to the first line. If the edge of the hypothenuse of the triangle be 
placed in contact with the ruler, lines drawn along one edge of the triangle will 
be at right angles to those drawn along the other. 

Through a given 'point to draiu a line parallel to a given line (Fig. 77). 

Place one of the shorter edges of the triangle along the given line A B, and 
bring the ruler against the hypothenuse ; slide the triangle up along the edge 
of the ruler until the upper edge of the ruler is sufficiently near to the given 
point C to allow a line to be drawn through it. Draw the line, and it will be 
parallel to A B. 

If the triangle be slid farther up along the edge of the ruler, and a line be 



CONSTRUCTION OF GEOMETRICAL PROBLEMS. 



23 



drawn through C along the other edge of the triangle (Fig. 78), this line will 
be perpendicular to, A B. If the triangle be slid still farther up along the 




Fig. 77. 



edge of the ruler, and a third line be drawn touching A B, the figure con- 
structed will be a rectangle ; and if E D be laid off on A B, equal to C E, the 
figure inclosed is a square (Fig. 79). 

It wili be seen that the triangle and ruler afford a much readier way of 



A 




Fig. 78. 



Fig. 79. 



drawing parallel lines, and lines at right angles, than the compasses and ruler, 
and may be used in solving the following problems : 

The area of a figure is the 
quantity of space inclosed by its 
lines. 

Construct a right angle (Fig. 
80). Divide the base and the 
perpendicular by dividers into 
any number of equal spaces ; for 
instance, ten on the one and five 
on the other. Construct a rec- 
tangle with this base and perpen- 
dicular, and through the points of division lay off lines parallel to the base and 
perpendicular. The rectangle will be divided into fifty equal squares, and its 




Fig. 80. 



24 



CONSTRUCTION OF GEOMETRICAL PROBLEMS. 



measure in squares will be the divisions ten in the base, multiplied by the five 
in the perpendicular. If the division were inches, then the area of- this rec- 
tangle would be fifty square inches ; if 
feet, then fifty square feet. If there 




' B 




Fig. 81. 



Fig. 82. 



were but five divisions in the base and five in the perpendicular, the surface 
would be twenty-five squares. Therefore, a rectangle has for its measure the 
base multiplied by its adjacent side or height. 

Draw a diagonal, and the rectangle is divided into two equal triangles. 
Each triangle must therefore have for its measure the base multiplied by half 
the perpendicular, or, as is usually said, by half the altitude. 

Take any triangle (Fig. 81), and from its apex draw a line perpendicular to 
the base. The triangle is divided into two right-angled triangles, which must 
have for their measure A D X i C D, and D B X i C I), and the sum of the 
two must be A B X i D. 

If the perpendicular from the apex falls outside the triangle (Fig. 82), then 
the triangle B D and ADC will have for their measure B D X J C D and 

A D X |- C D, consequently their 
difference, ABC, must have for 
its measure A B X ^ C D. Any 
polygon can be divided into trian- 
gles (see Fig. 54), and its area is 
made up of the sum of the areas of 
the triangles. By graphic con- 
struction the sum of the areas of 
the different triangles composing a 
polygon may be resolved readily 
into a single triangle and its area 
taken. For instance, take a six- 
sided polygon (Fig. 83), draw a line 
from A to C, and a line parallel to A C, at B intersecting the extended base at 
B', a diagonal drawn from A to B' will give one side of the triangle ; draw a 
diagonal from A to E, extend the side E D of the polygon indefinitely, draw a 
line at F parallel to A E, and intersect the extended side at e, draw the line 
A D and a parallel to this at e, intersecting the extended base at E'. A di- 
agonal drawn from A to E' will, with the side previously obtained and the base, 
give a triangle equal in area to the polygon. 




Fig. 83. 



CONSTRUCTION OF GEOMETRICAL PROBLEMS. 



25 



\\\\\\\\\\\\\\\\\\\\\\\1\U 



:'\ 



I 
I 

I 



rf 



rs 



-sL§ 



mo 



lio 



SCALES. 

The distances given in Fig. 80 may represent feet, yards, miles, or any other 
unit of measure. Thus, if they represent miles, the figure represents an area 
of fifty square miles. With a scale of equal 
parts, each part may represent any unit of 
measure, and a drawing on paper to that scale 
represents the object from which it is drawn 
in a reduced form, from which measures in 
detail by the scale may be more readily and 
as accurately taken as from the natural ob- 
ject in the shop or on the estate, and if de- 
signs are made to a scale they can be exe- 
cuted conformably and accurately in all their 
parts in either enlarged or reduced size. 

Practically a two-foot rule, with its divis- 
ions into inches, halves, quarters, eighths, and 
sixteenths, may be made use of as a scale of 
equal parts, any division being taken as the 
unit to represent a foot, a yard, or a mile ; but 
among drawing instruments scales especially 
adapted to the purpose are found in great 
variety of forms, divisions, and material. Fig. 
84 represents a convenient form of scale, as it 
contains, in addition to the simply divided 
scales, a protractor along its edges. 

The simply divided scales consist of a series 
of equal divisions of an inch, which are num- 
bered 1, 2, 3, etc., beginning from the second 
division on the left hand ; the upper part of 
the left division in each is subdivided into 
twelve equal parts, and the lower part into ten 
equal parts. The scales are marked at the left 
1 inch, f, I", ^, and when used in drawing the 
scale is written as 1 inch, f , J, or \ inch to a 
foot, rod, or mile, or whatever may be the 
unit of actual measure. When the unit is the 
inch the first scale will be full size, the second 
f , the third |, and the fourth i full size. If 
the scale adopted is such a part of an inch to 
the foot, then the upper subdivisions will 
represent inches. 

Above the simply divided scales there is a 
scale marked C, which is a scale of chords; taking a radius equal to C-60, the 
chords of the different angles are represented by the division ; thus an angle of 
20° the chord will be C-20. 



^ 



A- 



^ 



0€ 



01 



i////////////iiniiiiim\\\\ 



Fig. 84. 



26 



CONSTRUCTION OF GEOMETRICAL PROBLEMS. 



SIMILAR TRIANGLES. 



Triangles which are equiangular are similar, and have their homologous 
sides — that is, their sides adjacent to the equal angles — proportional ; conversely, 
two triangles which have their homologous sides proportional are equiangular. 

Two triangles which have their sides parallel (Fig. 85) or perpendicular to 





Fig 85. 

each other (Fig. 86) are similar. A line c drawn parallel to one side c' of a 
triangle (Fig. 87) forms a triangle a c b whose sides are proportional to the 
original triangle. 

In Fig. 88 a polygon is divided into trian-gles by lines from an interior 
point to its angles and these lines intersected by lines parallel to the sides of 
the polygon. The figure thus constructed is a polygon similar to the original 
polygon composed of triangles similar to the triangles into which it ■ was 
divided. 

In the figure the parallel lines are drawn across the sides of the triangles at 
one half their length, and the areas of the small triangles are therefore equal to 
the square of one half or to one quarter that of the original triangles ; conse- 
quently the area of the interior 
polygon is one quarter that of the 
exterior one. As this construction 
obtains at any intersecting length, 
it affords a means of reducing the 
scale of the original polygon. 

To a scale of i inch (Fig. 89) 




lay off a line and divide from by equal units to 6 ; at 6, with a radius equal 
to 6 on scale (i inch), describe an arc, and from with a scale of f inch, with 
a radius equal to 6, intersect the previous arc. Complete the triangle through 
this intersection, and draw lines parallel to 6, 6' through the divisions of the 



CONSTRUCTION OF GEOMETRICAL PROBLEMS. 



27 



first line ; the triangle will be divided into six similar triangles of which the 
homologons sides are proportional and represented on their different scales by 
the same number of nnits. 




Fig 

Fig. 90 illustrates the application of scales to the measurement of lines 
which are inaccessible. Thus the lines a b and a c, with their inclosed angle, 
can be measured, and, if plotted to any scale, the line c b can be measured on 
the same scale. 

The height of an object may be obtained by the application of similar tri- 
angles, or by the length of the shadow cast, which is merely another applica- 
tion of the same method. The observer measures 
off, say, 60 feet from a flag pole (Fig. 91), and a 
rod is held at, say, 12 feet from the observer; a 
sight is then taken to the top and bottom of the 
flag pole at the 60-feet distance, and the points at 
which the sights intersect the rod are found to be 
10 feet apart. Then by construction the height of 
the flag pole is found by scale to be 50 feet. By 
means of shadows, if the length of the shadow is 
found to be 40 feet and the shadow cast by a 10- 
foot rod is 8 feet, then by plotting the height is found, as before, 50 feet. 

The value of the above solution of geometrical problems depends on the 
accuracy of the drawing. 

To construct a square equal to one half of a given square (Fig. 92). 

Let a b c d he the given 
square, and draw diagonals 
in it. The square, e b f d, 
constructed on one half of 
one of these diagonals, will 
be equal to one half the 
given square. 




Fig. 90. 



t 








Fig. 91. 



Fig. 9;^'. 



To construct a square equal to double a given square (Fig. 93). 
Construct a square on one of the diagonals in the given square, or inclose 
the square with parallels to the diagonals of the square. 



28 



CONSTRUCTION OF GEOMETRICAL PROBLEMS. 



To construct a square equal to three times a give?i square (Fig. 94). 

Extend the base of the given square to the length of its diagonal. Draw a 
line from the point at which this line ends to the extreme angle of the square, 
and upon this line erect a square, which will be the square required. 

For a square four times the size of a given square, make the base double 
that of the given square. 





To construct a square equal to Jive times a given square (Fig. 95). 

Extend the base of the given square, making the extension to d e equal to 
c d. From e draw a line to a, and on this line construct a square, which will 
be the square required. 




Fig. 95. 



Assuming the side of the given square in Figs. 92, 93, 94, and 95 to be the 
radius (or diameter) (Fig. 96) of a given circle, then the side of the square to 
be constructed half, twice, three, four, or five times the size of the given square 
will be the radii (or diameters) of the circles half, twice, three, four, or five 
times the size of the given circle. 



CONSTRUCTION OF GEOMETRICAL PROBLEMS. 



29 



It will be seen by Fig. 93 that the square constructed on the diagonal of a 
square is equal to double that of the original square. 




On any right-angled triangle A C B (Fig. 97) let fall a perpendicular from 
the vertex of the right angle to the hypothenuse A B ; the triangle will be 
divided into two similar triangles, similar to each other and to the original 
triangle, and 

AD:AC::AC:AB; that is, A C^ = A D X A B ; 
BD:BC::BC:AB; that is, B C^ = B D X A B. 

AD-1-BD = AB, and the sum of the two equations is A B^ = A C^ + 
BC2. 

Therefore the square constructed 
on the hypothenuse of a right-angled 
triangle is equal to the sum of the 
squares of the other two sides (Fig. 
98). 

To determine lioio much is added 
to a given square by extending its base 
and constructing a square thereon 
(Fig. 99). 

Let a represent the side C D of the given square. The area of the square 
is « X rt or a^. 

Extend the side C D by a length, D O, represented by b. Then the new 




30 



CONSTRUCTION OF GEOMETRICAL PROBLEMS. 



square {a -{- b) X {a -\- h) will be made up of the old square, or a^, and two rec- 
tangles, D G E H and P E K L, or 2 {a X b) or 2 a b, and one square, E H K J, 

b X b, or W. The area 




c 



Fig. 98. 



(ci-^rbY 



-^2ab + b\ 




To determine hoiv much 
is taheyi from the area of a 
given square^ by reducing^ 
its base and constructing a 
square (Fig. 99). 

Let a represent Gr, 
the side of the given square. 



E 



H 



Fig. 99. 



Reduce C G, the length G D, represented by b. The new square (a — by is 
the given square, or a^, diminished by two rectangles, D G J K and P L J H, 
or — 2 <^ b excepting one square, E H J K, Z> X ^ or -}- J^. The area {a — by 
= a'-2ab-i-b\ 

The last two constructions, in default of a table of squares, may often be 
found of use. 



constkuctio:n" of the ellipse, parabola, hyperbola, and spiral. 

An ellipse is an oval-shaped curve (Fig. 100), in which, if from any point, P, 
lines be drawn to two fixed points, F and F', called foci, their sum will always 

be the same. The line A B pass- 
I ~^~^.^ ing tjirough the foci is the major 

axis, and the perpendicular C D at 
the centre of it is the minor axis. 

To constricct an ellipse, the axes 
being known (Fig. 100). 

1st Method. — Let the two axes 
be the lines A B and C D. From 
C as a centre, with a radius equal 
to E B (half the major axis), de- 
scribe an arc cutting this axis at 
two points, F and F', which are 
the foci. Insert a pin in each of 
the foci, and loop a thread upon them, so that, when stretched by a pencil 




CONSTRUCTION OF GEOMETRICAL PROBLEMS. 



31 




Fig. 101. 



inside the loop, the point of the pencil will coincide with C. Move the pencil 
round, keeping the loop evenly stretched, and it will describe an ellipse. This 
construction follows the definition above given of an ellipse, that the sum of 
the distances of every point of the curve from the foci is equal. It is seldom 
used by the draughtsman, as it is difficult to keep a thread evenly stretched ; 
but for gardeners, laying out beds or plots, it is very convenient and sufficiently 
accurate. 

There are many forms of ellipsographs for drawing ellipses, and various 
sizes of ellipses in hard wood and rubber on sale. Pattern-makers usually lay 
out ellipses by means of a trammel 
(Fig. 101), which consists of a 
rectangular cross, with guiding 
grooves in which movable rods at- 
tached to sliders on a bar are 
fitted, so as to move easily and uni- 
formly. In describing an ellipse 
place the trammel with its grooves 
on the lines of the axes with the 
bar on the line of the major axis ; 
set the pencil or marker on the 
extremity of this axis, and slip the 
outer rod to the crossing of the 
grooves and clamp it to the bar. Now slide the rod down the minor axis, and, 
with the pencil at the extremity of this axis, clamp the intermediate rod to the 
bar at the crossing of the guides. Revolve the bar, the intermediate rod fol- 
lowing the major-axis groove, and the extreme rod that of the minor axis, 
and the pencil will describe the ellipse. Light trammels are made for the 

use of draughtsmen, but, as 
the necessity of drawing el- 
lipses is not frequent, it can 
be readily done by the use 
of a strip of cardboard (Fig. 
102). Lay off the major 
and minor axes on the pa- 
per ; these represent the 
grooves of the trammel. 
Now take a strip of card- 
board with a straight edge, 
lay it along the line of the 
major axis, and mark the 
positions a at the extremity 
of this axis, and c at the crossing of the axes ; place the mark a on the ex- 
tremity of the minor axis, and mark on the ed'ge of the card at b the cross- 
ing of the axes. Revolve the card as described for the trammel, mark the posi- 
tions of a by points, and connect them for the curve. 

To construct an approximate semi-ellipse hy means of five arcs of circles. 
Let A B (Fig. 103) be the major axis, and D the semi-minor axis. Draw 
the semicircles A C B and d D d'. Divide these semicircles into equal parts 




Fig. 102. 



32 



CONSTRUCTION OF GEOMETRICAL PROBLEMS. 



by the radial lines e, 0/, e\ Of. From the points of intersection of 
these radial lines with the semicircumference draw g h^h a^li' a\ g' b\ parallel 
to the major axis. From e,/, e',/', intersections of the radial lines with the 




semicircumference A C B, draw e Z>, fa, e' a\ and f h' parallel to the minor 
axis. The intersections of these lines with i g, a h, etc., will be points on the 
ellipse. Xow through the three points or, D and a' construct an arc of a circle. 
Connect a and h with a chord, bisect it with a perpendicular ; where this per- 
pendicular intersects a S 
at c is the centre of the 
arc a h. 

Connect h and c; d, 
the intersection oihc with 
A B, will be the centre of 
the arc h A. Arcs through 
a' V and B can be con- 
structed in the same way, 
or the centres can be 
transferred. 

The ellipse can in the same way be made up of any number of arcs of 
circles. 

To drmv a tangent to an ellipse through a given point in the curve (Fig. 104). 




CONSTRUCTION OF GEOMETRICAL PROBLEMS. 



33 



TJ 



K 



From the given point T draw straight lines to the foci, F, F' ; produce F T 
beyond the curve to c, and bisect the exterior angle c T F' by the line T d. 
This line T d is the tangent 
required. 

To draiu a tangent to an 
ellipse from a given point 
without the curve (Fig. 105). 

From the given point T 
as a centre, with a radius 
equal to its distance from 
the nearest focus F, describe 
an arc ; from the other focus 
F', with the major axis as 
radius, cut the arc at K, L, and draw K F', L F', touching the curve at M, N ; 
then the lines T M, T N, are tangents to the curve. 



^^^^- 


' ^ 


^"~^^ 


^-^.--V'"' 


/ 


fj 




i \ 


If' 








^^^--^ 


--_____ 


___^^ 


/ 



E 

Fig. 105. 



The Parabola. 

The parabola may be defined as an ellipse whose major axis is infinite ; its 
characteristic is that every point in the curve is equally distant from the direc- 
trix E N and the/ocws F (Fig. 106). 

To construct a parabola lohen the focus and directrix are given. 
I 1st Method (Fig. 106).— Through the 

\e E^ focus F draw the axis A B perpendicular 

to the directrix E N, and bisect A F 




a^ 




E 



N 



Fig. 106. 



Fig. 107. 



at e, the vertex of the curve. Through a series of. points, C, D, E, on the di- 
rectrix, draw parallels to A B ; connect these points, 0, D, E, with the focus 
F, and bisect by perpendiculars the lines F 0, F D, F E. The intersections 
of these perpendiculars with the parallels will give points, C, D', E', in the 
curve, through which trace the parabola. 

2d Method (Fig. 107). — Place a straight-edge to the directrix E N, and 
apply to it a square LEG-; fasten at Gr one end of a cord, equal in length to 
4 



34: 



CONSTRUCTION OF GEOMETRICAL PROBLEMS. 



E G ; fix the other end to the focus F ; slide the square steadily along the 
straight-edge, holding the cord taut against the edge of the square by a pencil, 
D, and it will describe the curve. 

To construct a parabola ivlien the vertex, the axis, and a point of the curve 
are given (Fig. 108). 

Let A be the vertex, A B the axis, and D the point in the curve. Con- 
struct the rectangle A B D C ; divide D C into, say, four equal parts at 12 3, 
and A C into the same number at 1' 2' 3' ; draw diagonals, A 3, A 2, A 1 ; and 



c 


3 _2_ 








/ / 




1 / 


, 


_l /-^^^ 


1 






^^-^l^^J^^""^ ^1 


^^,.2 




.""^ ^- 


'" hx/ >'^ y^^ ! 


,-""^^.3 










/^k" ' 1 


^ / 


^' 1 1 1 


b' a' J\ a h c 


Fig. 


108. 



parallels to the axis through 1' 2' 3'. The intersection of the diagonals A 3> 
A 2, A 1 with the parallels 3', 2', 1' at G, F, E will be points in the required 
curve. 

Extend the axis to B^ making A B'=A B ; draw perpendiculars to the axis 
from Gr, F, E, D ; lay off toward B', a'—K a, A &'=A Z>, A 6''= A c ; and draw 
B' D, c' E, V F and a' G-. These lines will be tangents to the curve at D, E, 
F, G, and lines perpendicular to the tangents at these points will be perpen- 
dicular to the curve. 

The Hyperbola. 

An hyperlola is a curve from any point, P, in which, if two straight lines 
be drawn to two fixed points, F, F', the foci, their difference will always be 
the same. 

To describe an hyperbola (Fig. 109). 

From one of the foci, F, with an assumed radius, describe an arc, and from 
the other, focus F', with another radius exceeding the former by the given 

difference, describe two small arcs, cut- 
ting the first as at P and p. Let this 
operation be repeated with two new 
radii, taking care that the second shall 
exceed the first by the same difference 
as before, and two new points will be 
determined ; and this determination of 
points in the curve may thus be con- 
tinued till its track is obvious. By 
making use of the same radii, but 
transposing, that is, describing with the 
greater about F, and the less about F', 
pjq io9_ we have another series of points equal - 





W 



CONSTRUCTION OF GEOMETRICAL PROBLEMS. 



35 



ly belonging to the hyperbola, and answering the definition; so that the hyper- 
bola consists of two separate branches. 

The curve may be described mechanically (Fig. 110) by fixing a ruler to 
one focus, F', so that it may be turned round on this point, and connecting the 
other extremity of the ruler, K, to the 
other focus, F, by a cord shorter than 
the whole length of the ruler by the \p 



given 



difference 




Fig. 110. 



Fig. 111. 



keeping this cord always stretched, and at the same time pressing against the 
edge of the ruler, will, as the ruler revolves around F', describe an hyperbola. 

To draw a tangent to any point of an hyperbola (Fig. 111). 

Let P be the point. On F' P lay off P jt?, equal to F P ; draw the line Y p; 
from P let fall a perpendicular on this line, P p^ for the tangent. 

To describe a spiral (Fig. 112 and Fig. 113, the primary on a larger scale). 

Divide the circumference of the primary into any number of equal parts, 
say not less than eight. To these points of division o, e,/, *, etc., draw tangents, 





Fig. 112. 



Fig. 113. 



and from these points draw a succession of circular arcs ; thus, from o lay off 
g^ equal to the arc a o reduced to a straight line, and connect a and ^ by a 
curve ; from e, with the radius e g, describe the arc g li ; from / the next arc, 
and so on. Continue the use of the centres successively and repeatedly to the 
extent of the revolutions required. 



DRAWING INSTRUMENTS 




The simple drawing instruments illustrated and applied in the construc- 
tion of the preceding problems, together with scales of equal parts, a protractor, 
and a drawing-pen, are all the instruments essential for topographical or me- 
chanical drawing. It is often convenient, for-facility in working, to have com- 
passes of various sizes and modifications, and these, together with an assortment 
of rulers, triangles, squares, scales, and protractors adapted to varied work, are 
included in boxes of drawing instruments furnished by dealers. The smaller 
rulers and triangles are generally of hard rubber, and the larger of wood. As 
it is often inconvenient to carry long rulers, or straight-edges, and difficult to 

procure them ready-made, the draughts- 
man may have to depend on a carpenter 
or joiner for them. 

The drawing-board in its simplest 
form consists merely of narrow strips of 
thoroughly seasoned white-pine wood, 
free from knots, closely joined and glued, 
and held together either with a ledge at 
each end or with battens screwed to the 
back. For small boards, the former 
kind is in some ways the best, as it ad- 
mits of being planed on all four edges. 

Fig. 114 is more elaborate and one 
of the best drawing boards, possessing 
all the qualities of a first-class board. It 
is made of pine wood, glued up to the 
required width, with the heart side of 
each piece of wood at the surface. A 
pair of hard -wood battens are screwed to 
the back, the screws passing through the ledges in oblong slots that are bushed 
with brass, which fit closely under the heads, and yet allows the screws to 
move freely when drawn by the contraction of the board. To give the battens 
power to resist the tendency of the surface to warp, a series of grooves are 

36 




Fig. 114. 



DRAWING INSTRUMENTS. 



37 




Fig. 115. 



Slink, half the thickness of the board, over the entire back. These grooves 
take the transverse strength out of the wood and allow it to be controlled by 
the battens, leaving at the same time the longitudinal strength of the wood 
nearly unimpaired. 

To make the two working edges perfectly smooth, allowing an easy move- 
ment of the square, a slip of hard wood is let into the end of the board. The 
slip is afterward sawed apart at about every inch to admit of contraction. The 
drawing-board should be truly rectangular and have perfectly straight sides, 
for the use of the T square. Two sizes are sufficient for ordinary use — 41x30 
inches for double elephant paper, and 
31 X24 inches for imperial and smaller 
sizes. Boards smaller than these are 
too light, and unsteady in handling. 

The drawing-table should be about 
6 feet long and 4 feet wide, of IJ 
inch stuff, constructed similarly to 
the drawing-board, and it is usually 
supported by a pedestal the height 
and inclination of which is adjusta- 
ble, or on trestles, or a strong frame at 
such height that the draughtsman 
may not have to stoop to his work. 

Fig. 115 shows an excellent form 
of trestle ; the upper part of the horses is attached to hard-wood supports, 
which slide through the body of the trestle and are provided with numerous 
holes ; by means of strong pins passing through the body of the horses and 
the holes the board may be set at various angles, the steel points in the top 
preventing the drawing-board from sliding or slipping off. 

Straight-edges are made of close-grained, thoroughly seasoned wood, such 
as mahogany, maple, pear, etc. ; also of celluloid, hard rubber, steel, or German 
silver. Those made of maple or pear wood answer every purpose and have the 
advantage of soiling the paper less than rubber or metal. No varnish of any 
description should be applied to any of the instruments used in drawing, as 
varnish will retain dust and soil the paper. Use the wood in its natural state, 
keeping it carefully wiped. Straight-edges should be .about -J inch thick in the 
square or slightly rounded edges and 1 to 2|- inches wide, according to their . 
length. As the accuracy of a drawing depends greatly on the straightness of 
the lines, the edge of the ruler should be perfectly straight. To test this, 
place a sheet of paper on a perfectly smooth board ; insert two very fine 
needles in an upright position through the paper into the board, distant from 
each other nearly the length of the ruler to be tested ; bring the edge of the 
ruler against these needles, and draw a line from one needle to the other; 
reverse the ruler, bringing the same edge on the opposite side and against the 
needles, and again draw a line. If the two lines coincide, the edge is straight ; 
but if they disagree, the ruler is inaccurate, and must be rcjointed. When 
one ruler has been tested, others can be examined by placing their edges against 
the correct one, and holding them between the eye and the light. 

Triangles may be made of the same kinds of wood as the ruler, somewhat 



38 



DRAWING INSTRUMENTS. 



thinner, and of various sizes. They should be right-angled, with acute angles 
of 45°, or of 60° and 30°. The most convenient size for general use measures 




from 3 to 6 inches on the side. A larger size, from 8 to 10 inches long on the 
side, is convenient for making drawings to a large scale. In the smaller trian- 
gles circular openings are made in the body for the insertion of the end of the 
finger, to give facility in sliding the triangle on the paper. Triangles are 
sometimes made as large as 15 to 18 inches on the side ; but in this case they 

are framed in three pieces, about 1^ inch 
wide, leaving the centre of the triangle open. 
The value of the triangle in drawing perpen- 
dicular lines depends on the accuracy of the 
right angle. To test this (Fig. 116), draw a 
line with an accurate ruler on paper. Place 
the right angle of the triangle near the 
centre of this line, and make one of the ad- 
jacent sides to coincide with the line ; now 
draw a line along the other adjacent side, 
which, if the angle is strictly a right angle, will be perpendicular to the first 
line. Turn the triangle on this perpendicular side, bringing it into the position 
ABC; if now the sides of the triangle agree with the line B C and A B, 
the angle is a right angle, and the sides are straight. If they do not agree, 
they must be made to do so with a plane, if right angles are to be drawn 
by the triangle. The straightness of the hypothenuse or longest side can be 
tested like a common ruler. 




£ 

Fig. 116. 



C' 




Fig. 117. 



The T square is a thin straight-edge or ruler (Fig. 117), fitted at one end 
with a stock, applied transversely at right angles. The stock being so formed 



DRAWING INSTRUMENTS. 



39 



as to fit and slide against one edge of the drawing-board, the blade reaches 
over the surface, and presents an edge of its own at right angles to that of the 
board, by which parallel straight lines may be drawn npon the paper. The 
stock should be long enough to give sufficient bearing on the edge of the board, 
and heavy enough to act as a balance to the blade, and to relieve the operation 
of handling the square. The blade should be sunk flush into the upper half of 
the stock on the inside, and very exactly fitted. It should be inserted full 
breadth, as shown in the figure ; notching and dovetailing is a mistake, as it 
weakens the blade, and adds nothing to the security. The upper half of the 
stock should be about i inch broader than the lower half, to rest firmly on the 
board and secure the blade lying flatly on the paper. 

One half of the stock c (Fig. 118) is in some cases made loose, to turn upon 
a brass swivel to any angle with the blade a, and to be clenched by a screwed 




Fig. 118. 

nut and washer. The loose stock is useful for drawing parallel lines obliquely 
to the edges of the board, such as the threads of screws, oblique columns, or 
connecting-rods of steam-engines. 

T squares are also made with a single movable head, shown in Fig. 119 ; 



«« 




Figs. 119, 120. 



the blade, turning on «, is clamped in position by the thumb-nut h. Fig. 120 
illustrates a T square wdth a protractor at the head, convenient for laying off 
lines of designated angles. 

In many drawing-cases will be found the parallel ruler (Fig. 121), consist- 




FiG. 121. 



40 



DRAWING INSTRUMENTS. 



ing of two rulers connected by two bars moving on pivots, so adjusted that the 
rulers, as they open, form the sides of a parallelogram. The edge of one of the 
rulers being retained in a position coinciding with, or parallel to, a given line, 
when the other ruler is moved, lines drawn along its edge are also parallel to 
the given line. This instrument is only useful in drawing small parallels, and 
in accuracy and convenience does not compare with either the triangle and 
ruler or T square. 

Another form of parallel ruler (Fig. 122) consists of a strip of wood with 
bevelled edges, having two holes to receive two broad wheels, <z, a^ which are 




Fig. 122. 

connected by an axle passing under the metal cover, ^, Z>, and revolving in. the 
supports, c, c ; the wheels come slightly below the surface of the wood, as 
shown in the end elevation. In drawing parallel lines the fingers are placed 
with a firm pressure about the centre of the metal cover, and the raler is 
moved in the proper direction. This ruler is more easily applied than the 
former, but is more liable to error. 

VAKIABLE CURVES. 

For drawing arcs of a large radius, beyond the range of ordinary compasses, 
and lines varying in curvature, thin slips of wood, termed curves, are usually 
employed. These forms are of very general application, but others of almost 
every form, and made of hard rubber, pear wood, or celluloid, can be pur- 
chased. Whatever be the nature of the curve, some portion of the instrument 
will be found to coincide with its commencement, and it can be continued 
throughout its extent by applying, successively, such parts as are suitable, care 
being taken that the parts are tangent to each other, and that the continuity is 
not injured by unskilful junction. 

Fig. 123 shows an adjustable curve ruler, the main features of which are a 
hard-rubber face, «, which holds the form of the required curve by a bar of 




Fig. 123. 

soft lead, h, kept in contact with the rubber face by the fasteners, c, and a flat 
spring inside these fasteners. This curve, while useful in the coarser kinds of 
draughting, does not do as neat or accurate work as the separate curves above 
given. 

Thin splines are also to be had, which, held in position by leaden weights, 
serve admirably for a guide to the pen in describing curves (Fig. 124). For the 



DRAWING INSTRUMENTS. 41 

t 

same purpose a thin, hard-rubber ruler, with soft-rubber backing, answers well, 
and, as it can be readily rolled up, is extremely portable. 

The weights above shown are very convenient in holding the drawing-paper 
on the board, but thumb-tacks (Fig. 125), steel points with large, flat heads,. 
are in general use. They can be readily forced into the wood, and as readily 
raised, but thumb-tack lifters can be purchased. 




Elliptic, parabolic, and hyperbolic (see above) curves are furnished in 
sets, but the draughtsman can make a model out of thick cardboard or cellu- 
loid, with which he can draw a very uniform curve. 

For the drawing of ellipses, very neat trammels or compasses with elliptic 
guides or patterns may be purchased. 



42 



DRAWING INSTRUMENTS. 





Fig. 124. 



Fig. 125. 



The drawing or right-line pen (Fig. 126) consists of two blades with steel 
points, fixed to a handle ; and they are so bent that a sufficient cavity is left 
between them for the ink. The blades are set with the 
points more or less open by means of a mill-headed screw, 
so as to draw lines of any required fineness or thickness. 
For red inks, the blades of the pen should be nickle-plated 
or German silver. One of the blades is framed with a joint, 
so that by taking out the screw the blades may be complete- 
ly opened, and the points effectively cleaned after use. The 
ink is put between the blades by a common pen. In using 
the pen, it should be slightly inclined in the direction of. 
the line to be drawn, and care should be taken that both 
points touch the paper. These observations equally apply 
to the pen-points of the compasses. The drawing - pen 
should be kept close to the ruler or straight- 
edge, and in the same direction during the 
whole operation of drawing the line. Care 
must be taken to hold the straight-edge 
firmly with the left hand, that it does not 
change its position. 

For drawing close parallel lines in me- 
chanical and architectural drawings, or to 
represent railroads, canals, or roads, a rail- 
road pen (Fig. 127) is frequently used, a 
double pen with an adjusting screw to set the pens to any required small 
distance. This instrument is also made with pencil points (Fig. 128). 

Border - pens (Fig. 
129), for drawing broad 
lines, are double pens 
with an intermediate 
blade, and are applicable 
to the drawing of map- 
borders. The same work 
may be done by drawing 
heavy outer lines with 
the common drawing- 
pen, and filling in with a 
brush or writing-pen. 

The curve-pen (Fig. 
130) is especially de- 
signed for the ready 
drawing of curved lines. 
The axis of this pen is 
carried through the han- 
dle and fastened by a 
nut on top, allowing the 
This instrument, made 




Fig. 128. 



Fig. 129. 



Fig. 130. 



pen to revolve, and thus more easily follow the curve, 
with two pens (Fig. 131), is called a railroad cnrve-pen 



DRAWING INSTRUMENTS. 



43 



The dotting-peii (Fig. 132) has on the back blade a pivot, on which may be 
placed a dotting-wheel, resembling the rowel of a spur ; the screw is for open- 




FiG. 131. 

ing the blades to remove the wheel for cleaning after use or replace it with one 
of another character of dot. A variety of dotting-wheels accompanies the in- 
strument, each producing a different-shaped dot. These are used as distin- 
guishing marks for different classes of boundaries on maps ; for instance, one 
kind of dot distinguishes county boundaries, another kind town boundaries, a 
third kind distinguishes that which is both a county and a town boundary, etc. 




Fig. 132. 

In using this instrument, the ink must be inserted between the blades above 
the dotting-wheel, so that, as the wheel revolves, the points pass through the 
ink, each carrying with it a drop, and marking the paper as it passes. It 
sometimes happens that the wheel will revolve many times before it begins to 
deposit its ink on the drawing, thereby leaving the first part of the line blank, 
and, when it is gone over again, the first-made dots are liable to get blotted. 
This evil may be avoided by placing a piece of blank paper over the drawing 
to the very point the dotted line is to commence at, and drawing the wheel 
over the blank paper first, so that by the time it 
reaches the proper point the ink begins to flow. 

The dotting -instrument (Fig. 133) works on the 
principle of the drawing-pen. The outer wheel is 
rolled on the edge of a T square or straight-edge, 
and turns a ratchet wheel which causes the pen to 
move up and down. The flat point close to the 
pen must slide on the paper. To change the pat- 
tern of the dotted lines, the spring which holds the 
wheels on the axle is thrown back, and the proper ratchet wheel inserted. 

The best pricking -point is a fine needle held as in Fig. 134, and is used to 
transfer drawings by pricking through at the points of a drawing into the paper 




Fig. 133. 



Fig. 134. 

placed beneath. The handle of the ordinary drawing-pen often contains a 
pricking-point, which may be used by unscrewing the pen where it is joined to 
the handle. 

When drawings are transferred by tracing — a prepared black sheet being 
placed between the drawing and the paper to receive the tracing — the eye end 
of the needle forms a good tracing-point. 



44 



DRAWING INSTRUMENTS. 



The stylus (Fig. 135) is a piece of polished agate placed in a handle, and is 
used as a tracing-point. 



Fig. 135. 

Compasses are fitted with ink-points and with lengthening bars for drawing 
larger circles. Compasses should have joints in the legs, so that the points, 
pencil, and pen may be set perpendicular to the planes in which the 
circles are described (Fig. 136). Compasses of this general form may 
be had in sizes of 3|- to 7 inches. 

For the measurement and laying off 
of small spaces, and the describing of 
small circles, there are small how com- 
passes (Fig. 137). These are sometimes 
made with an adjusting screw between 
QJ ^ ?^ the legs. 

For the measurement or laying off 



& 



i 






Fig. 136. 



Fig. 137 



Fig. 138. 



of distances the plain dividers are convenient, but for ready and close ad- 
justment the hair dividers (Fig. 138) are most suitable. The only difference 
is that in the hair dividers one of the points is attached to the body by a 




Fig. 139. 



spring, and by means of the screw h it can be moved a very little toward or 
from the fixed point more accurately than by closing or opening the dividers. 
In dividing a line into equal parts especially, it enables one to divide the excess 
or deficit readily. 



DRAWING INSTRUMENTS. 



45 



For convenience of carrying in the pocket, there are portable or tiirn-iji 
compasses (Fig. 139). There is a small attachment for a common pencil 
which enables it to be used like compasses. 




Fig. 140. 

Three-legged dividers (Fig. 140) are convenient, while transferring measures 
from a drawing to a copy on an equal scale, for locating a third point when two 
are established. 

For setting off very long .lines, or describing circles of large radius, beam 
compasses are used (Fig. 141). These consist of a mere strip of wood. A, and 
two brass or German silver boxes, B and C, which can easily be attached to the 
beam ; connected with the brass boxes are the two points of the instrument, 
G and H. The object of this instrument is the nice adjustment of the points 
G and H at any definite distance apart ; at F is a slow-motion 
screw, by which the point G may be moved any very minute dis- 
tance after the distance from H to G has been adjusted as nicely 
as possible by the hand alone. The wheel attachment, I, is to 
carry the weight of the beam. The metal parts of this instru- 
ment occupy but little space. Lv#1<7 

There are beam compasses in which the beam is graduated, 
and in which the boxes corresponding to B and C are fitted with 
vernier or reading plates, to afford the means of minutely subdi- 
viding the divisions on the beam. 

Beam compasses are also made of small round German-silver 
bars, one screwing into the other, on which are slides adapted for 
carrying pen or pencil and points. 




Fig. 142. 



Proportional dividers (Fig. 142), for copying and reducing drawings, are 
found in most cases of instruments. 

Closing the dividers and loosening the screw C, the slide may be moved up 



46 DRAWING INSTRUMENTS. 

in the groove until the mark on the index corresponds with the required num- 
ber ; then clamping the screw, the space inclosed between the long points, A B, 
will be as many times that between the short points, E D, as is shown by the 
number opposite the index. If the lines are to be reduced, the distances are 
measured v/ith the long points, and set off by the short ones ; if the lines are 
to be enlarged, then vice versa. 

Proportional dividers are also used for dividing the circumference of a 
circle into a number of parts. A special scale along the graduated edge, 
marked circles, is used, it being only necessary to move the slider to the 
proper number on this scale to obtain a chord of the proper length. It 
often happens that the length of the points becomes reduced by use or acci- 
dent. In this case it is only necessary to loosen the screw holding the short- 
ened point, take it out, grind to a point, and set to its former length. 

Scales. — The application of simple scales to the construction of diagrams 
has been explained ; but among drawing instruments scales especially adapted 
to plotting are to be found in great varieties of form, divisions, and material. 
It is usual, especially in topographical drawings, for the draughtsman to con- 
struct a scale upon the finished sheet on account of its ready application to the 
determination of measures, and when the drawing is to be reduced or enlarged 
by photographing it is indispensable. Moreover, paper expands and contracts 
under hygrometric changes ; the scale should be subject to those same changes. 
To remedy this inconvenience Mr. Charles Holzapfel has introduced paper 
scales, which are portable and cheap ; but as all kinds of paper are , not 
equally susceptible to changes of condition on the atmosphere, the detached 
paper scale affords only a partial correction. 

The scale should be written or drawn in all drawings ; also the date of com- 
pletion and name or initials of the draughtsman, as these data may be of value 
in the identification of the drawing. 

In all working architectural and mechanical drawings, use as large a scale 
as possible ; and even then do not depend upon the mechanics employed in the 
construction measuring correctly, but write in the dimensions as far as prac- 
ticable. For architectural plans, the scale of ^ of an inch to the foot is in very 
general use and is convenient for the mechanic, as the common two-foot rule 
carried by all mechanics is subdivided into :j-ths, -g-ths, and sometimes sixteenths 
of an inch, and the distances on a drawing to this scale can therefore be easily 
measured by them. This fact should not be lost sight of in working drawings. 
When the dimensions are not written, make use of such scales that the dis- 
tances may be measured by the subdivisions of the common two-foot rule ; 
thus, in a scale of |- or :J- full size, 6 inches or 3 inches represent one foot ; 
in a scale of an inch to the foot or twelfth full size, each |- an inch repre- 
sents 6 inches, ^ of an inch, 3 inches ; but when -J or ^^ an inch to the foot, 
or any similar scale, is adopted, it is evident that these divisions can not be 
taken by the two-foot rule. 

Plotting scales (Fig. 143) are scales of equal parts, with the divisions usu- 
ally on a bevelled edge, by which any length may be marked off on the paper 
without using dividers. There are also small offset scales, for use of which see 
" Topographical Drawing." 

Sometimes these scales are made with edges bevelled on both sides, and 



DRAWING INSTRUMENTS. 



47 



graduated to four different scales. Sometimes the section of the scale is tri- 
angular (Fig. 144), with six scales on the different edges. To avoid confusion 



ylll 011^ Is 18 IL 19 .IS IJT IE \Z \l |0 

MHIIIilllllll'linill'l l||!IIIIMIIIIII!lllinillllll|i|:'|l IIMIIIIIIIIIIIIIIIIMimilinMillllllliUllllTr" 



Fig. 143. 



from having many scales on one ruler, the triangular scale has a small slip of 
metal, A, readily put on, which covers partially the scales not in use. 




Fig. 144. 




Fig. 145 



To divide a given line into any number of equal }) arts (Fig. 145). 
Let A B be the line, and the number of parts be ten. Draw a perpendicu- 
lar at one extremity. A, of the line ; with a plotting scale place the zero at the 
other extremity, B, of the line ; make the mark 10 
on the scale coincide with the perpendicular ; draw 
a line along the edge of the scale, and mark the 
line at each division of the scale 1 to 9 ; draw per- 
pendiculars through these marks to the line A B, 
and they will divide A B into ten equal parts. 

The above figure illustrates the construction of 
diagonal scales. The simply divided scales give 
only two denominations, primaries and tenths, or 

twelfths ; but more minute subdivision is attained by the diagonal scale, which 
consists of a number of primary divisions, one of which is divided into tenths, 

and subdivided into 
hundredths by diago- 
nal lines (Fig. 146). 
This scale is con- 
structed in the follow- 
ing manner : Eleven 
parallel horizontal lines 
are ruled, inclosing ten 
equal spaces ; from one 
end set off the primary 
unit divisions, 0, 1, 2, 3, 
and draw vertical lines 
through these points; 
subdivide the extreme unit to the left on the upper and lower lines into ten 
equal parts, 1, 2, 3, etc. ; connect on the upper line with 1 on the lower line 




Fig. 146. 



48 



DRAWma INSTRUMENTS. 



by a diagonal, and draw lines parallel to it through the other subdivisions. To 
take a measurement of, say, 168, we place one foot of the dividers on the pri- 
mary 1, and carry it down to parallel 8, and then extend the other foot to the 
intersection of the diagonal which falls from the subdivision 6 with this par- 
allel. The primaries may, of course, be considered as yards, feet, or inches ; 
and the subdivisions as tenths and hundredths of these respective denomina- 
tions. If the number of parallel spaces be eight and the subdivision be 
twelve, we can measure feet, inches, and eighths. In the diagonal scale the 
vertical subdivisions are often omitted. 

The diagonals may be applied to a scale where only one subdivision is re- 
quired. Thus, if seven lines be ruled (Fig. 147), inclosing six equal spaces, 

and the length be divided 
into primaries, as A B, B C, 
etc., the first primary, A B, 
may be subdivided into 
twelfths by two diagonals 
running from 6, the mid- 
dle of A B, to 12 and 0. 
We have here a very con- 
venient scale of feet and inches. From C to ^6 is 1 foot 6 inches ; and from 
C on the several parallels to the various intersections of the diagonals we obtain 
1 foot and any number of inches from 1 to 12. 

For the designing of machinery, it is very convenient to have some scale of 
reference by which to proportion the parts ; for this purpose a vertical and 
horizontal scale may be drawn on the walls of the room. 

Vernier scales are preferred by some to the diagonal scale already described. 
To construct a vernier scale (Fig. 148) by which a number to three places may 
be taken, divide all the primary divisions into tenths, and number these sub- 




FiG. 147. 



10 




2 4\ 6 8 


5 


^ 


_ _ _ f 'Jll 




M 1 1 1 1 1 M 


1 1 M i 1 1 1 1 


1 1 1 1 1 1 1 1 1 1 1 1 i 1 1 M 1 1 Ml 


100 


1 1 1 1 1 1 1 1 1 




w_ 


8 6 \ 4- 2 





Fig. 148. 

divisions 1, 2, 3, from left to right. Take off now with the compasses eleven 
of these subdivisions, set the extent off backward from the end of the first 
primary division, and it will reach beyond the beginning of this division, or 
zero point, a distance equal to one of the subdivisions. Now divide the extent 
thus set off into ten equal parts, marking the divisions on the opposite side of 
the divided line to the lines marking the primary divisions and the subdivisions, 
and number them 1, 2, 3, etc., backward from right to left. Then, since the 
extent of eleven subdivisions has been divided into ten equal parts, so that 
these ten parts exceed by one subdivision the extent of ten subdivisions, each 
one of these equal parts, or, as it may be called, one division of the vernier 
scale, exceeds one of the subdivisions by a tenth part of a subdivision, or a 
hundredth part of a primary division ; thus, if the subdivision be considered 
10, then from to the first division of the vernier will be 11 ; to the second, 
22 ; to the third, 33 ; to the fourth, 44 ; to the fifth, 55, and so on, 66, 77, 
88, 99. 



DRAWING INSTRUMENTS. 



49 



To take off the number 253 from this scale, place one point of the dividers 
at the third division of the vernier ; if the other point be brought to the pri- 
mary division 2, the distance embraced by the dividers will be 233, and the 
dividers must be extended 
to the second subdivision of 
tenths to the right of 2. 
If the number were 213, 
then the dividers would have 
to be closed to the second 
subdivision of tenths to the 
left of 2. The number, thus 
taken, may be 253, 25*3, 
2 "53, according as the pri- 
mary divisions are taken as 
hundreds, tens, or units. 

The construction of this 
scale is similar to that of the 
verniers of theodolites and 
surveying instruments. 

The sector in its old 
form carried several scales 
on its faces. As given in 
Fig. 149, there are only 
double scales starting from 
the centre joint, which, 
without drawing, may be 
iipplied to the solution of problems on similar triangles. 

Let the lines A B, A C, represent the legs of the sector, and A D, A E, two 
€qual sections from the centre ; then, if the points B C and D E be connected, 
the lines B and D E will be parallel ; therefore, the triangles A B C, A D E, 




Fig. 149. 




will be similar, and, consequently, the sides A B, B C, A D, D E, proportional 
—that is, as A B : B C : : A D : D E ; so that if A D be the half, third, 
5 



60 



DRAWING INSTRUMENTS. 



or fourth part of A B, then D E will be a half, third, or fourth part of 
B C ; and the same holds of all the rest. Hence, if D E be the chord, 
sine, or tangent of any arc, or of any number of degrees to the radius A D, 
then B will be the same to the radius A B. Thus, at every opening of 
the sector, the transverse distances D E and C B from one ruler to another are 
proportional to the lateral distances, measured on the lines A B, A C. It is to 




Fig. 151. 

be observed that all measures are to be taken from the inner lines, since these 

only run accurately to the centre. 

On the scale in common boxes of drawing instruments, the edges of the 

sides are divided as a protractor (Fig. 84) for 
the laying out of angles. The ordinary pro- 
tractor consists of a semicircle of thin metal or 
horn (Fig. 150), whose circumference is divided 
into 180 degrees (180°). In the larger protrac- 
tors each of these divisions is subdivided. 

Application of the protractor. — To lay off a 
given angle from a given point on a straight 
line, let the straight line ai of the protractor 
coincide with the given line, and the point c 
with the given point ; now mark on the paper 
against the division on the periphery coinciding 
with the angle required ; remove the protractor, 
and draw a line through the given point and the 
mark. 

Fig. 151 is a protractor with a straight-edge 
revolving on a horn centre. Where the straight- 
edge is intersected by the edge of the protractor 
a vernier is attached, and will be found useful in 
close work for dividing the degrees into tenths. 
This protractor is often extended to full circles. 
For plotting field-notes expeditiously, drawing-paper can be obtained with 




DRAWING INSTRUMENTS. 



51 



large, full circular protractors printed thereon, on which the courses can be 
readily marked, and thus transferred to the part of the paper required by a 
parallel ruler, or by triangle and ruler. These sheets are of especial use in 
plotting at night the day's work, as, on account of the large size of the protrac- 
tor, angles can be laid off with greater accuracy than by the usual protractor of 
a drawing-instrument case, with less confusion of courses, and more expe- 
ditiously. 

The pantagrajjli is used for the copyiug of drawings, either on the same 
scale, on a reduced scale, or on an enlarged scale. 

Fig. 152 shows its simplest form and its application. The lower left-hand 
point, around which the frame is turned, is fixed, and the proportion of the 
drawing is determined by the position of the screw eyes in the holes of the 



arms. 



Fig. 153 is another form, of more finished construction. It consists of a 
set of jointed rulers. A, B, and another, C, D, about one half the length of the 




Fig. 153. 

former. The free ends of the smaller set are jointed to the larger at about the 
centre. Casters are placed at a <2, etc., to support the instrument and to allow 
an easy movement. 

DRAWING-PAPERS. 

Papers adapted to drawing may be obtained of various qualities, thicknesses, 
and dimensions, either in sheets, pads, or rolls. Machine-made papers are 
generally used, and are to be had from stock in rolls up to 62 inches in width, 
but to order much wider. They are generally made from cotton for the more 
finished drawings ; but stronger papers for working drawings and details are of 
manilla or of coarse heavy stock. 

Roll and sheet papers can be had mounted or backed with cotton cloth, 
which prevents them from being torn, and permits of their being hung to the 
walls as maps. 

Hand-made drawing-papers are usually made in certain standard sizes, about 
as follows : 



Cap 13 inches by 17 inches. 

Demy 15 " 20 " 

Medium 17 " 22 " 

Royal 19 " 24 " 

Super Royal 19 " 27 '* 



Imperial 22 inches by 30 inches. 

Atlas 26 " 34 " 

Double Elephant 27 " 40 " 

Antiquarian 31 " 53 " 



Tracing-paper is a prepared tissue paper, transparent and qualified to re- 
ceive ink lines and tinting without spreading. When placed over a drawing 



52 DRAWING INSTRUMENTS. 

already executed, the drawing is distinctly visible through the paper, and it 
may be copied directly or traced in pencil or ink. 

Tracing-paper often becomes tender with age, is apt to break in the folds, 
is not easily rolled. It is not suitable, therefore, for permanent drawings ; but 
the tracing can be readily transferred to drawing-paper by means of transfer 
'paper. Place the fair sheet on the drawing-board, above it the transfer sheet 
with the prepared face down, then the tracing, and steady the whole by weights 
or by thumb-tacks fixed into the drawing-board. A fine, smooth point is then 
passed over each boundary and line on the tracing with a pressure of the hand 
sufficient to cause a clear line to be left by the transfer paper on the fair sheet. 
Finish these lines in ink. The copyist should be careful in his manipulation 
that no unnecessary lines or smutches be left on the fair sheet. Transfer paper 
can be readily obtained in sheets, either in black, blue, vermilion, or graphite, 
or it can be made by smearing with a piece of flannel one surface of thin paper 
with a coating of lard and graphite and, after a day's drying, wiping off the 
superfluous portion with a soft rag. 

Parchment papers are much stronger than tracing-papers, and are usually 
transparent enough to serve the same purpose ; the thicker kinds are well 
adapted for drawing and engrossing. De La Eue's process for the manufac- 
ture of parchment paper is to plunge unsized paper for a few seconds into 
sulphuric acid, diluted with half to a quarter its bulk of water, the solution 
being of the same temperature as the air, and afterward wash with weak 
ammonia. 

A drawing may be made to accompany a letter by saturating the letter 
paper with benzine till it becomes transparent, then using it as tracing-paper, 
copying the design in pencil, and finishing in copying-ink after the benzine 
has evaporated, so that it can be transferred with the descriptive writing to the 
letter book. 

Transparent tracing-cloth can be had in wide and long rolls. It is much 
stronger than tracing-paper, and serves a permanent purpose. Should the 
tracing-cloth refuse to take ink lines well, almost any fine white powder will 
remedy this, such as chalk, fuller's earth, pipe clay, or plaster of Paris sprinkled 
on and rubbed in well. 

It is usual to draw on the dull side of the cloth, except where colour is to 
be put in, when the ink lines are drawn on the glossy side and the colour on 
the dull back. Designs and finished drawings made in pencil on paper are 
traced on cloth in ink, and in this form are preserved as originals and can be 
copied by the heliographic process,.either wholes or details as needed. When a 
white sheet of paper is placed behind the tracings, the drawing may be readily 
photographed on a reduced or enlarged scale, and much more cheaply than by 
any other process ; and such negatives may be used in process engraving for 
book illustrations. 

Heliographic paper can readily be had in sheets or rolls, and the mixture 
for the preparation of the paper can also be purchased, or can be made by 
dissolving 1-J ounce of common citrate of iron in 8 ounces of water, and \\ 
ounce of red prussiate of potash in 8 ounces of water, and then mixing them 
just previous to using. Papers and mixtures must be kept from the light or 
they will lose their sensitiveness. The above is a mixture for the most com- 



DRAWING INSTRUMENTS 53 

mon form of sun prints, called the ferro-prussiate or blue process, in which 
white lines are developed on a blue ground. By the cyanotype process blue 
lines are developed on a white ground ; by the nigrosine process, black lines on 
a white ground ; by the chromide dry process, dark lines on a tinted ground. 
Papers for all of the above processes are on sale, with directions for use. If 
none can be had, and it is desired to prepare some, use the ferro-prussiate 
process as the simplest, of which a recipe has been given above, the paper 
should be chemically neutral, of even material, and capable of being washed. 
Inks are to be had especially adapted for the tracings in bottles and cakes. It 
is necessary for a good print that the lines should be of a deep black. If not 
sufficiently opaque, burnt Sienna, burnt umber, or gamboge added to the ink 
improves the prints. 

For the manipulation there is needed plate glass and a blanket a little larger 
than the drawing, also a shallow tray, that the drawing can be placed in flat for 
washing. 

Lay down the blanket on the drawing-board, above that the ferro-prussiate 
paper, next the drawing, and then the glass. Expose to the sunlight until the 
background is a metallic gray. The length of exposure may be from five min- 
utes up, depending on the intensity of the sunlight, the age of the prepared 
paper, and the transparency of the tracing. Now lay the ferro-prussiate paper 
in the tray, cover with water, and leave it for five to ten minutes ; wash thor- 
oughly and dry. 

The usual form of printing-frame, as purchased of dealers, shown in Fig. 
154, consists of a frame into which fits a sheet of glass, preferably of plate glass, 




Fig. 154. 

with a hinged backboard, to the inner side of which a piece of felt is glued in 
the smaller sizes, while in the larger the felt is separate ; on the back of this 
board are two brass springs fitting under the metal catch, making a close con- 
tact with the glass. As shown in the small seqtional drawing, the frame is 
turned upside down. The glass is placed in first, then, successively, the tracing 
with its face to the glass, the prepared paper with the prepared side to the 
tracing, and the felt ; then the backboard is placed and held in position by the 
springs, the frame is turned up, and the directions given above as to exposure 
and washing are properly carried out. 

When it is necessary to make additions and alterations on blue prints, a 



54 DRAWING INSTRUMENTS. 

special ink can be procured ; lines made with this preparation on the blue 
ground turn white. (See Free-hand Drawing.) 

The helios process is useful for copying not only drawings, but contracts, 
estimates, tables, etc., when they are written on transparent paper or cloth; and 
so is the nigrosine process. 

Bristol hoard is a cardboard with a very fine surface. It can be obtained of 
various thicknesses and of the same dimensions as sheet drawing-papers. It is 
adapted to water-colours, pen-and-ink sketches, and fine line-drawings ; the 
Patent Office requires sheets 10 by 15 inches, and these can be obtained with 
border and wording of witness, inventor, and attorney properly printed in. 

Mouth glue^ for the sticking of the edges of drawing-paper to the board, is 
made of glue and sugar or molasses ; it melts at the temperature of the mouth, 
and is convenient for the draughtsman. 

Drawing-paper may be fixed down on the drawing-board by thumb-tacks at 
the corners, by weights, or by gluing or pasting the edges. The first is 
sufficient when no shading or colouring is to be applied, and if the sheet is 
not to be a very long time on the board ; and it has the advantage of preserv- 
ing the paper in its natural state. For shaded or tinted drawings, the paper 
must be damped. 

Damp-stretching is done as follows : The e4ges of the paper should first be 
cut straight, and, as near as possible, at right angles to each other. The sheet 
should be enough larger than the intended drawing and its margin to admit of 
being afterward cut from the board, leaving the pasted or glued border. , 

The paper must first be placed on the drawing-board and thoroughly and 
equally damped with a sponge and clean water on the side on which the draw- 
ing is to be made. This done, lay a straight flat ruler on the paper, with its 
edge parallel to, and about half an inch from, one of its edges. The ruler must 
now be held firm, while the projecting half inch of paper is being turned up 
along its edge ; then a piece of mouth glue, having its edge partially dissolved 
by holding it in warm water for a few seconds, must be passed once or twice 
along the turned-up edge of the paper, after which, by sliding the ruler over 
the glued border, it will be again laid flat, and, the ruler being pressed down 
upon it, that edge of the paper will adhere to the board. If sufficient glue has 
been applied, the ruler may be removed directly, and the edge finally rubbed 
down by an ivory book-knife or by the bow of a common key, rubbing it on a 
slip of paper placed on the drawing-paper, so that the surface of the latter may 
not be soiled ; this will firmly cement the paper to the board. Another edge of 
the paper is then treated in like manner, and the remaining edges in succession. 
Sometimes strong paste or mucilage is used instead of glue. 

The wetting of the paper is done for the purpose of expanding it ; and the 
edges, being fixed to the board in its enlarged state, act as stretchers upon the 
paper, while it contracts in drying, which it should be allowed to do gradually. 
All creases or undulations by this means disappear from the surface, and it 
forms a smooth plane to receive the drawing. 

After the drawing is finished, cut off the paper inside the pasted edge, and 
remove the edge by warm water and the knife. 



DRAWING INSTRUMENTS. 55 

MOUNTITS'G PAPER AND DRAWINGS, VARNISHING, ETC. 

When paper of the requisite quality or dimension can not be purchased 
already backed, it may be mounted on muslin. The cloth should be well 
stretched upon a smooth flat surface, being damped for that purpose, and its 
edges glued down, as was recommended in stretching drawing-paper. Then 
with a brush spread strong paste, beating it in till the grain of the cloth be all 
filled up ; for this, when dry, will prevent it from shrinking when subsequently 
removed ; then, having cut the edges of the paper straight, paste one side of 
every sheet, and lay them upon the muslin sheet by sheet, overlapping each 
other slightly. If the drawing-paper is strong, it is best to let every sheet lie 
five or six minutes after the paste is put on it, for, as the paste soaks in, the 
paper will stretch, and may be better spread smooth upon the cloth ; whereas, 
if it be laid on before the paste has moistened the paper, it will stretch after- 
ward and rise in blisters when laid upon the cloth. The paper should not be 
cut off from its extended position till thoroughly dry, which should not be 
hastened. Leave it in a dry room to do so gradually, if time permit ; if not, it 
may be exposed, to the sun ; in the winter season the help of a fire may be neces- 
sary ; but it should not be placed too near a scorching heat. 

In joining two sheets of paper together by overlapping, it is necessary, in 
order to make a neat joint, to feather-edge each sheet ; this is done by care- 
fully cutting with a knife half way through the paper near the edges on the 
sides which are to overlap each other and then stripping off a feather-edged 
slip from each, which, if done dexterously, will produce a very neat and effi- 
cient joint. 

For mounting and varnishing drawings or prints, stretch a piece of linen 
on a frame, to which give a coat of isinglass or common size ; paste the back of 
drawing, which leave to soak ; and then lay it on the linen. When dry, give it 
at least four coats of well-made isinglass size, allowing it to dry between each 
coat. Take Canada balsam diluted with the best oil of turpentine, and with a 
clean brush give it a full flowing coat. 

When drawings are not mounted on muslin, the edges may be protected 
from tearing by binding with gummed tape, or strips of paper which may be 
cut or purchased. 

Drawings, as far as possible, should be preserved flat in drawers, and this is 
especially desirable for tracings which are to be often sun-printed. 

The classification of drawings is varied. The common method is to devote 
a separate drawer to the drawings of each machine, or of each group or class of 
machine ; another is to have drawers of various sizes and arrange the drawings 
according to sizes. 

^ MANAGEMENT OF THE INSTRUMENTS. 

In constructing preparatory pencil- drawings', it is advisable, as a rule of 
general application, to make no more lines upon the paper than are necessary 
to the completion of the drawing in ink ; and also to make these lines just 
dark enough to be sufficiently distinct. 

It is often beneficial to ink in one part of a drawing before touching other 
parts at all; it prevents confusion, makes the first part easy of reference, and 



56 DRAWING INSTRUMENTS. 

allows of its being better done, as the surface of the paper inevitably contracts 
dust and becomes soiled in the course of time, and therefore the sooner it is 
done with the better. 

Circles and circular arcs should, in general, be inked in before straight lines, 
as the latter maybe more readily drawn to join the others than can the former. 
When a number of circles are to be described from one centre, the smaller ones 
should be inked first, while the centre is in better condition. When a centre 
is required to bear some fatigue, it should be protected with a thickness of stout 
card glued or pasted over it, to receive the compass-leg. 

India-rubber is the ordinary medium for cleaning a drawing and for cor- 
recting errors of the pencil. For slight work it is quite suitable ; that sub- 
stance, however, operates to destroy the surface of the paper ; and, by repeated 
application, it so ruffles the surface as to spoil it for fine drawing, especially if 
ink shading or colouring is to be applied. It is much better to leave trivial 
errors alone, if corrections by the pencil may be made alongside without confu- 
sion, and not clear away superfluous lines till the inking is finished. 

When ink lines have to be erased to any considerable extent, the best way 
is to use an ink-erasing rubber. Single lines may be erased by cutting a long 
narrow slit in a piece of thin cardboard or celluloid and erasing through it. 

For cleaning a drawing, a piece of bread two days old is preferable to India- 
rubber, as it cleans the surface well and does 'not injure it. A sponge rubber 
may also be used for this purpose. For ordinary small erasures of ink lines, a 
sharp rounded pen-blade, applied lightly and rapidly, does well, and the sur- 
face may be smoothed down by the thumb-nail. In drawings intended to be 
highly finished, particular pains should be taken to avoid the necessity for cor- 
rections, as everything of this kind detracts from the appearance. 

The best work can only be accomplished by keeping the instruments in 
good order; their working parts should be carefully preserved from injury. 
The scales must be kept scrupulously clean ; the inking tools should have 
especial care, and the blades kept well set, for which a small oil-stone is con- 
venient. 

To dress up the tips of the blades of the pen or of the bows, as they usually 
become worn unequally, they may be screwed up into contact in the first place, 
and passed along the stone, turning upon the point in a directly perpendicular 
plane, till they acquire an identical profile. Being next unscrewed and exam- 
ined to ascertain the parts of unequal thickness round the nib, the blades are 
laid separately upon their backs on the stone, and rubbed down at the points, 
till they be brought up to an edge of uniform fineness. It is well to screw 
them together again, and to pass them over the stone once or twice more, to 
bring up any fault ; to retouch them also on the outer and inner side of each 
blade, to remove barbs or fraying ; and, finally, to draw them across the palm 
of the hand. 

India ink, which is commonly used for line-drawing, should be rubbed 
down in water to the degree that avoids the sloppy aspect of light lining with- 
out making the ink too thick to run freely from the pen. This medium degree 
may be judged of after a little practice by the appearance of the ink on the 
palette. The best quality of ink has a soft feel when wetted and smoothed, 
being then free from grit or sediment, and has a musky smell. 



DRAWING INSTRUMENTS. 5'^ 

Slabs of many forms and different materials are used in grinding down the 
ink. The one shown in Fig. 155 is a square slab of slate, with a countersunk 
circular recess and a well in the centre to hold the ink ; the cover is a piece of 
heavy glass. 

A quantity of ink may be prepared at one time, but it must be kept well 
covered to exclude dust and prevent evaporation. The pen should be filled by 




Fig. 155. 

a narrow strip of paper, dipped in the ink and inserted between the blades. 

India ink and ink of various colours can be purchased in bottles, and this 
answers very satisfactorily for most work. Waterproof ink, which admits of 
being washed over, can be bought in sticks or in bottles. 

It is of primary importance to keep the blades of the inking tools free from 
obstruction ; this may be readily accomplished without unscrewing the pen by 
passing a slip of paper between the blades, or by drawing the point firmly over 
a piece of paper or on the fleshy part of the hand. 

Exercises with the Drawing-Pen-. 

Before proceeding to the construction of finished drawings, skill should be 
acquired in the use of the drawing-pen, supplemented often by the writing-pen. 
Beginning with lines, outlines of figures, alphabets, and the like, the draughts- 
man should strive to acquire the habit of readily drawing clean, uniform lines, 
without abruptness or breaks where straight lines connect with curved ones. 
Draw straight lines of different grades : 

as, fine 

medium — 



coarse 



at first, lines of indefinite length, taking care that they are drawn perfectly 
straight and of uniform width or grade. Then' draw lines of definite length 
between assumed points, taking care to terminate the lines exactly at these 
points. Lines as above sa^Q full lines. The grades depend on the effect which 
the draughtsman wishes to give. 

Draw dotted lilies^ hrolcen lines, and hroken and dotted lines, of different 
grades : 



•58 



DRAWING INSTRUMENTS. 



Draw fine lines at uniform distances from each other : 






Fig. 156. 



To give uniform appearance, the lines must be of uniform grade and equally 
spaced. Practice in lines of this sort is important, as they are much used in 
drawing to represent sections, shades, and conditions, as soundings on charts, 
density or characteristics of population, areas of rain, temperature, and the like. 
Draw lines as in Fig. 156. These lines are diagonal with the border-lines, and 

are used to represent sections 

^^^^^^^^^^^^^^^p of materials. In the figure, 

lines differently inclined rep- 
resent different pieces of the 
same material. 

Instruments called section- 
liners are to be had for draw- 
ing these lines, but for the usual needs of a drawing office the triangle and 
straight-edge, with the drawing-pen, will be sufficient. 

Sections of different materials may be represented in different kinds of 
lines (see page 177). 

To represent cylindrical surfaces (Fig. 157). 

Draw a semi-circumference, and mark on it a 
number of points, at equal distances apart, and 
through these points draw lines perpendicular to 
the diameter across the surface to be represented. 
It is not absolutely necessary that the central space 
should be equal to the others; it will be more 
effective to leave out two of the lines, and make 
it to this extent wider. 

To construct a mass of equal squares (Fig. 
158). 

Lay off a right angle, and on its sides mark 

as many points at equal distances apart as may 

be necessary ; through these points draw lines 

parallel to the sides. 

mark on its sides as many points, at equal dis- 




FiG. 157. 



Or, 



construct a rectanarle 



tances apart, as may be necessary ; through these points draw the lines. 
To construct the squares diagonally to the lase (Fig. 159). 



DRAWING INSTRUMENTS. 



59 



Mark on the sides of the right angle as many points, at distances apart 
equal to the diagonal of the required squares, as may be necessary. Connect 
these points by lines as shown, and 



Fig. 158. 



The whole 



through the same points draw lines 
at right angles to the others. 

To cover a surface with equilat- 
eral triangles (Fig. 160). 

Construct an angle of 60°, and 
mark on its sides points at dis- 
tances apart equal to the side of 
the triangle. Connect these points 5 
and through these points draw lines 
parallel to the sides of the angle. 

Two such triangles joined at the 
base form a lozenge. Six triangles may be arranged as a hexagon, 
surface may be arranged in lozenges or hexagons. 

To cover a surface ivitli octagons and squares (Fig. 
161). 

Lay off the surface in squares having sides equal to the 
width of the octagons. Corner the outer squares to form 
octagons (Fig. 68). Extend the sides of these octagons 
across the other squares, and similar corners will be cut 
off, and the octagons and squares required will be com- 
plete. 

With the aid of paper thus 
covered with squares, triangles, 
or lozenges, various geometrical 
designs may be readily con- 
structed, pleasing in their effect, 
and affording good practice to 
young draughtsmen. 

Any design can be copied by 
covering it and the clean sheet 

with squares. Mark the positions of points in the design or the sides of cor- 

C 

F 




Fig. 159. 




Fig. 160, 



60 



DRAWING INSTRUMENTS. 



responding squares, and draw the connecting lines. To enlarge or reduce 
the design, make the squares or triangles proportionately larger or smaller. 



3 4 




Fig 162. 



Fig. 163. 




Fig. 164. 



In transferring designs and drawings from books or plates, on which squares 
can not be drawn, it is very convenient to have a square of glass, with squares 
upon it, which may be laid on the drawing, and thus serve the same purpose as 

if squares had been drawn. The 
glass may be readily prepared by 
painting one of its surfaces with a 
thin coat of gum, and drawing 
squares upon it with the drawing- 
pen ; if every fifth or tenth line be 
made fuller or in a different colour, 
it will be still more convenient for 
reference. 

Fig. 162 gives the front and side 
views of an acanthus leaf, the surface being covered with squares, and on a 
ground of like squares in Fig. 163 the side view is transferred, but in a re- 
versed position. This is done by making the position of the outline and then 
of the interior lines with reference to the squares, as designated by letters and 
numerals. Fig. 164 is a transfer of both figures on a reduced scale. 

Designs for w^oven goods, oil cloths, ceiling and wall ornamentation, and the 
like are usually based on geometrical figures, and in certain proportions sym- 
metry and subordination of one part to another fall within the term 
of artistic. 

The following are designs in which the ruling figure is a trefoil : 
" In the equilateral triangle (Fig. 165), each side is divided by 
a dot, and from the centre of the triangle lines are drawn to each 
angle, and from the dot in the middle of each side to the opposite sides of the 
figure. The geometrical plan of the design is thus laid out, and the figure is 
easily filled in by drawing simple curves from the centre of the form to the 




DRAWING INSTRUMENTS. 



61 



dot on each side of it, and, lastly, filling in the form of the trefoil a little below 
the point of each corner of the triangle. 

"The square (Fig. 166), which is the next form, is developed in much the 
same manner. The sides are bisected, and from a point in the centre lines are 






Fig. 165. 



Fig. 166. 



Fig. 167. 



carried to each angle, and to all the dots on the sides. As in the preceding 
figure, slight curves are made on either of the side-lines, and the trefoil is 
added to each angle, with the base of the middle leaf touching the transverse 
working-lines between the sides. 
It will be seen that the penta- 
gon (Fig. 167) and the hexagon 
(Fig. 168) also are formed in 
the same general manner, but 
the proportion of the top of 
the trefoil varies from its sides. 
" In drawing the circular 
rosette (Fig. 169), the circum- 
ference should be constructed 
on a vertical and a horizontal diameter, with two other diameters bisecting 
it at equal angles, which divide it into eight sections, the half diameters, upon 




Fig. 168. 



Fig. 169. 




Fig. 170. 

all of which curved lines and the top of the trefoil are made. A series of 
arcs may be added at the pleasure of the designer. In the two pieces of 
moulding (Figs. 170 and 171) the trefoil is inserted vertically to the sides in 
one and horizontally in the other. In the latter, a half of the trefoil is added 
upon the sides to enrich the elementary figure ; and the double line and the 
transverse lines which form the squares are repeated for the sake of symmetry, 
and as affording an impression of agreeable repose. 

" It is from such a basis as this that all these various patterns are derived, 
and they produce a result which an inexperienced eye, unaccustomed to analyze 
designs, could scarcely resolve into its elements." 



62 



DRAWING INSTRUMENTS. 



Figs. 172-175 are other illustrations of the same principle, of varieties of 
rosettes constructed on a similar plan. 




Fig. 171. 



All of these designs can be constructed mechanically, but more grace is 
given to the design by the filling in with free hand, and it is an excellent prac- 




FiG. 172. 



Fig. 173. 



Fig. 174. 



Fig. 175. 



tice in the execution of the more elaborate Saracenic and Moorish diaper. 
In all of these where there are repetitions of the same figures it is usual to 
draw but one, and then transfer this, with the finish in crayon or pencil. 

Lettekikg. 

In Fig. 176 are examples of block letters constructed on squares, a rudimen- 
tary form of mechanical letters, which can be made with the aid of cross-sec- 
tion paper. 

Although lettering admits of an endless variety of forms, the draughtsman 
should comprehend that there are rules on which letters should be constructed 
before he undertakes the free-hand method. 

Fig. 177 gives the designation of various parts of a letter to which reference 
is made in the description. In the Roman letters the square is taken as the 
scale of construction. Fig. 178 gives the scale of proportionate width. W 
takes the whole square, its height and width being equal ; I is one quarter as 
wide ; A, five sixths, etc. To obtain the width of any letter according to this 
scale, the height may be marked off on the vertical 12. Where the horizontal 
line from this point intersects the diagonals of the desired letter the width is 
measured. 

The thickness of the body stroke of the letters is about one fifth the height,* 
the thickness of the body curve is slightly in excess of this, and the excess is 
added outside the letter; otherwise in comparison with the straight body 
strokes the curved stroke would appear too thin. 

All letters are of the same height, except those curved or pointed at the top or 



DRAWING INSTRUMENTS. 



63 



bottom, such as C, G, J, 0, S, U, A, V, W. When the curved or pointed parts 
are at the top they must extend a little above the line and when at the bottom 



Klwffi 




1 1 
1 — 1 — 


ZLLI 

-A 


F 




1 1 1 

1 1 1 


m 


1=1 




t 


1 I 

_LlJ 




i±i 






HI 


til 


iBicSi 


Wr 





M^F 


m 1 ^\ \_^ 




i 


#== 


^\ 1 




_i 



LLLLI 
:iJ_Ll_[ 
I I I I I 

rrrn 

TMILL 



J I j^ri I 
ziEUI: 



:r.^^iirrrii|i 


1 

1 


'%^i i~^^T 


=b 



Bi 




Fig. 176. 



below the line, otherwise they will look smaller than those of square outline. 
The lower feet of letters and the feet of T extend about one third the height, 
but the upper feet are a trifle smaller. 

The intermediate horizontal hair stroke in B, E, F, H, and R is a little 



N 
ID _l > 

Z U- X 
^ LU > 






~^ 


1 










/ 


7 


/tf 


7 






1 








, 


/ . 
/ 


V 


t^ 






1 








/ 


// 


/ 


/a 






1 






/ 


/ / 


/ 


/ 


Q- 


— 










/ 


/ / 


/ 


/ 




6 

5s 










// 




/ 














A 


V 










T 


— 






/ 


VA 


■/ 










O 






//A 


y 












Q 






4 


'/ 














6 


— 








































f 



Fig. 177. 



Fig. 17 



above the centre, P slightly below the centre, and A about one third of the 
height above the lower line. 

The hair strokes and outlines are first put in ; the outline is then filled with 
a writing-pen, toothpick, or brush. 



64 



DRAWING INSTRUMENTS. 




However well proportioned the letters may be, an even effect is not produced 

unless a proper space is made between them. In letters of square form the 

spacing is equal, but where such combinations as LT, AT, A A, and numerous 

others occur the spacing must be less. No general rule 

can be given for this, and it must be left to the practised 

eye of the draughtsman. 

The only rule necessary for the construction of small 
Koman letters is that for ascertaining their height as 
compared with the capitals : Let a vertical line a h (Fig. 
179), equal to the height of the capital, be drawn, and 
a line at right angles at the top of this line, equal to one 
half its length ; connect d to a, and lay off the length 
of the line d e, equal ioh d; then a e, will be the height 
required. When the learner has acquired some dexterity 
in lettering, the upper and lower line alone will be nec- 
essary for his guidance ; he may then attempt the ex- 
ecution of the curves, without the compass, by free 
hand. 

In Italic letters the proper angle for their slant 
is 23° from the vertical ; the proportions are the same 
as in the Roman letters. 

In stump letters the capitals are the same as Italics. The small letters differ 
somewhat, and are made with one bold stroke of the pen, the hair line gliding 
imperceptibly into the body stroke. 

Block letters, of which an example has been given, constructed on squares, 
are one of the most valuable types, being very distinct and readily drawn by 
the drawing-pen. The letters are of the same proportional width as the Eoman, 
except that the M is a square. The height and width of the letters are varied 
to suit their application. There are lettering 
triangles (Fig. 180) made to give the angles 
with the verticals of inclined letters. 

Old English and German text and other let- 
ters of a similar character may be quickly and 
neatly written by the use of a wooden toothpick 
for the body strokes, the hair lines and termina- 
tions being afterward put in with a fine pen. 

An old style of writing that has lately gained 
considerable popularity in this country is round 
writing. This resembles ordinary writing in 
that one letter is joined to the next, and each 
word written as a whole. There are special pens 
made for this writing, which are very useful; 
but in place of these the ordinary stub pen can 
be used. This writing consists of a very few 
elements, merely shaded semicircles, straight 
shaded lines, and diagonal hair strokes ; the pen is held in such a manner that 
you are able to draw a fine hair line at an angle of 45° with both nibs of the 
pen, and the pen is held in this position for all letters. 




Fig. 180. 



DRAWING INSTRUMENTS. 65 

HOMAN 

ABCDEFGHIJK 
LMNOPQRSTUV 

abcdeWXYZ fghij 
kl m n p qr s t uvwxy z 

ITAUC 

ABCDEFGHIJK 
LMNOPQRSTUV 

ahcdeWXYZ fghiJ 
klm n op qrs t uvwxy z 

acefg h ik m.s v wxy z 

urmiyvMWATnixxLCDM 

0123456789 



6Q DRAWING INSTRUMENTS. 

ABCDEGHJKLMNOPRSTUWY 
ABODE GHJKLMNOPRSTUVWY 

ABCDEFGHJKLMNOPRSTUYWr 
ABCDEFGHIJKLMNOPQBSTUYWY 








A^. 1 ^3AS6Z890 



DRAWING INSTRUMEOTS. 67 

ENGLISH GOTHIC. 

ABC DE FGH IJ KLMN OP 

QRST UV WX U 

1234567890 



ITALIC. 



ABC DE FGH IJ KLMN OP QBST 

UV WX YZ 

a be de fgh ij Ulmn op qrst uv ivx yz 



TUSCAN. 

ABC DE FGH IJ KLMN OP QRST 

UV WX YZ 
1234567890 

ABC DE FGH IJ 
KLMNOPQEST 

U7WZ YZ 

ate de fgh ij klmn op 

qrst UV -WX ys 



68 DRAWING INSTRUMENTS, 



ENGLISH CHURCH TEXT. 



lie ic #'«! %% iirmi 

abr if fgli ij klmn Bp !\ni m m ijj 



MEDIvEVAL 



m(i m fan n %m» <^? <&»i8® 

aidr bp fgl^ ij hlinn Ojp ^rsl^ uti tof q^ 

alic d.e fg:h; ij klmn op qrat utr wx tjz 
COAST CHART No. 20 

NEW YORK BAY AKD HARB OR 

NEW YOKK 



DRAWING INSTRUMENTS. 



69 




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70 DRAWING INSTRUMENTS. 




PLAN FRONT ELEVATION 
REAR SIDE TRANSVERSE 
LONGITUDINAL SECTION 



The character and size of the letters should be in accordance with the draw- 
ing on which they are to appear. Thus in engineering or mechanical drawing 
nothing is so appropriate as the block and Eoman letter. 

In topographical or map drawing several styles of various sizes are used ; 
Eoman capitals of different sizes are used in designating States, countries, and 
cities, while State boundaries and towns, large, villages, summits, and boundaries 
of countries are written with an initial capital and small Roman letters. Large 
bodies of water are denoted in Italic capitals, smaller bodies, such as streams, 
creeks, small lakes, and ponds, with an initial Italic capital and stump letters, 
the general direction of the letters following the course of the stream. Capital 
block letters differing in size represent ranges of mountains, railroads, stations, 
streets, and prominent objects on a map. Oblique capital block letters repre- 
sent railroads and canals. 

Old English and Oerman text are the styles most employed for the en- 
grossing of certificates and similar uses. 

Letters on topographical drawings are written horizontally, so as to be read 
from the lower right-hand corner of the map, except such as follow the course 
of a stream or a railroad ; and these can usually be arranged to be read from 
the same direction. 

A number of specimen titles are given, illustrating the use of the different 
styles of letters, but it will be found that the plainer the letters the better the 
effect produced, and for this reason it is generally well to omit fancy letters. 
No better example of neat and dignified titles can be found than those on the 
maps issued by the United States Coast Survey, the chief beauty of which con- 
sists in the admirable adjustment of the sizes of letters, the few styles, and the 
almost perfect execution. 

The illustrations of letters and titles given are taken from those in general 
use, but the draughtsman should make a large collection of titles of maps and 
books, drawings of machinery, advertisements, and business cards, copying 
carefully such as may suit him, by which he will gain ease of manipulation 
and taste in selection, to give character and finish to his own drawings. 



DRAWING INSTRUMENTS. 



n 



Profile and Cross-section" Paper. 

Paper printed in squares is used by designers of figures for calicoes, silks, 
and woollens. For the engineer, there is a class of papers called profile and 
cross-section papers^ sold in sheets or rolls, and of various scales. In the first, 
which is almost entirely applicable to lines of surveys of railroads and high- 
ways, the vertical scale is to the horizontal as 20 to 1. This is the usual dis- 
tortion to make grades, with the cuts and fills apparent. The latter originally 




UNITED states UNITS. 
Fig. 181. 



intended, as the name implies, for cross-sections of railway or canal cuts, 
but now extensively employed by the architectural and mechanical designer 
for the rough sketches of works either executed or to be executed ; by the 



72 



DRAWING INSTRUMENTS. 



sanitarian, for the plotting of death-rates ; for thermometric and hygrometric 
readings ; by the broker and merchant, for the graphic representation of 
the prices of gold, stocks, or articles of merchandise, during a term of years; 
by the railway superintendent, for the movement of trains ; and f®r a multitude 
of other uses. Cross-section papers most generally applicable are in divisions 
of tenths ; but as mechanics are more conversant with the two-foot rule, of 
which the divisions are in eighths, paper with like divisions are more convenient, 
and designs on it more intelligible to them. 

Eig. 181 shows a graphical method of determining the equivalent values of 
the metric system of measurements in United States units, or vice versa. The 
vertical scale represents the metric units, and the horizontal the common or 
United States units. 

Example. — What is the equivalent value of seven kilometres in miles ? Read 
upward on the metric scale to 7, then read on that horizontal line to the point 
of intersection with the line designated " Miles and Kilometres," that is, at 
the point on the United States scale of units representing 4*35, and you find 
that seven kilometres are equal to 4*35 miles. 

What is the value of five pounds in kilogrammes ? The process is the same 
as the foregoing, except that, to change United States units into the metric 
units, you first read horizontally, then upward. In this case five pounds is 
found equal to 2-25 kilogrammes. The divisions may represent single units, 
ten units, one hundred units, etc. Of late it has been common here and in 
England, to write ft. lbs., instead of lbs. ft., but where Erench weight and 
measures obtain, the rule is to say kilogrammetres, that is the weight before 
the distance moved. 

Eig. 182 shows the method of finding the average of a number of observa- 
tions, to determine the velocity of a current of water. The figure represents 
the path of a float in a wooden flume or channel, of rectangular section, from 



3 




















WIDTH OF FLUME 






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Fig. 182. 



Erancis's " Lowell Hydraulic Experiments." The width of the cut represents 
the width of the flume, each abscissa being one foot ; the ordinates are the 
speeds of float in divisions of 0*1 foot per second ; the small circles represent 
the floats in their observed path and speed ; and the curved line shows the 
average velocity in the different threads of the stream, from which the lines 
of average velocities of the entire width of flume are deduced. 

The velocities were taken by tin tubes loaded so as to float within about an 
inch of the bottom of the flume, with the top plugged and projecting a few 
inches above the surface of the water. The results were checked bv flows. 



DRAWING INSTRUMENTS. 



Y3 



measured over a weir ; but for all practical purposes the velocities as taken by 
the floats may be considered averages on each thread of the stream. A full 
set of tubes were prepared adapted to the depths of the water, and taken to 
the flumes while experimenting. For general use a cylinder may be adapted 
as a float with an open pipe sliding down it adjustable to the depth. 

Fig. 183 is a diagram illustrating graphically the difference between the 
cliarge on a ton of merchandise per mile on the New York Central and Hud- 
son River Railroad and the Erie Canal for every year between 1857 and 1880. 
The higher values in every case represent the railroad rates and the lower the 
canal rates. The black band shows the difference between them. 



1880 
1879 
1878 
1877 
1876 
1875 
1874 
1873 
1872 
1871 
1870 



1867 
1866 
1865 
1864 
1863 
1862 
1861 
1860 
1859 
1858 
1857 



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Fig. 183. 



Fig. 184 is a graphic representation made up from the records of " The 
Engineering and Mining Journal," exhibiting the amount of pig iron made in 
the United States per year for thirty-one years. In constructing the diagram 



u 



DRAWING INSTRUMENTS. 



cross-section paper was used, but in tracing the vertical cross lines were 
omitted. 




Fig. 184. 

Fig. 185 is made up from the time-table of the New York, New Haven and 
Hartford Railroad, showing the movement of trains, two from New York and 
two from New London, the horizontal lines being cut off on a scale of miles for 
each station, and the vertical lines being a scale of hours. If the speed had 
been uniform, the line showing the movement of trains would have been 
straight, but the line represents the practical running time. 



DRAWING INSTRUMENTS. 



75 




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76 



DRAWING INSTRUMENTS. 



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Range of Temperature degrees 
A Percentage of Humidity daily 


daily 




55.2 


T. Total deaths from all cause 


5 


L. Deaths from Local Diseases 




1. Infant Mortality under 1 yea 


r of age 


Z. Mortality from all Zymotic 


Diseases 














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J_N 

1 JUNE 


JULY AUGUST SEPTEMBER 



1870 

Fig. 186. 



DRAWING INSTRUMENTS. 



YT 



Fig. 186 is a graphic representation of the mortality and general classes of 
diseases as registered by the New York City Board of Health for the months 
of June, July, August, and September, 1870 ; with the daily records of tem- 
perature and humidity ; to complete these diagrams there should be one of the 
daily rainfalls. For meteorological purposes it is usual to take at observatories 
the commencement, termination, and amount of rainfall. 



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Above is an ornamental design in straight lines on the bases of lines parallel 
to the sides of an equilateral triangle. 

In pages 78, 79 are given designs on the bases of lines ruled in rectangles 
and lozenges. The figure, page 80, illustrates how colors may be represented 
in a design. 

In pages 81, 82 are illustrations in single lines of the tracery of Gothic 
windows of which the lines of construction are left to assist the draftsman 
in completion of the design, which will afford excellent practice in the intricate 
work of making lines tangent to each other. 



78 



DRAWING INSTRUMENTS. 





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DRAWING INSTRUMENTS. 



79 



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80 



DRAWING INSTRUMENTS. 






f^ P^kI n;vh»| Rhk p^0^ 

4J ^s^fl '^^fl^B ■^'^ m2|irm 








DRAWING INSTRUMENTS. 



81 











82 



DRAWING INSTRUMENTS. 








PLOTTING. 

Plotting is the laying out on paper in plan, or horizontal projection, the 
boundaries of portions of the earth's surface of greater or less extent, from the 
notes of surveys or other records. When the extents are large, embracing de- 
grees of latitude and longitude, the plots are designated as maps ; but if of 
small extent, as lots, estates, and farms, they are usually designated as plans or 
plots. After completing the outlines, it is usual to fill up the plot with the charac- 
teristic features, geographical, geological, agricultural, industrial, and domestic, 
which are expressed conventionally, as will be shown under the head of " Topo- 
graphical Drawing." 

Scales. — The choice of the scale for the plot depends on the purpose for 
which the drawing is intended. It should be large enough to express all de- 
sirable details which it is intended to illustrate, and the place it is to oc- 
cupy. 

Plans of house-lots and small plots of farm surveys are usually so many 
feet to the inch ; maps of surveys of States, so many miles to the inch ; and 
maps of railway surveys, so many feet to the inch or so many inches to the 
mile. Formerly the lines of farms were measured by the four-rod chain. Two 
to three chains to the inch was then a very common scale. 

On the United States Coast Survey all the scales are expressed fractionally 
and decimally. The original surveys are generally on a scale of one to ten or 
twenty thousand, but in some the scale is larger or smaller. The public sur- 
veys embrace three general classes : 1. Small harbour charts. 2. Charts of 
bays, sounds, etc. 3. General coast charts. 

The scales of the first class vary from -^-qq to -g-o^ Q-g-, according to the nature 
of the harbour and the objects to be represented. 

The scale of the second class is usually fixed at -g-QWo- Preliminary charts, 
are, however, issued of various scales, from -5-5^0- to -g-o-oVoir- 

Of the third class the scale is fixed at iq^q^^q for the general chart of the 
coast from Gay Head to Cape Henlopen, although considerations of the prox- 
imity and importance of points on the coast may change the scales of charts of 
other portions of our extended coast. 

On all plots of large surveys, it is very desirable that the scales adopted 
should bear a definite numerical proportion to the linear measurement of the 
ground to be mapped, and that this proportion should be expressed fractionally 
on the plan, even if the scale be drawn or expressed some other way, as miles to 
the inch. The decimal system has the most to recommend it, and is generally 
adopted in government surveys. 

For railroad surveys, the New York general railroad law directs the scale of 



84 



PLOTTING. 



map which is to be filed in the State Engineer's office to be 500 feet to ^ foot, 



or 



5 0' 



For canal maps, a scale of two chains to the inch, y^^g^, is employed. In 
England plans and sections for projected lines of inland communication, or 
generally for public works requiring the sanction of the legislature, are re- 
quired by a standing order to be drawn to scales not less than four inches to 
the mile, 1 : 15,840, for the plan, and 100 feet to the inch, 1 : 1,200, for the 
profiles. 

In the United States engineer service the following scales are prescribed : 



General plans of buildings 

Maps of ground with horizontal curves 1 foot apart 
Topographical maps, 1^ mile square . 
Topographical maps, 3 miles square . 
Topographical maps, between 4 and 8 miles 
Topographical maps, 9 miles square . 
Maps not exceeding 24 miles square . 
Maps comprising 50 miles square 
Maps comprising 100 miles square 
Surveys of roads and canals . 



10 feet to the inch, 1 : 120 



50 



mile to 



50 feet to 



a 


1:600 


2 feet, 


1 : 2,640 


1 foot. 


1 : 5,280 


6 in.. 


1 : 10,560 


4 " 


1 : 15,840 


2 " 


1 : 31.680 


1 inch 


1 : 63,360 


i " 


1 : 126,720 


1 ^' 


1:600 



TOOOO- 



Many government maps are made on a scale of -^o" ^^ 

It is always desirable that the scale should be drawn on maps and plans, as 
they are often reduced by photography. 

In cities and towns, plots of lots and squares are generally rectangular, and 
they can be readily plotted on any convenient scale. 

Fig. 187 is a plan of the usual New York city lot, 25X100, on a scale of 20 
feet to the inch, or ^ro' 

Fig. 188 is a city square containing thirty-two of these lots, on a scale of 
100 feet to the inch, or -j^g-o- The most accurate way is to plot the large rec- 
tangle 400 X 200 feet, and then subdivide it. 

Fig. 189 is a plan of the city squares, with the inclosing streets, on a scale 
200 feet to the inch, or -u4Vo- 

But many lots and most estates are not rectangular, and these, the angles 
being recorded, must be plotted by the aid of a protractor. 

If the survey has been made by triangles, the principal triangles are first 
laid down in pencil by the intersection of their sides, the length being taken 
from the scale and described with compasses. In general, when the surveys 
have been conducted without instruments, the positions of the points on paper 
are determined by the intersection and construction of the same lines as has 
been done in the field. 

Surveys are mostly conducted by measuring the inclination of lines to a 
meridian or to each other by the compass or by the transit. In the survey of 
farms, where great accuracy is not required, the compass is mostly used. 
The compass gives the direction of a line with reference to the magnetic 
meridian. The true meridian can be obtained from the observations of the 
polar star or from the magnetic meridian corrected from the records of the 
variations by the geodetic surveys of the United States at the place and 
time. 

The plane table is very convenient for filling in the details of a survey when 



PLOTTING. 



85 



the principal points have been determined by triangulation, and its records are 
readily transferred to the drawing. 

At the left of Fig. 190 are the notes of a compass survey, from which the 
figure is plotted by drawing a meridian through each station and laying off the 



Fig. 187. 



Fig. 188. 



angle of deflection. In small drawings it is more convenient, as shown in Fig. 
191, to plot all the bearings on a single meridian and then transfer them to the 
places where they are wanted by any instrument for drawing parallel lines, or 
to lay off on a single meridian as many bearings as. convenient and then trans- 
fer the meridian for another plot. 

If, as in Fig. 192, the plot fails to close — that is, if the termination a of the 
last line does not join the commencement of the first line at 1, either the sur- 
vey or the plotting is incorrect. If the latter be correct, the error of the sur- 
vey must be balanced, or distributed through the lines and angles of the plot 
(Fig. 192). Connect 1 with a, and draw lines parallel to 1 a through 2, 3, 4, 



86 



PLOTTING. 



5, of the plot. Draw an indefinite line, 1 a (Fig. 193), and on this, with any 
convenient scale, lay off consecutively the lines of the survey, 1-2, 2-3, 3-4, 



J 



n 




r 



Fig. 189. 



4-5, b-a. Erect perpendiculars at the extremities of the lines, 2, 3, 4, 5, and 
a. On the perpendicular a &, lay off 1 « from the plot and connect h 1. The 

3.23 



-(5)- 
3.55 



-(3)- 
1.29 



-(2)- 
2.70 



H 




Fig. 190. 



intersections of the perpendiculars by this line will determine how much each 
of the points of the plot is to be moved on the parallels to 1 « to distribute 
the error. The dotted lines on the figure show the corrected outline. If the 
amount by which the plot fails to close is large, the plot should be resurveyed. 



PLOTTING. 



87 



By the aid of the Traverse Table a plot of a survey may be balanced. 
The Traverse Table (see appendix) is a table of differences of latitudes and 




Fig. 192. 



departures, the difference of latitude between two stations being the difference 
north and south between them ; the difference of departure, the difference east 
and west. 

Thus, N S (Fig. 194) being the meridian, 
and A B the course, A C is the difference of 
latitude, and A D the departure. 

The differences vary according to the length 
of A B, and the angle it makes with the merid- 
ian. 

Taking the field notes of the following sur- 




\V^ 




— E 



vey, we make a table as follows of the stations, bearings, and distances, leaving 
columns for latitudes and departures : 





Bearing. 


Distance. 


LATITUDES. 


DEPARTURES. 




N. 


s. 


E. 


w. 


1 


N. 52° E. 

S. 29f ° E. 
S. 31|° W. 
N. 61° W. 


1,063 
410 
769 
713 


655 

... 

346 


356 
. 654 

... 


838 
203 




2. .... 




3 


405 


4 


624 







Find by the Traverse Table the number of degrees of the angle or bearing 
on the left-hand side of the page if less than 45°, and on the right-hand side if 
more. The numbers on the same line running across the page are the latitudes 
and departures for that angle and for the distances which may represent any 



88 



PLOTTING. 



unit, as feet, chains, links, metres, etc. The traverse table gives the latitudes 
or departures for a single unit ; 10, 100, 1,000, or any other decimal quantity 
may be obtained by moving the decimal point one, two, three, or more places 
to the right. 

Thus let us take station 1 in previous survey, in which the latitude and de- 
partures of a course having a distance of 1,063 feet and a bearing of 52°, and 
then take out the latitude and departure for 1, 6, 3, and place them as below : 



Distance. 
1,000 
60 
3 

1,063 



Latitudes. 

616-0° 

36-94 

1-847 

654-787 



Departures. 

788-0 
47-28 
2-364 

837-644 



If the survey has been accurately performed, the northings and southings 
of the latitude and the eastings and westings of the departures will balance and 
the survey will close. In the preceding survey they do not balance ; it there- 
fore becomes necessary to balance it. This operation consists in correcting the 
latitudes and departures of the courses so that the sums of the northings and 
southings of the latitudes and the eastings and westings of the departures shall 
be equal. This is done by distributing the difference of their sums among the 
courses in proportion to their length. 

The difference between the northings and southings of latitude, which is 9, 
is divided by the total length, 2,955, which gives the amount per foot to be 
added to the lesser column and subtracted from the greater column in propor- 
tion to the length of the courses to cause the northings and southings to 
balance. The departures are balanced in a similar manner. 

The following table gives the original latitudes and departures and the cor- 
rected ones : 





Bearings. 


Dis- 
tances. 


LATITUDES. 


DEPARTURES. 


CORRECTED 
LATITUDES. 


CORRECTED 
DEPARTURES. 


S 

CO 


N. 


S. 


E. 


w. 


N. 


s. 


E. 


w. 


1 

2 
3 

4 


N. 52° B. 
S. 29|° E. 
S. 31f ° W. 
N. 61° W. 


1,063 
410 
769 
713 


655 
**346 


"356 
654 


838 
203 


"'405 
624 


658 
"348 


'■355 

651 


834 

201 


408 
. 627 




2,955 


1,001 


1,010 


1,041 


1,029 


1,006 


1,006 


1,035 


1,035 



After the latitudes and departures have been corrected, it is necessary to 
make a drawing of the plot. How this is done will be readily seen by the accom- 
panying illustration of this survey (Fig. 195). This figure also illustrates a 
very convenient and accurate method of determining the area of the survey 
mathematically. By means of the latitudes and departures the area of the 
full parallelogram is taken, and the triangles on the four sides of the plot are 
deducted from it, leaving 489,245 square feet as the area of the figure. 

The use of the compass is now confined to the surveying of land areas of 
large extent and little value, or as a means of checking the bearings as taken by 
the theodolite or transit. Forcing should not be attempted with the latter in- 
struments. If the survey does not balance almost exactly, it should be resur- 



PLOTTING. 



89 



veyed; otherwise it could not be used in a court of lav/ except as approximately 
correct. The steel tape divided decimally is almost exclusively used in accu- 
rate work. 

The system of plotting by traverse is the same for the survey by transit as 



DejD. S34 



Pep. 201 




Dep. 627' 



Dep. 408 



Fig. 195. 



by compass, except as the angles are taken to minutes and seconds. The latitudes 
and departures are to be taken by logarithmic sines and cosines ; if these are 
not obtainable, the table for natural sines and cosines in the appendix will give 
minutes, and seconds can be obtained by interpolation of differences. 

Fig. 196 is the plot of a survey by transit. Any side of the plot may be 
assumed as a meridian. The bearings are always taken to the right of it. 
After it has been plotted it can be checked by the traverse. Meridians de- 
scribed through each of the angles will show the meridional angle. The lati- 
tudes and departures may be obtained as follows : 



Angle. 
41° 40' 

Angle. 
41° 40' 



Nat. sine. 

0-66480 

Nat. cosine. 

0-74703 



Distance. 

350 
Distance. 

350 ' 



Departure. 

233 

Latitude. 

261 



In the third line of the third column the angle, instead of 120°, is set 
down at 30°, because, when an angle is in excess of 90°, 180°, or 270°, the ex- 
cess is the angle of which sine and cosine are to be found. 

There can be no division of distance into latitude and departure when the 
course is either at right angles to or parallel with the meridian. It is then 



90 



PLOTTING. 




either all departure or all latitude. In the tables the latitudes are identical for 
angles and for their supplements, and so are the departures. Eeference to Fig. 
75 will illustrate this, calling the sine latitude and the cosine departure. 



Course, 



0-1 
1-2 
2-3 
3-4 
4-5 
5-6 
6-0 



Azimuth. 



41° 40' 

85 30 

120 00 

154 29 

228 00 

288 30 

360 00 



Angle. 



41° 40' 

85 30 

30 00 

64 29 

48 00 

18 30 

00 00 



Dis- 
tance. 



350 
280 
320 
300 
700 
420 
484 



Latitudes. 



261 
22 
-160 
-271 
-469 
133 
484 



Depar- 
tures. 



233 
279 
277 
129 
-520 
-398 
000 



Triangles deducted. 



261 X 233 

2 
22 X 279 

2 
277 X 160 



= 30,406 



= 3,069 



Rectangles deducted. 



233 X 22 



5,126 



= 22,160 ! 
^ ! 129 X 160 = 20,640 



129x271 




321,521 



25,766 



Circumscribed rectangle, 918 x 900 = 826,200 
Deduct 221,521 + 25,766 = 247,287 



578,913 square feet. 



PLOTTING. 



91 



When it is difficult to measure along the boundaries of an estate, the sur- 
veys should be made along more convenient and accessible lines, which may be 
by a closed plot, as in Fig. 196, or by base lines from which the intersections of 
boundaries are established by offsets carefully determined by measures and 
angles from points of the survey. 




Fia. 197. 



The first work of the draughtsman is to complete the plot along the lines 
of the survey ; work up the estimate of contents by traverse, and check by 
measures on the plot. 

Fig. 197 is an illustration. 

Find the cosine 49° 10' distance 215 = llO'l sine 163-1 
" " 55° 25' " 152= 86-3 " 125-1 



226-4 



38 



Line 525—226-4 = 298-6 

301-0 the line of plot. 

= -12706 = sine of 7° 18' 



V(298-62 + 382) 
38 



298-6 

90°-7° 18' = 82° 42' 90° - 49° 40' = 40° 20'. 

By similar construction 34° 30' and 78° 30' are calculated. 

360°--(82° 42' + 40° 20' + 34° 30' + 78° 30') = 123° 58'. 

The line of the plot, 301, and the adjacent angle, 123° 58', are thus ob- 
tained, and all lines and angles of the plot are established in the same way. 
The plot is then transferred to a clean sheet, with lines and angles as calcu- 
lated, but without any lines of survey. 

When the lines of a plot are irregular, as in Fig. 198, divide the plot into 
equal spaces, and draw parallel lines across the figure through the points of 
division, add together the two extreme lines, divide the sum by two, and to 
this dividend add the lengths of the other lines and multiply their sum by the 



92 



PLOTTING. 



equal vertical distance between the parallel 
lines, which will give very closely the entire 



area. 



Fig. 198. 



Having completed the plot, that is, the 
main lines of the survey, the filling of other 
points may in general be done on paper in 
the same way as they have been established in the field. Intersections of the 
main lines by roads, streams, fences, and the like are measured off ; other points 



^^a 




Fig. 199. 



not intersecting, are usually fixed by triangles or by offsets^ or lines run on 

purpose by angles from the main lines. 

In case of unimportant lines, as the crooked 
brook, for instance (Fig. 199), offsets are taken to 
the most prominent angles, as a a a, and the inter- 
mediate bends are sketched by eye into the field- 
book, and similarly on the plan. 

The most rapid way of plotting the offsets is by 
the use of a plotting and offset scale (Fig. 200), the 
one being fixed parallel to the line A B from which 
the offsets are to be laid off, at such a distance from 
it, that the zero-line on the movable or offset scale 
coincides with it, while the zero of its own scale is 
on a line perpendicular to the position of the station 
A from which the distances were measured. In the 
field-book all the offsets are referred to the point of 
beginning on any one straight line. Move the offset 
scale to the first distance by the scale at which an 
offset has been taken, and mark off the length of the 
offset on its corresponding side of the line ; establish 
thus repeated points, and join the points by lines as 
they are on the ground. It may not always be pos- 
sible to obtain the same scales as those of the plan ; 
but they ' may be made of thick drawing-paper or 
pasteboard. For extensive plotting, as in govern- 
ment surveys, the offset scale may be made to slide 
in a groove upon the plotting scale. 

In protracting the triangles of an extended trigo- 
nometrical survey in which the sides have been cal- 
culated or measured, it is better to lay down the 
triangles from the length of their sides ; for ordina- 
ry surveys, the triangulation is most expeditiously 
plotted by the means of a protractor. 




Fig. 200. 



PLOTTING. 



93 



The outlines of the survey having been balanced and plotted in, with the 
subsidiary points, as established by offsets and by triangles, the filling in of the 
interior detail, with the natural features of the ground, from, the skeleton or 
suggestions in the field-book or other records, is done according to conventional 
signs, to be shown under " Topographical 'Drawing." 

The public lands of the United States are surveyed, mapped, and divided 
into nearly square tracts, according to the following system : 

Ranges. — Standard lines must first be determined from which to measure. 
Accordingly, in each land-district some meridian line is run due north and 
south ; this is called the principal meridian. From some point of the principal 
meridian is also run a line due east and west, called the base line. 

Other lines are then run in the same direction as the principal meridian, at 
distances of six miles, measured on the base line, on each side of it. The strip 
between the principal meridian and the first line, thus run east of it, is known 
as Eange 1 East, the second strip as Range 2 East, etc. And so on the west. 
This division is shown in Fig. 201. 







• 


V 










Tp.2 














North 






§> 


& 


^ 


^ 


















s 


jj 


s 


•g 










^ 


'^ 


^ 


^ 




Tp.l 






t^ 


k* 


Ki 


?^ 




North 




W— 














» 7? 


fV ^" 




Base 


Line 








^jji 




f 


1 


1 


1 




Tp.l 

South 












3 

z! 






Tp.2 








5 








South 




- 



Fig. 201. 



Fig. 202. 



Toiunships. — In like manner, lines are run north and south of the base 
line at intervals of six miles. These lines cut at right angles those which 
separate the ranges, and with them form squares six miles on each side, called 
townships. Each township contains thirty-six square miles. 

The township nearest the base line on the north is known as Toiunship 1 
Worthy of the particular range it is in ; the next .farther north is Toivnship 2 
North., of that range, and so on. In like manner, going south from the base 
line, we have in succession Toivnship 1 South., Toivnship 2 South, etc. 
(Fig. 202). 

Sections. — Each township is divided into thirty-six squares, called sections, 
each one mile long and one mile wide, and therefore having an area of one 
square mile. The sections of a township are numbered 1, 2, 3, etc., up to 36, 



94 



PLOTTING. 



beginning at the northeast, and running alternately from right to left and from 
left to right, as shown in Fig. 203. 

A section may be subdivided into half-sections, quarter-sections, eighths, and 
sixteenths, designated as in the example that follows : 

Let F G (Fig. 204) be Section 3 of Township 2 North, in Eange 1 West ; 
then — 



6 


5 


4 


3 


2 


1 


7 


8 


9 


10 


11 


12 


18 


17 


16 


15 


14 


13 


19 


20 


21 


22 


23 


24 


30 


29 


28 


27 


26 


25 


31 


32 


33 


34 


35 


36 



1 mile. 



F 



1 

A 


B 


C 


D 


U 



Fig. 203. 



Fig. 204. 



A is N. (north) -|- of Section 3, Township 2 North, Eange 1 West. 

B is S. W. (southwest) \ of Section 3, Township 2 North, Range 1 West. 

C is W. (west) |- of S. E. (southeast) J of Section 3, Township 2 North, 
Range 1 West. 

D is N. E. i of S. E. i of Section 3, Township 2 North, Range 1 West. 

E is S. E. i of S. E. i of Section 3, Township 2 North, Range 1 West. 

Correction Lines. — If the meridian lines were parallel to each other, the 
townships and sections would be exact squares. But as these lines gradually 
converge toward the north, meeting at the pole, the townships deviate some- 
what from squares, being narrower on the north than on the south ; and the 
northern sections of a township are a little smaller than the southern ones. In 
order that the townships of a range may not thus keep getting smaller and 
smaller as we go toward the north, a new base line, called a correction line^ is 
taken at intervals, differing in length in different land-districts, and new north- 
and-south lines are run at distances of six miles measured on the correction 
lines. 

The system of survey described above is not used in Texas, the public lands 
there being State property. 



TOPOGRAPHICAL DRAWING. 

Topographical Drawing is the delineation of the surface of a locality, 
with the natural and artificial objects, as houses, roads, rivers, hills, etc., upon 
it in their relative dimensions and positions, giving, as it were, a miniature 
copy of the farm, field, district, etc., as it would be seen by the eye moving 
over it. Many of the objects thus to be represented can be defined by regular 
and mathematical lines, but many other objects, from their irregularity of out- 
line, it would be very difficult thus to distinguish ; nor are the particular 
irregularities necessary for the expression. Certain conventional signs have 
therefore been adopted in general use among draughtsmen, some of which 
resemble, in some degree, the objects for which they stand, while others are 
purely conventional. These signs may be expressed by lines, by tints, or by 
both. 

Figs. 205 and 206 represent meadow or grass land, the short lines being 



m n. IV il> 111 
» M u u a a 
M m 1> »' Hi 



• t. n «• III m 01 II. 

Fig. 205. 



Fig. 206. 




% %, -(^y. 

Fig. 208. 



-a 



supposed to represent tufts of grass ; the bases of the tufts should always be 
parallel to the base of the drawing, whatever may be the shape of the in- 
closure. 

Figs. 207, 208, 209, and 210 give various methods of representing trees. 
Figs. 207 and 208 represent in plan a forest and an orchard respectively. The 



t § ^ 

^ # $ ># 

ii ^ ^ 

t §- # € 
i 1. ^ 

Fig 209. 




i|(M 



Fig. 210. 



Fig. 211. 



method of Figs. 209 and 210, showing the same in elevation, while it is not 
consonant with the projection of the plan, to many is more expressive and in- 
telligible. 



95 



96 



TOPOGRAPHICAL DRAWING. 



Fig. 211 represents cultivated land. The lines are supposed to represent 
plough-farrows, and adjacent fields should be distinguished from each other 
by different inclinations of lines. 

Figs. 212 and 213 represent marsh or bog land. Fig. 212 is the more ordi- 
nary mode of representing fresh-water bog ; Fig. 213, salt marsh. 




Fig. 212. 



:MUD-^^^=^= 



^toa?^"' 







^^^' 



p^ 



Fig. 213. 



Fig. 214. 



Fig. 214 represents a river, with mud and sand banks. Sand is designated 
by fine dots, made with the point of the pen ; mud by a series of short parallel 
lines. Gravel is represented by coarser dots, and stones by irregular angular 
forms. 

Water is almost invariably represented, except in connection with bogs, by 
drawing a line parallel to the shore, following its windings and indentations 
closely, then another parallel a little lighter and a little more distant, a third 
still more so, and so on. Brooks, and even rivers when the scale is small, are 
represented by one or two lines. Fig. 215 gives a plan and sectional view of 
water, in which the white curves represent the character and direction of the 




Fig. 215. 




Fig. 216. 



flow of streams, retarded at bottom and sides, and more rapid near the surface 
and at centre. The direction of the current may also be shown by arrows. 
Fig. 216 represents a bold shore bounded by cliffs. 



TOPOGRAPHICAL DRAWING. 



97 



Fig. 217 represents a turnpike. If the toll-bar and marks for a gate be 
omitted, it is a common highway. Fig. 218 represents a road as sunk or cut 
through a hill ; Fig. 219, one raised upon an embankment. Fig. 220 is a rail- 



Sa Bar 



Fig. 217. 



Fig. 218. 



Fig. 219. 



Fig. 220. 



road, often represented without the cross-ties by two heavy parallel lines, some- 
times by but one. 

Fig. 221 represents a bridge with a single pier; Fig. 222, a swing or draw 
bridge ; Fig. 223, a suspension bridge ; and Fig. 224, a ford. Fig. 225 is a lock 



IXI ,^11 



nr^ --irr ~inr 



Fig. 221. 



Fig. 222. 



Fig. 223. 



Fig. 224. 



of a canal. Canals may be represented like roads, except that in the latter the 
side from the light is the shaded line ; in the former, the side to the light. Or 

by H ^ II ■ M^ I 

Conventional signs for the more important ob- 
jects that are likely to need representation on a 
map are ; 



Fig. 225. 



Signal of Survey, A 

Telegraph, ^^ 

Court-house, ffi 

Post-office, ^J 

Tavern, ^^ 

Blacksmith^ s shop, ^L 

Guide-hoard, \ 

Quarry, j5? 

Grist-mill, © 



Saw-mill, 

Wind-mill, 

Steam-mill, 

Furnace, 

Woolen-factory 

Cotton-factory, 

Dwellings, 

Churches, 

Grave-yards 



* 




OIBECTVON OF THE CURRENT 



Anchorage for ships, f 

Anchorage for coasters, J^ 

Rocks always covered, T 
8 



Buoys, t ] 
Wrecks, -^ 
Harbors, ^5^ 



Light-house, ^ 

Signal-house, ^ 

Channel-marks, <bkO 



98 



TOPOGRAPHICAL DRAWING. 



The localities of mines may be represented by the signs of the planets, which 
were anciently associated with the various metals, and a black circle is used 
for coal, thus, ^ Mercury, ? Copper, "^ Lead, D Silver, Gold, ^ Iron, 71 
Tin, • Coal. 

The Representation of Hills. — The two methods in general use for rep- 
resenting with pen or pencil the slopes of ground are known as the vertical 
and the horizontal. In the former (Fig. 226), the strokes of the pen follow the 
course that water would take in running down these slopes. In the second 
(Fig. 227), they represent horizontal lines traced round them, such as would be 
shown on the ground by water rising progressively by stages, 1, 2, 3, 4, 5, 6, up 
the hill. The last is the more correct representation of the general character 
and features of the ground, and, when vertical levels or contours have been 
traced by level at equal vertical distances over the surface of the ground, they 
should be so represented ; or when, by any lines of levels, these contours can 
be traced on the plans with accuracy, the horizontal system should be adopted : 
but where, as in most plans, the hills are but sketched in by the eye, the verti- 
cal system should be adopted ; it affords but proximate data to judge of the 
slope, whereas, by the contour system, the slope may be measured exactly. It 
is a good maxim in topographical drawing not to represent as accurate any- 
thing which has not been rigorously establisljed by surveys. On this account, 
for general plans, when the surface of the ground has not been levelled, nor is 
required to be determined with mathematical precision, use the vertical system 
of representing slopes. 

On drawing hills on the vertical system, it is very common to draw contour- 
lines in pencil as guides for the vertical strokes. If the horizontal lines be 
traced at fixed vertical intervals, and vertical strokes be drawn between them 
in the line of quickest descent, they supply a sufficiently accurate representa- 
tion of the face of the country for ordinary purposes. It is usual to make the 
vertical strokes heavier the steeper the inclination, and systems have been pro- 
posed and used by which the inclination is defined by the comparative thick- 
ness of the line and of the intervening spaces. 




Fig. 226. 




TOPOGRAPHICAL DRAWING. 



99 



In describing ground with the pen, the light is generally supposed to 
descend in vertical rays, and the illumination received by each slope is di- 
minished in proportion to its divergence from the plane of the horizon. Thus, 
in Fig. 228, it will be seen that a horizontal surface receives an equal portion 
of light with the inclined surface 
resting upon it, and, as the- inclined 
surface is of greater extent, it will be 
darker than the horizontal in propor- 
tion to the inclination and conse- 
quent increase of the surface, and on 
this principle varied forms of ground 
are represented by proportioning the 
thickness of stroke to the steepness of the slope. 

In the German system proposed by Major Lehmann for representing 




the 



slopes of ground by a scale of shade, the slope, at an angle of 45°, is indicated 
by black, the horizontal plane by white. 

A modification of Lehmann's method, proposed by the United States Coast 









Fig. 229. 

Survey, has the advantage of discriminating between slopes of greater inclina- 
tion than 45°. The table gives the proportions of black and white for different 
inclinations, and the construction may easily be un- 
derstood from Fig. 229. 

Contour - Lines. — Conceive a hill to be com- 
pletely covered with water. Then suppose the water 
to be drawn down, say five feet at a time. Each 
line of contact of the hill and the water will be a 
contour-line., or a line every point of which is at the 
same height or level above a fixed horizontal plane, 
called the datum-plane. For a small hill, stake out 
the ground in squares of say fifty feet to the side, 
and take levels at each point of these squares, and as 

many intermediates as the change of slope makes necessary. To draw the map, 
lay off these squares to a scale, and mark the elevation of each point and the 
intermediates in pencil. Then by the eye draw in th-e contours at such vertical 
distances apart as the requirements of the map call for. For a large survey, 
say of a mountain, such a method is impracticable. In this case, the surveyor 
fixes a number of points at the same level, the points being absolutely estab- 
lished by the transit or compass, so that they can be plotted accurately. Con- 
nect all points on each level, and fill in the distances between by the eye, on the 
supposition that the slope is uniform between these lines. The lines absolutely 



Slope. 


Proportion of 


Black. 


White. 


2i° or 2f ° 


1 


10 


5 or 6 


2 


9 


10 or 11 


3 


8 


15 or 18 


4 


7 


25 or 26 


5 


6 


35 


6 


5 


45 


7 


4 


60 


8 


3 


75 


9 


2 



100 



TOPOGRAPHICAL DRAWING. 



established and those merely sketched in must not be confounded, and should 
be distinguished apart either by colour, by size of lines, or by dotting. The 
contour-lines denoting every five, ten, etc., feet above the datum or plane of 
reference may be numbered with such height. This is an effective way of rep- 




resenting hills, but is only to be recommended when lines have been traced 
and it becomes a record of facts. Fig. 230 represents, on double the scale, the 




Fig. 230. 



half of the hill (Fig. 227), with one half completed by drawing the interme- 
diate contour-lines. 

The objection to the drawing of hills by any system is that the depths of 
shade representing different slopes conflict with the lights and shades of the 



TOPOGRAPHICAL DRAWING. 



101 



drawing, and are therefore confusing. The plan adopted by Von Eggloffstein 
in his maps was to form a model by cutting out of sheet-wax under the needle 
of a sewing machine, on the lines of contours, and then properly superimposing 
them on one another. A mould was then taken from them in plaster. A 




Fig. 231. 



model from the mould, also in plaster, was then taken. This was watered while 
fresh by a vertical rain from a water-pot, which broke down the vertical edge 
of the contours, and gave natural lines of watershed. This model was then 
photographed under an inclined light, and gave an admirable projection. 

Fig. 231 is a contoured map of Greenwood Cemetery and vicinity. Brook- 
lyn, N. Y. 

Fig. 232 is a map of the harbour and city of New Haven, reduced from the 
charts of the United States Coast Survey. 

Plate VI is a map of a farming country. These two maps illustrate the 
practical applications of topographical conventionalities. 



102 



TOPOGRAPHICAL DRAWING. 




Fig. 232. 



TOPOGRAPHICAL DRAWING. 



103 



Railway Surveys are usually plotted by tangents. The curves are then put 
in, and the topographical features for the width necessary. The curves are 
designated by degrees, as a curve of 1°, 2°, 3°, etc., 
according as the angle subtended at the centre by a 
100-feet chord is 1°, 2°, 3°, etc. 

Knowing the tangent points, it is easy to plot in 
the curve, as the centre of the curve must be the 
intersection of the perpendiculars to the tangents 
at these points; or, with one point of tangency, 
erect a perpendicular at this point, and lay off the 
radius on it to get the centre of the curve. 

When the curves are larger than can be de- 
scribed by the dividers or beam compasses, they can 
be plotted as shown in geometrical problems, or 

points of a curve may be obtained by calculation of their ordinates, and the 
curves drawn from point to point by variable curves. Knowing the central 
ordinate of the curve between two points, the central ordinate of one half that 
curve will be approximately one quarter of the first ; but the greater the num- 
ber of degrees in the arc, the less near to the truth is the rule. 

31.r3FcdIal lT)cr M iXt ^^ Level 



Degree. 


Radii, ft. 


Central 
ordinate. 


r 


5729-65 


0-218 


2 


2864-93 


0-436 


3 


1910-08 


0-655 


4 


1432-69 


0-873 


5 


1146-28 


1-091 


6 


955-37 


1-309 


7 


819-02 


1-528 


8 


716-78 


1-746 


9 


637-27 


1-965 


10 


573-69 


2-183 




Fig. 234 represents a plot of a railway line ; in this plot the curve is repre- 
sented as a straight line, the radius of curvature being written in. This method 
is sometimes adopted when it is desirable to confine the plot within a limited 
space upon the sheet, and it is convenient plotted thus directly beneath the 
profile or longitudinal section (Fig. 233). 

In plotting the section, a horizontal or base line is drawn, on which are laid 
off the stations or distances at which levels have been taken ; at these points 
perpendiculars, or ordinates, are erected ; upon them are marked the heights of 
the ground above the base ; and the marks are joined by straight lines. 

Where borings or soundings have been made, and it is necessary to indicate 
the character and define the limit of the material, the rock may be shown by 
diagonal hatchuring, streams as in Figs. 222 and 223, and other substances by 
a combination of lines and dots, resembling as nearly as possible the material 



104 



TOPOGRAPHICAL DRAWING. 



which it is to represent, and the name inserted. If there is a bog or mud in 
which soundings have been made, the position and depth of soundings should 
be given ; but when work is to be done by contract, characteristics, unless well 
established, should not be definitely marked. 

Since it would be in general impossible to express the variations of the sur- 
face of the ground in the same scale as that adopted for the plan, it is cus- 
tomary to make the vertical scale larger than the horizontal, usually in the 
proportion of 10 or 20 to 1. Thus, if the horizontal scale of the plan be 400 




feet to the inch, the vertical scale would be 40 or 20 feet to the inch. For the 
purpose of facilitating the plotting of profiles, profile-paper can be obtained 
from stationers, on which are printed horizontal and vertical lines. 

In the plotting of sections across the line which are extended but little 
beyond the line of the cut or embankment, equal vertical and horizontal scales 
are adopted ; these plots are mostly to determine the position of the slope, or 
to assist in calculating the excavation. When cross sections are extended to 
show the grade of cross-road, or changes of level at considerable distance from 
the line of rail, the same scales, vertical and horizontal, are adopted as in the 
longitudinal section or profile. 

In Fig. 233 the upper or heavy line represents the line of the rail, the 
grades being written above ; this is the more usual way, but sometimes, as in 
Fig. 235, the profile and plan are combined ; that is, the heights and depths 
above and below the grade line of the road are transferred to the plan, and re- 




FlG. 235. 

ferred to the line in plan, which becomes thus a representation both in plan 
and elevation. 

Cross sections, for grades of cross-roads, etc., are usually plotted beneath or 
above the profile or across the line when plan and profile are combined. 

Besides the complete plans, as above, giving the details of the location, land 
plans are required, showing the position and direction of all lines of fences and 
boundaries of estates, with but very few of the topographical features. The 
centre line of the road is represented in bold line, and at each side, often in 
red, are represented the boundaries required for the purposes of way. In gen- 



TOPOGRAPHICAL DRAWING. 



105 



eral, a width of 100 feet is the aDiount of land set off, lines parallel to the cen- 
tral line being at a distance of 50 feet on each side ; but when, owing to the 
depth of the cut or embankment, the slopes run out beyond this limit, the ex- 
tent is determined by plotting a cross section and transferring the distances 
thus found to the plan, and inclosing all such points somewhat within the 
limits as set off for railway purposes. These plans are generally filed in the 
register's office for the county through which the line passes. 

Hydrometrical or Marine Surveys. — In plotting hydrometrical or marine 
surveys, the depths of soundings are seldom expressed by sections, but by 
figures written on the plan, expressing the sounding or depth below a datum 








„^o» i{- "V' '''"'' '/ 
r^ =M / .■■■••■■■< 

"« / . s. / ,■■■■■ -^ 

<3i 













Fig. 236. 



line, generally that of high water, the low-water line being usually represented 
by a single continued line. The soundings are expressed in fathoms or in feet. 
Fig. 236 is a map of Cape Cod Bay plotted by this method. The depths are 
expressed in feet, and the dotted lines are contour-lines or lines of equal depths. 



106 



TOPOGRAPHICAL DRAWING. 



An effective way of making a marine chart is to express the different depths 
by lines varying in direction, distance apart, width, etc. Fig. 237 is a chart of 
the Isle of Wight and the surrounding water, with the depths .expressed as 
shown at the bottom of the cut. Sections are often used for rivers, especially 
rivers like those of the West, that have a very changeable bottom. By plot- 
ting sections, taken at different times, over one another, distinguishing 




Depth under 5 Fathoms. 5 to 10 Fathoms. 



10 to 20 Fathoms. 



Over 20 Fathoms. 



5 Miles. 



Fig. 237. 



them apart by a difference in colour and variety of line, the changes that take 
place in the bottom of the river, and the erosion of the banks, are boldly shown. 

In a geological profile the different rocks or formations are sometimes dis- 
tinguished by colours, explained by marginal notes and squares, but more often 
by marks, dots, or cross-hatchings. 

The geological and statistical features of a country may be expressed simi- 
larly and graphically in lines, as in Fig. 238, a preliminary survey of Kentucky, 
illustrating the principal geological features; and in Fig. 239, in a broader 
form, giving a larger extent of country, including the portion of the United 
States east of the Eocky Mountains and the southeasterly portion of Canada. 

These maps give the larger geological divisions, and are suited for books, 
but are not as effective nor comprehensive of the smaller subdivisions, of which 
Plate X is an example of a portion of a map of the State of New Jersey. 



TOPOGRAPHICAL DRAWING. 



107 




108 



TOPOGRAPHICAL DRAWING. 




Fig. 239. 



STRATIFIED ROCKS 





Sections of horizontal and inclined strata. 
Fig. 240. 



TOPOGRAPHICAL DRAWING. 



109 




Tapir, Peccary, Bi'aon, Llama. 
Megatherium, Myludoiu 



Equu3. 

Equus Beds. 

f-A/itm.. Taj'irus, EUphaa. 

Pliohippus Beds. 

Pliohij'pus, Mailodon, Bos, etc. 

Miohippus Beds. 

Miohipj'un, Biccrat/ierium, Thinohyus. 

Oreodon Beds. 

Edentates, Jli/anodon, Ili/racodoiu 

Brontotheriiim Beds. " 

ilesuhipf'U.'i, Menodus, Ehitherium. 

Diplacodon Beds. 

kjiihi pfius, Amynodon, 

Dinoceras Beds. 

Tiiweeras, Uintatherium, Limnoh'jus, 
Oro/iippiis, Ilelahtes, Colonoceras. ^ 

Coryphodon Beds. 

EuhippHs, Monkeys, Carnivores, Ungulatea, TUlodonts, Rodents, 
Serpents. 



Lignite Series. 

Hijdrasaurus, Dryjitosaurus. 



Pteranodon Beds. 

IJirds with Teeth, Ilesperornis, Ichtkyornis, 
Pterodactyls, Plesiosaurs. 




Dakota Group. 



Atlantosaurus Beds. 

Dinosaurs, Ajjutoaaurus, Allosaurus, Nanosaurus. Turtles. Di- 
plosaurus. 



Connecticut Kiver Beds. 

First Mammals (Marsupials), (Dromatherium). 
Dinosaur Foot-prints, Amp/ti 
Crocodiles (Beludon). 



Permian. 



Coal-Measures. 

First Reptiles («). 



Sub-carboniferous. 

First known Amphibians (Labyrinthodonts). 



Corniferous. 



Schoharie Grit. 
First known Fishe 



Upper Silurian. 



Lower Silurian. 



Primordial. 



Huronian. 



Laurentian. 



No Vertebrates known. 



Section of the earth's crust to illustrate vertebrate life in America. 
Fig. 241. 



Fig. 241 is an ideal section from Le Conte, in which all the most important 
American strata occurring in different places are brought together and ar- 
ranged in the order of time. 

In the diagram the different rock-systems are placed one on top of the 
other, and the vertical black spaces represent by their breadth the relative 
dominance of different classes at different times. 

The subdivisions of these again into periods and epochs are founded on 
more local unconformities, and especially on less important changes in the 
species. 



110 TOPOGRAPHICAL DRAWING. 

Transferring. — It is usual, in plotting from a field-book, to make first a 
rough draft, and then a finished copy on another sheet. 

In the copy, only the established points and lines for the outlines are to be 
transferred. Many lines of construction, balances of surveys, and trial lines of 
the rough draft are to be omitted, and it is well to sketch in roughly the natural 
features on the rough draft for aid in the completion of the finished copy. 

The most common way of transferring, for a fair copy, is by superposition, 
of the plan above the sheet intended for the copy, and pricking through every 
intersection of lines on the plan and all points necessary to preserve. The 
clean paper should be laid and fastened smoothly on the drawing-board ; the 
rough draft should be laid on smoothly, and retained in its position by weights, 
glue, or tacks. The needle must be held perpendicular to the surface of the 
plan, and pressed through both sheets ; begin at one side and work with sys- 
tem, so as to prick through each point but once, nor omit any ; make the 
important points a trifle the larger. For the irregular curves, as of rivers, make 
frequent points, but very small ones. On removing the plan, select the impor- 
tant points, those defining leading lines ; draw in these, and the other points 
will be easily recognised from their relative position to these lines. When any 
point has not been pricked through, its place may be determined by taking any 
two established points adjacent to the one required, and with radii equal to 
their distance on the plan from the point required, describing arcs on the copy 
on the same side of both points ; the arcs will intersect at the point desired. 
In this way, as in a trigonometrical survey, having established the two extremes 
of a base, a whole plan may be copied. In extensive drawings it is very com- 
mon to prick off but a few of the salient points, and fill in by intersections, as 
above, or by copying detached portions on tracing-paper and transferring them 
to the copy ; the position of each sketch being determined by the points pricked 
off, the transfer is made by pricking through, as above, or by transfer-paper 
placed between the tracing and the copy. 

Plans may be copied, on a reduced or enlarged scale, by means of the pan- 
tagraph or by the method of squares. 

Map Projections. — For a farm or other small survey, the surface of the earth 
is conceived to be flat, and the map as a horizontal projection of the plane sur- 
face on a reduced scale. But for large maps, as of countries. States, rivers, or 
the like, where the meridians and parallels of latitude are represented, such a 
system would be erroneous. The surface of the earth being a sphere, it is in- 
capable of development on a plane, so that it becomes necessary to make the 
best approximation possible in form, relation, and proportional area of the por- 
tions to be represented on a map or chart. There are many different kinds of 
projection, all more or less imperfect. 

In general, map projections may be divided into two classes : perspective 
and developments. The most useful of the perspective projections are the 
orthographic^ the stereographic, and the globular or equidistant. 

Orthographic Projection (Figs. 242 and 243). — In this projection the eye is 
supposed to be at an infinite distance, and the plane of projection perpendicu- 
lar to the line of sight. Let the circle ALA' M (Fig. 242) represent a hemi- 
sphere ; draw the diameters A A' and L M at right angles ; divide the arc A L 
and A M into nine parts, making the parallels thus 10° apart ; and through 



TOPOGRAPHICAL DRAWING. 



Ill 



these divisions draw lines across the sphere parallel to A A' ; mark off consecu- 
tively on a strip of paper the points where the parallels intersect the central 
meridian L M, and apply and mark off these points along the equatorial diam- 
eter A A'. Draw meridians with centres on the extension of the line of the 
equator intersecting the points marked off on this line, and meeting at the poles. 
Stereograpliic Projection (Figs. 244 and 245). — As in the last example, draw 
a circle with a central and an equatorial diameter (Fig. 244) ; on the central 
meridian describe a circle E D F, with a diameter equal to the radius of the 





Fig. 242. 



Fio. 243. 



larger circle ; through the centre of this smaller circle draw a diameter E F, and 
divide the arcs E and F into nine equal parts ; and from the pole D, 
through each of these points, draw lines intersecting the equator. These lines 
divide the equator into eighteen parts, each containing 10° of longitude, and 
through these points and the poles meridians are described. Mark off the equa- 
torial divisions on a slip of paper and transfer them to the central meridian ; 





Fig. 244. 



Fig. 245. 



divide each quarter of the circumference of the sphere into nine equal parts, 
though these points and the divisions on the central meridian describe arcs. 
Glohidar or Equidistant Projection (Fig. 246). — A good practical projec- 



112 



TOPOGRAPHICAL DRAWING. 



tion can be made by drawing a circle with a diameter for the equator and 
another at right angles for the central meridian, dividing each quadrant and 
each radius into nine equal parts. Meridians, with centres on the line of the 
equatorial diameter, can now be drawn passing through the equatorial divisions, 
and the poles and parallels of latitude on the line of the central meridian 
through the divisions of this line and those of the quadrant. 

The foregoing perspective projections in their application to astronomy and 
geography are usually confined to the representation of the hemisphere, and 
but rarely to smaller surfaces ; they are therefore of but little practical use to 

the engineer or surveyor, and for land and 
sea charts on a large scale and of limited 
extent they are not well adapted. To ren- 
der developments possible a cylindric or 
conic surface is substituted in place of the 
ordinary plane of projection, which surface 
is afterward developed in a plane. The 
eye is supposed either at the centre of the 
sphere or else its position is arbitrary. This 
conception gives rise to two kinds of de- 
veloped projections, one kind employing 
a cylinder, tangent generally at the equa- 
tor, the other employing a cone, tangent 
generally at the middle parallel. 

The more useful of these projections 
are Mercator's, the conic. Bonne's, and the polyconic. 

Mercator^s Projection (Fig. 247). — This is especially valuable to the navi- 



- etV 



FiG. 246. 




/60 140 

Fig. 247. 



TOPOGRAPHICAL DRAWING. 



113 



gator, as by it he can lay off his course on a straight line. In this projection 
the surface of the sphere is developed on a tangent cylinder. Conceive the 
outlines of the continents to be drawn on this, and afterward the surface to be 
unrolled and laid flat ; the result is a chart on Mercator's projection. 

Let P Q P' R (Fig. 248) be the projection of a sphere, P P' and R Q its 
diameters, and U Y X Z a portion of the tangent cylinder in the axis of which 

X 
U 




60 120 

Fig. 248. 



m 



2i0 



300 



TO 



70 

360 



is contained the axis of the sphere. Divide the quadrant P Q into 10° parts, a 
line drawn from C through these points, intersecting the tangent X Z, will be 
the point for the parallel of that degree. Make the equator of the projection 
3'14 times the diameter of the cylinder, and divide it into twenty-four equal 
parts ; these points will be 15° apart, or hour distances. Verticals are drawn 
through these points, giving us parallels of latitude. 

Conic Projection. — Instead of on the surface of a 
sphere, the map is projected on the surface of a cone. 
The projection may be developed either on a tangent 
cone or an intersecting cone. The developed arc of the 
middle latitude is employed for the graduation of longi- 
tudes. Fig. 249 gives an illustration of the development 
on a tangent cone in which P B is the sphere and 
A M is the distance from the apex of the cone to the 
middle parallel and point of contact ; A M will be the 
radius for the central parallel and A the point from which all parallels are 
described. Fig. 250 shows the cone developed on a plane surface. The 
length of a degree on a meridian of the earth is 69-41 miles at the poles and 
68-70 at the equator. 

Bonnets Projection. — In this projection a central meridian and a central 
parallel are employed, the latter being the development of the circle of contact 
of the tangent cone. The other parallels are concentric arcs, as in the simple 
9 




Fig. 249. 



114 



TOPOGRAPHICAL DRAWING. 



conic projection drawn through the graduation of the central meridian. Each 
parallel, however, is divided in accordance with the varying lengths of a degree 
of longitude in the different latitudes (see table) and an arc passed through 




Fig. 250. 



these points. The map is slightly distorted at the corners on account of the 
parallels, as projected, being concentric arcs. The great advantage of Bonne's 
projection is that true proportions of areas are preserved. This method is al- 




most universally employed for the detailed topographical maps based on the 
trigonometrical surveys of the different countries of Europe. 



TOPOGRAPHICAL DRAWING. 



115 



Polyconic Projection. — This employs a tangent cone for every parallel. 
Each parallel of latitude therefore is independently developed. This has the 
effect of increasing the length of the degrees of latitude in proportion as we 
recede from the central meridian. To draw a map according to the tables, 
lay off (Fig. 251) on the straight line N S, representing the middle meridian, 
the lengths representing the 10° of latitude between 20°, 30°, 40°, etc. 
Through these points draw circular arcs with the radii designated by R in the 
table. On these arcs lay off the lengths of 10° of longitude for each corre- 
sponding 10° of latitude on each side of the central meridian. Through the 
points thus formed draw the meridians, which will be found slightly concave 
toward the middle one. If the scale is so large that it is impossible to draw 
the circular arcs with beam compasses, erect perpendiculars at the points 20°, 
30°, 40°, and 50°, and on them lay off the values D M from the tables. At 
each of the points so found erect perpendiculars, and set off on them the corre- 
sponding values of D P. Through the points thus found draw the parallels 
and meridians. By this projection there is little distortion at any portion of 
the map ; a scale of degrees and minutes of the parallels and meridians, by 
means of which positions, determined by their latitudes and longitudes, may 
be inserted in the maps ; the use of a linear scale in any portion or direction ; 
and the intersection of parallels and meridians at nearly right angles. 





Co-ordmates of Curvature 


in Miles 


for Maps of Large Extent. 






Latitude 20°. 


Latitude 34°. 


Latitude 28°. 


Latitude 32°. 
















TUDE. 




















D. M. 


D. P. 


D. M. 


D. p. 


D. M. 


D. P. 


D. M. 


D. P. 


2° 


130-0 


0-8 


126-4 


0-9 


122-2 


1-0 


117-4 


1-1 


4 


260-0 


3-1 


252-8 


3-6 


244-4 


4-0 


234-8 


4-3 


6 


390-0 


6-9 


379-2 


8-1 


366-5 


9-0 


352-0 


9-8 


8 


520-0 


12-4 


505-5 


14-4 


488-6 


16-0 


469-3 


17-3 


10 


649-8 


19-4 


631-7 


22-4 


610-4 


25-0 


586-3 


27-1 


12 


779-7 


27-8 


757-9 


32-2 


732-4 


36-0 


703-5 


39-1 


14 


909-2 


38-0 


883-6 


43-9 


853-7 


49-0 


819-6 


53-1 


16 


1039-2 


49-6 


1009-9 


57-4 


975-7 


64-1 


936-8 


69-5 


18 


1168-1 


62-8 


1134-8 


72-6 


1096-0 


80-9 


1051-9 


87-8 


20 


1298-0 


77-6 


1261-2 


89-7 


1218-8 


100-1 


1169-2 


108-6 


R. 


10892 


8905 


7458 


6848 





Latitude 36°. 


Latitude 40°. 


Latitude 44°. 


Latitude 48°. 




















TUDE. 




















D. M. 


D. P. 


D. M. 


D. P. 


D. M. 


D. P. 


D. M. 


D. P. 


2° 


112-0 


1-2 


106-1 


1-2 


99-7 


1-2 


92-7 


1-2 


4 


224-0 


4-6 


212-2 


4-8 


198-9 


4-8 


185-4 


4-8 


6 


335-9 


10-3 


318-1 


10-7 


298-7 


10-9 


277-9 


10-8 


8 


447-7 


18-4 


423-9 


18-9 


398-0 


.19-3 


370-3 


19-2 


10 


559-2 


28-7 


529-4 


29-7 


497-1 


30-2 


462-3 


30-0 


12 


670-5 


41-3 


634-7 


42-8 


595-9 


43-4 


554-1 


43-2 


14 


781-6 


56-2 


739-7 


58-2 


694-3 


59-1 


645-6 


58-8 


16 


892-3 


73-4 


844-3 


76-0 


792-3 


77-1 


736-5 


76-7 


18 


1002-6 


92-8 


948-5 


96-1 


889-9 


97-5 


827-0 


97-0 


20 


1112-5 


114-5 


1052-3 


118-5 


986-9 


120-2 


916-9 


119-6 


R. 


5461 


4729 


4110 


3c 


»75 



116 



TOPOGRAPHICAL DRAWING. 



Length of a 


Degree of Longitude at Diffet 


^ent Latitudes, and at Sea- Level. 


Deg. 




Deg. 




Deg. 




Deg. 




Deg. 




^oT 




of 


Miles. 


of 


Miles. 


of 


Miles. 


of 


Miles. 


of 


Miles. 


Miles. 


Lat. 




Lat. 




Lat. 

28 




Lat. 
42 




Lat. 




Lat. 
70 







69-16 


14 


67-12 


61-11 


51-47 


56 


38-76 


23-72 


2 


69-12 


16 


66-50 


30 


59-94 


44 


49-83 


58 


36-74 


72 


21-43 


4 


68-99 


18 


65-80 


32 


58-70 


46 


48-12 


60 


34-67 


74 


19-12 


6 


68-78 


20 


65-02 


34 


57-39 


48 


46-36 


62 


32-55 


76 


16-78 


8 


68-49 


22 


64-15 


36 


56-01 


50 


44-54 


64 


30-40 


78 


14-42 


10 


68-12 


24 


63-21 


38 


54-56 


52 


42-67 


66 


28-21 


80 


12-05 


12 


67-66 


26 


62-20 


40 


53-05 


54 


40-74 


68 


25-98 


82 


9-66 




COLOUKED TOPOGRAPHY. 



Topographical features may be represented effectively and expeditiously by 
means of the brush and water-colours, either by India ink alone, or by various 
tints, or by the union of both. (For preparing colours for tints and their ap- 
plication, see page .) 

The most important colours for conventional tints are, besides India ink, 
indigo, carmine or crimson lake, and gamboge, used separately or compounded, 
and burnt sienna, yellow ochre, and vermilion, generally used alone. 

The following conventional colours are used by the French military engineers 
in their coloured topography : Woods, yellow, using gamboge and a very little 
indigo ; grass land, green, made of gamboge and indigo ; cultivated land, hrown, 
made of lake, gamboge, and a little India ink or burnt sienna will answer. 
Adjoining fields should be slightly varied in tint. Sometimes furrows are in- 
dicated by strips of various colours. Gardens are represented by small rec- 
tangular patches of brighter ^reew "and brown; uncultivated land, marbled 
green and light brown ; brush, brambles, etc., marbled green and yellow ; heath, 
furze, etc., marbled green and pink ; Yineyards, purple, composed of lake and 
indigo ; sands, light brown, made of gamboge and lake, or yellow ochre will do ; 
lakes and rivers, light blue, with a darker tint on their upper and left-hand sides ; 
seas, dark blue, with a little yellow added ; marshes, the blue of water, with 
spots of grass green, the touches all lying horizontally ; roads, broivn, between 
the tints for sand and cultivated ground, with more India ink ; hills, greenish 
brown, made of gamboge, indigo, lake, and India ink. Woods may be finished 
up by drawing the trees and colouring them green, with touches of gamboge 



®C5® 



TOPOGRAPHICAL DRAWING. . I17 

toward the light (the upper and left-hand side), and of indigo on the opposite 
side. 

In addition to the conventional colours, an imitation of the conventional 
signs is introduced in colour with the brush, and shadows are almost invaria- 
bly introduced. The light is usually supposed to come from the upper left- 
hand corner, and to fall sufficiently oblique to allow of a decided light and 
shade to the slopes of hills, trees, etc. After the shadow has been painted, the 
outline of the object is strengthened by a heavy black line on the side opposite 
the light. The flat tints are first laid on as above, and then the conventional 
signs are drawn in with a pencil and coloured in with appropriate and more 
intense tints ; the shadows are generally represented in India ink. 

For the shading of hills, wash the surface first with the proper flat tint, 
trace in with a pencil the outlines, then lay on in India ink tints proportioned 
in intensity to the height of the hills and steepness of the slopes. To soften the 
tints, a water brush is used ; the tints are laid on with the colour brush, and 
softened by passing the water brush rapidly along the edges. The water brush 
must not have too much water, as it would in that case lighten the tint more 
than is intended, and leave a ragged, harsh edge. Tints may be applied in 
very light shades, one over another, with the boundary of the upper tint not 
reaching the extreme limit of the tint below it. 
When depth of shade is required, it is best produced 
by application of several light tints in succession ; 
no tint is to be laid over the other until the first is 
dry. 

In shading by contours it is usual to increase the 
intensity of the shade beyond that of the mere super- 
position of one shade on another; where there are 

high altitudes and numerous contours, the lower ones should be put in with 
a different tint, as burnt sienna or sepia, with increasing shades, and above 
these graduated shades of India ink, beginning at the same intensity as that of 
the colour last put on (Plate IX). 

When woods have to be represented, the shading used for the trees, instead 
of interfering with the shadows due to the slopes, may be made to harmonize 
with them, and contribute to the general effect by presenting greater or less 
depth, according to the position of the woods on the sides or summits of the 
hills. 

An expeditious and effective way of representing hills with a brush, imitat- 
ing hills drawn with a pen on the vertical system, is effected by pressing out 
the brush flat to a comb-like edge, drawing this over a nearly dry surface of 
India ink, and then brushing lightly or more heavily between the contours, 
according to the steepness of the slope, each of the comb- like teeth making its 
mark (Plate VII). 

Rivers and masses of water may be shaded in with a colour and water brush ; 
or, by superposition of light tints, a shadow may be thrown from the bank 
toward the light, and the outline of this bank strengthened with a heavy black 
line ; the tints are to be in indigo. 

Topographical drawings may be made in water-colour with but one tint, as 
India ink, or ink mixed with a little sepia. The conventional signs are made 



118 TOPOGRAPHICAL DRAWINQ. 

in imitation of pen drawings, the hills in softened tint, or drawn with the comb- 
edged brush. 

Artistic and effective drawings are made of hills as they would appear in 
nature under an oblique light, the sides of the hills next the light receiving it 
more brilliantly according as they are inclined nearer to right angles with its 
rays, and the shades on the sides removed from the light increasing in intensity 
as the slopes increase in steepness. 

Having damp-stretched the paper upon the drawing-board, first draw in the 
lines in pencil, and afterward repeat them with a very light ink-line ; a soft 
sponge, well saturated, should then be passed quickly over the surface of the 
drawing in order to remove any ink that would be liable to mix with the tint 
and mar its uniformity. 

The moistened surface will prevent the tint from drying too rapidly at the 
edges. In tinting, never allow the edge to dry until the whole surface is cov- 
ered ; leave a little superfluous colour along the edge while filling the brush. In 
applying a flax tint to large surfaces, let the drawing-board be inclined at an 
angle of five or six degrees, to allow the colour to flow downward over the sur- 
face. With a moderately full brush, commence at the upper outline, and carry 
the colour along uniformly from left to right and from right to left in horizon- 
tal bands, taking care not to overrun the outlines, in approaching which the 
point of the brush should be used, and at trie lower outline let there be only 
sufficient colour in the brush to complete the tinting. 

The colour should not be allowed to accumulate in inequalities of the paper, 
but should be evenly distributed over the whole surface. 

Too much care can not be given to the first application of colour ; attempt- 
ing to remedy a defect by washing or applying fresh tints generally makes bad 
worse. 

Erasers should never be used on a tinted drawing, as the paper, when 
scratched, receives the tint more readily, and retains a larger portion of colour 
than other parts, thereby causing a darker tint. 

Marbling is done by using two separate tints, and blending them at their 
edges. A separate brush is required for each tint ; before the edge of the first 
is dry, pass the second tint along the edge, blending one tint into the other, and 
continue with each tint alternately. 

In reference to general effect in tinted topographical drawings, intensity and 
everything else should be subordinate to clearness. No tint should be prom- 
inent or obtrusive. Tints that are of small extent must be a little more intense 
than large surfaces, or they will appear lighter in shade. Keep a general tone 
throughout the whole drawing. Beginners will find it best to keep rather low 
in tone, strengthening their tints as they acquire boldness of touch. 

Plate VIII gives an example of coloured topography. 

The plan is usually so drawn that the top may represent the north ; the 
upper left-hand corner is then the northwest. 

In inking in, commence first with the light lines, since a mistake in these 
lines may be covered by the shade-lines. Describe all curves before drawing 
the straight lines, for it is easier to join neatly a straight line to a curve than 
the opposite. Ink in with system, commencing, say, at the top ; ink in all light 
lines running easterly and westerly, then all light lines running northerly and 



TOPOGRAPHICAL DRAWING. 119 

southerly, then commence in the same way and draw in the shade lines. Ele- 
vated objects have their southern and eastern outline shaded, while depressions 
have the northern and western ; thus, in conventional signs, roads and canals 
are shaded on opposite sides. Having inked in all lines that are drawn with a 
ruler or described with compasses, commence again at one corner to fill in the 
detail, keeping all parts of the plan except what you are actually at work 
upon covered with paper to preserve it from being soiled. The curved lines of 
brooks, fences, etc., are sometimes drawn with a drawing-pen, sometimes with 
a steel pen or goose-quill. 

Boundary lines of private properties, of townships, of counties, of States, 
etc., are indicated by various combinations of short lines and dots, thus : 



All plans shoTild have meridian lines drawn on them ; also scales, and the 
dates on which the plans were finished. Page 120 gives several designs for 
meridians and borders. Jn these diagrams it will be observed that both true 
and magnetic meridians are drawn; this is desirable when the variation is 
known, but in many surveys merely the magnetic meridian is taken ; in these 
cases this line is simply represented with half of the barb of the arrow at 
the north point, and on the opposite side of the line from the true meridian. 

Scales on drawings which are to be reproduced by photography should 
always be drawn in ; on others, the proportion of the plan to the ground should 
be expressed decimally, as -g-oVo? ti5"o"oo"? ^^ ^J stating the number of feet, 
chains, etc., to the inch. 



120 



TOPOGRAPHICAL DRAWING. 




ORTHOGRAPHIC PROJECTION. 




Architectural and mechanical drawings are usually the delineation of 
bodies by orthographic projection^ which is the representation on a sheet of 
paper, having only two dimensions, length and breadth, of solids, having three, 
length, breadth, and thickness, on such scales that dimensions can be taken 
from the parts, and structures and machines constructed therefrom. 

Place any surface, for instance, a sheet of paper or a drawing-board, at 
right angles to the sun's rays. This may be readily done by inserting a pin 
into the surface, and making it vertical to the surface in every direction by a 
right-angled triangle ; then place the surface in the direct rays of the sun, and 
in such a position that there will be no shadow on the surface from the pin ; 
the sun's rays are then perpendicular to the surface. Take a wafer or a circu- 
lar bit of paper and hold it over the paper by means of a long pin or wire, and 
we obtain shadows, as above, varying with the inclination of the wafer to the 
plane of the paper. When parallel with the plane, the shadow is a complete 
circle ; when at right angles, a line ; and it varies between them as the w^afer is 
inclined. These shadows are the orthographic projections of the wafer; no 
line can be longer than it is naturally, but, if inclined or vertical, it is reduced 
in length till it becomes a point only. The orthographic projection of the pin 
which has determined the position of the surface is merely the shadow of the 
head. If the pin be inclined at all, the body of the pin is projected as a 
shadow by a line ; if the pin be laid on the surface, its projection is the whole 
length of the pin. The sun's rays act as perpendiculars, which will be here- 
after spoken of as projecting the points of an object upon a surface which 
will represent the object itself in drawing ; and, should any confusion occur to 
the draughtsman of how an object is to be projected or drawn, if he can make 
the outline of the object on any convenient scale in wire and get its shadows 
by the sun's vertical rays on a plane, he can readily see how the object should 
be drawn. 

Since the surfaces of all bodies may be considered as composed of points, 
the first step is to represent the position in space of a point, by referring it to 
planes whose position is established. The projection of a point upon a plane 
is the foot of the perpendicular let fall from the point to the plane. 

If on two planes not parallel to each other, whose positions are known, we 

121 



122 



ORTHOGRAPHIC PROJECTION. 



have the projection of a point, the position of this point is determined by erect- 
ing perpendiculars from each plane at the projected points : their intersection 
will be the point. 

If from every point of an indefinite straight line, A B (Fig. 252), placed in 
any manner in space, perpendiculars be let fall on a plane, L M N 0, whose 
position is given, then all the points in which these perpendiculars meet the 
plane will form another indefinite 
straight line, a t : this line is called the 
projection of the line A B on this 
plane. It is only necessary to project 
two points of the line, and the straight 
line drawn through the two projected B 

points will be the projection of the 





Fig. 252. 



Fig. 253. 



given line. The projection of a straight line, itself perpendicular to the plane, 
is the point in which it meets the plane. 

If the projections a h and a' V of a straight line on the two planes L M N 
and L M P Q (Fig. 253) are known, this line A B is determined ; for if, through 
one of its projections, <x 5, a plane be drawn perpendicularly to L M ]^ 0, and 
if through a! V another plane be drawn perpendicular to L M P Q, the inter- 
section of the two planes will be the line A B. 

To delineate a solid, it must be referred to three planes, at right angles to 
each other. 

Thus, let « Z* c (Fig. 254) be a parallelopiped in an upright position, of 
which the plane a ^ is horizontal, and the planes a c and c b vertical. Let d e, 
df^ and d g\)Q the planes of projection. The sides of the body being parallel 
to these planes, each to each, let the figure of the parallelopiped be projected 
on them. Draw parallel lines from the angles of the body perpendicular to the 
planes, as indicated by the dotted lines ; then upon the plane d e, a' V is the 
projection of the surface a h^Ju\iQ plan of the object; upon the plane 6?/, a' c\ 
the projection of the surface a c, the front elevation ; and upon the plane d g^ 
the projection h' c' of the surface h c, the side elevation. Thus, three distinct 
views of the regular solid ah c are delineated on plane surfaces, any two of 
which are a sufficient description of the object. From the two figures a' c\ V c\ 
for example, the third figure a' V may be compounded, by drawing the vertical 
lines d h h' i and a' ^, c' I to meet the plane d e, and by producing them hori- 
zontally till they meet and form the figure a' V . Similarly, the figure V c' may 



ORTHOGRAPHIC PROJECTION". 



123 



be deduced from the other two by the aid of the lines h, i, from a' h' and the 
lines m, n, from a' c'. 

It is in this way that a third view of any piece of machinery is to be found 
from two given views ; and in many cases two elevations, or one elevation and 




Fig. 254. 



Fig. 255. 



a plan, may afford a sufficiently complete idea of the construction of a machine. 
When parts are inclosed by others, views of the interior are required, in which 
case the machine is supposed to be cut across by planes, vertical, horizontal, or 
inclined, to reveal its structure. Such views are termed sections^ and distin- 
guished, with reference to the planes of section, as vertical or liorizo7ital or 
inclined sections. 

In practice, the. drawings are done upon one common surface, the plane of 
paper. Suppose the plane d g (Fig. 254) revolved back into the position d g\ 
and d e also moved to d e\ both of these positions being in the plane of d f. 
This done, the three views are depicted on one plane surface (Fig. 255) ; d I 
and d m are the ground and vertical lines ; the positions of the same points in 
a' c' and a' V are in the same perpendicular from the ground-line ; and the 
position of a point in the plane may be found by applying the edge of the 
square to the same point as represented in the elevation. The same is true as 
between the two elevations, and establishes a method of drawing several views of 
one machine upon the same surface of paper in strict agreement with each other. 

PROJECTIONS OF SIMPLE BODIES. 

RigM projections of a regular hexagonal pyramid (Fig. 256). — Two distinct 
geometrical views are necessary to convey a complete idea of tlie form of the 
object: an elevation to represent the sides of the body, and to express its 
height ; and a plan to express the form horizontally. 



124 



ORTHOGRAPHIC PROJECTION. 



Draw a horizontal line L T through the centre of the sheet to represent the 
ground line. Then draw a perpendicular to the ground line, S S', to represent 
the axis of the pyramid. 

To construct the plan, from any point, S', on the line S S', as a centre, con- 
struct the hexagonal base ; the lines A' S', B' S', etc., represent the projections 
of its edges in the plan. 

Since the base of the pyramid rests upon the horizontal plane, it must 




be projected vertically upon the ground line. From each of the angles at 
A', B', C, and D' erect perpendiculars to that line. The points of intersec- 
tion, A, B, 0, and D, are the true positions of all the angles of the base ; and 
it only remains to lay off the height of the pyramid, from the point G- to S, and 
to draw S A, S B, S C, and S D, which are the only edges of the pyramid visi- 
ble in the elevation ; S A and S D, being in the vertical plane, are seen in their 
true length ; the points F' and E' being situated in the lines B B' and C C, the 
lines S B and S C are each the projections of two edges of the pyramid. 

To construct tlie projections of the same pyramid^ having its base set in an 
inclined position^ hut tvith its edges S A and S D still in the vertical plane 
(Fig. 257). 

With the exception of the inclination, the vertical projection of this solid is 



ORTHOGRAPHIC PROJECTION. 



125 



f 

Jniv. 



A--- 



precisely the same as in the preceding example, and it is only necessary to copy 
that elevation. To do this, fix the position of the point D upon the ground 
line, through which draw D A, making with L T the desired inclination of the 
base of the pyramid. Make D A equal to the A D of the preceding figure, and 
on this erect the vertical projection S A D of that figure. 

Since the edges S A and S D are still in the vertical plane, and the point 
D remains unaltered, the projection A' of the point A will still be in the line 
A' S'. The remaining points, B', C, etc., in the projection of the base, are 
found by the intersections of perpendiculars let fall from the corresponding 
points in the elevation, with lines drawn parallel to A' S', at a distance equal to 
the width of the base. Joining all the contiguous points, we obtain A' B' C D' 
E' F', the horizontal projection of the base, two of its sides being concealed by 
the body of the pyramid. The vertex S having been similarly projected to S', 
and joined by straight lines to the several an- 
gles of the base, the projection of the solid 
is completed. 

To find the horizontal projection of a trans- 
verse section of the same pyramid^ made hy a 
plane perpendicular to the vertical^ hut in- 
clined at an angle to the horizontal plane of 
projection^ letting all the sides of the base he 
inclined to the ground line (Fig. 258). 

Since none of the sides of the base are to 
be parallel with the ground line, draw a line 
A' D' making the required angle with that 
line, and from the points A' and D' set out the 
angular points of the hexagon. To obtain the 
projections of the edges of the pyramid, join 
the angular points which are diametrically 
opposite and project the figure thus obtained 
upon the vertical plane, as shown in the eleva- 
tion. 

If the cutting plane be represented by the 
line a dm. the elevation, it will expose, as the 
section of the pyramid, a polygon whose an- 
gular points, being the intersections of the va- 
rious edges with the cutting plane, will be 
projected in perpendiculars drawn from the 
points where it meets these edges respective- 
ly ; from the points a, f Z>, etc., let fall the 
perpendiculars a a', ff, h h\ etc. ; join their 
contiguous points of intersection with the 
lines A' D', F' C, B' E', etc. ; and the resulting 
six-sided figure represents the section required. The edges F S and E S, being 
concealed in the elevation, but necessary for the construction of the plan, are 
expressed by dotted lines, as also is the portion of the pyramid situated above 
the cutting plane, supposed to be removed, but necessary in order to draw the 
lines representing the edges. The ordinary method of expressing sections in 




Fig. 258. 



126 



ORTHOGRAPHIC PROJECTION. 



purely line drawings is by filling up the spaces comprised within their outlines 
with a number of parallel straight lines drawn at equal distances, called section 



To represent in plan and elevation a regular six-sided prism in an upright 
position (Fig. 259). 

Lay down the ground line G- K and draw the axis of the prism S S\ De- 
scribe the hexagonal plan A' B' C D' E' F', as in the previous example. From 
each of the angular points, A', B', etc., erect perpendiculars, and on one of these 
perpendiculars set off A G-, the height of the prism, and draw a parallel to the 
ground line, A D, which completes the vertical projection. The face, B H I, 
being parallel to the vertical plane, is seen in its true size, while G- H and I K 




Fig. 259. 



are each equal to one half of H I, which enables us to draw the elevation with- 
out constructing the plan — a fact to be remembered in the drawing of nuts, 
bolt-heads, etc., in machine drawing. 

To form the projections of the same prism, supposing it to have teen moved 
round the point G in a plane parallel to the vertical plane (Fig. 260). 



ORTHOGRAPHIC PROJECTION. 



127 



Copy the elevation (Fig. 259) on the inclined base G K ; let fall perpen- 
diculars from all the angles in the elevation ; and join the contiguous points of 
intersection with the horizontal lines appropriate to these points respectively. 
The plan remaining the same width as before, the polygon A' B' C D' E' F' is 
the projection of the upper surface, 
and G' H' I' K' L' M' that of the base 
of the prism. All the edges are rep- 
resented in the horizontal projection 
by equal straight lines, as D' K', A' G', 
etc., and the sides A' B \ G' H', etc., 4/ 
remain still parallel to each other, 
which affords the means of verifying 
the accuracy of the drawings. The 
upper surface and the base, seen ob- 
liquely in this projection, do not ap- 
pear as true hexagons in the plan. 

Required the projections of the 
same prism set into a position in- 
clined to both planes of projection 
(Fig. 261). 

Assuming the inclination of the 
prism upon the horizontal plane to be 
as in the preceding figures, copy the 
plan of Fig. 260 on an axis A' K' in- 
clined to the vertical plane of projec- 
tion. Since the prism preserves its 
former inclination to the horizontal 
plane, every point in it, as A, in as- 
suming its new position, simply moves 
in a horizontal plane, and will there- 
fore be at the same distance above the 
ground line that it was in the eleva- 
tion (Fig. 260), and it will also be in 
the perpendicular A' A ; the point of 
intersection A is, therefore, its projec- 
tion in the elevation. Determine the 
remaining angular points in this view and join the contiguous points and the 
corresponding angles of the upper and lower surface and the figure is complete. 




Fig. 261, 



CONIC SECTIONS. 

The plan of the cone (Fig. 262) is simply a circle, described from the centre 
S', with a diameter equal to that of the base. Its elevation is an isosceles 
triangle, obtained by drawing tangents A' A, B''B, perpendicular to and 
intersecting the ground line ; then set off upon the centre line the height 
C S, and join S A, S B. These lines are called the exterior elements of the 
cone. 

Given the projections of a cone, and the direction of a plane X X, cutting it 
perpendicularly to the vertical, and obliquely to the horizontal plane ; required 



128 



ORTHOGRAPHIC PROJECTION. 



to find, firsts the horizontal projection of this section; and, secondly, the out- 
line of the ellipse thus formed (Figs. 262, 263). 

Through the vertex of the cone draw a line S E to any point within the 
base A B ; let fall a perpendicular from E, cutting the circumference of the base 




in E', and join E' S' ; then 
another perpendicular let 
fall from e will intersect 
E' S' in a point e\ which 
will be the horizontal pro- 
jection of a point in the 
curve required ; and so on 
for any number of points. 

The exterior genera- 
trices A S and B S being 
both projected upon the 
line A' B', the extreme lim- 
its of the curve sought will 
be at the points a' and h' on that line, which are the projections of the points 
of intersection a and h of the cutting plane with the outlines of the cone. 
And since the line a' V divides the curve symmetrically into two equal parts, 
the points/', g\ h' , etc., will be obtained by setting off above that line, and on 
their respective perpendiculars, the distances d' d^, e' e^, etc. A sufficient num- 
ber of points having thus been determined, the curve drawn through them 
(which will be found to be an ellipse) will be the outline of the section re- 
quired. 

This curve may be obtained by another method, depending on the principle 
that all sections of a cone by planes parallel to the base are circles. Thus, let 
the line F G represent such a cutting plane ; the section which it makes with 
the cone will be denoted on the horizontal projection by a circle drawn from 



ORTHOGRAPHIC PROJECTION. 



129 



the centre S', with a radius equal to half the line F G; and by projecting the 
point of intersection H of the horizontal and oblique planes by a perpendicular 
H H', and noting where this line cuts the circle above referred to, two points 
H' and I' are determined in the curve. Additional points are obtained similarly. 
The preceding methods exhibit the section as fore-shortened. To solve the 
second question proposed, let the cutting plane X X be conceived to turn 
upon the point h, so as to coincide with the vertical line h k, and (to avoid con- 





■A~- 



FiG. 265. 

fusion of lines) let 5 ^ be trans- 
ferred to a' h\ which will repre- 
sent, as before, the extreme limits 
of the curve required ; take any 
point, as rZ, in this new position 
of the cutting plane, it will be 
represented by cP^ and, if the cut- 
ting plane were turned upon a' V 
(Fig. 263) as an axis till it is 
parallel to the vertical plane, the 
point which had been projected 
at d"^ would then have described 
round a! V an arc of a circle, 
whose radius is the distance d! d^ 

(Fig. 262). This distance, therefore, set off at d' and/' on each side of a' h' 
gives two points in the curve sought. The curve drawn through any number 
of points thus obtained will be an ellipse of the true form and dimensions of 
the section. 

To find the horizontal projection and actual outline of the section of a cone, 
made hy a plane Y Y parallel to one side or element, and perpendicular to the 
vertical plane (Figs. 264, 265). 

Determine by the second method laid down in the preceding problem any 
10 



Fig. 264. 



130 



ORTHOGRAPHIC PROJECTION. 



number of points, as F', G', J', K', etc., in the curve representing the horizon- 
tal projection of the section specified. The horizontal plane passing through 
M gives only one point M', which is the vertex of the curve sought. 

To determine the actual outline of this curve, suppose the plane Y Y to turn 
as upon a pivot at M, until it has assumed the position M B, and transfer M B 
to the parallel M' B" (Fig. 265). The point F will thus have first described 
the arc F E till it reaches the point E, which is then projected to E'^ ; suppose 
the given plane, now represented by M'^ B', to turn upon that line as an axis, 
until it assumes a position parallel to the vertical plane, the point E^ which is 
distant from the axis M' B' by the distance F' S' (Fig. 264), will now be pro- 
jected to F'^ and G^ two points in the curve required, which is a parabola. 

To draiu the vertical projection of the sections of tivo opposite cones made ly 
a plane parallel to their axis (Fig. 266). 




?' "n, H 








Let C E D and B A be the two cones, and X X the position of the 
cutting plane. Project in plan either of the cones, as Z* E' D' ; from its centre, 
with a radius equal to L H, describe a circle, and draw the tangent ha; ha 
will be the horizontal projection of the cutting plane. Draw the line H' M^ 
parallel to the cutting plane ; H', M' corresponding in position to the inter- 
sections H, M, of the plane with the cones. From H' and M' lay off distances 
equal to L K, K I, and the length of the cone, and through these points draw 
perpendiculars, as/' e', d' c\ V a\ etc., which must be made equal to the chords 
f e^ d c^ h a^ made by the cutting plane a J, with circles whose radii are G K, 
I F, and the radius of the base of the cone. Through the points «', c', e', H', /', 
d\ h\ draw the curve for the projection required. A similar construction will 
give the sectional projection of the opposite cone at M'. The curve thus found 
is the hyperbola. 



PEIS^ETKATIONS OR INTERSECTION'S OF SOLIDS. 

Represent the projections of two cylinders of unequal diameters meeting 
each other at right angles (Fig. 267). The one, the rectangle ABED for its 
vertical, and the circle A' H' B' T' for its horizontal projection ; the other, being 



ORTHOGRAPHIC PROJECTION. 



131 



horizontal, is indicated in the former by the circle L P I N, and in the latter by 
the rectangle L' I' K' M'. From the position of these two solids the curves 
formed by their junction will be projected horizontally in the curves 0' H' P', 
R' T' S', and vertically in L P I N. 

But, if the position of these bodies be changed into that represented by Fig. 
268, the lines of their intersection will assume in the vertical projection a 
totally different aspect, and may be determined as follows : 

Through any point taken upon the plan of Fig. 268 draw a horizontal line 
a' h\ indicating a plane cutting both cylinders parallel to their axes; this 




Fig. 267. 



plane would cut the vertical cylinder in lines drawn perpendicularly through 
the points c' d' . To find the vertical projection of its intersection with the 
other cylinder, conceive its base Y L', after being transferred to P 17, to be 
revolved about P L' as an axis parallel to the horizontal plane ; this is expressed 
in part by simply drawing a semicircle of the diameter P L^ Produce the 
line a' h' to a' ; then set off the distance a^ e' on each side of the axis I K, and 
draw straight lines through these points parallel to it. These lines a h, g /i, 



132 



ORTHOGRAPHIC PROJECTION. 



denote the intersection of the plane a' V with the horizontal cylinder, and 
therefore the points c, d^ m, o, where they cut the perpendiculars c c', d d\ are 
points in the curve required. By passing other horizontal planes similar to a! b' 
through both cylinders, and operating as before, any number of points may be 
obtained. The vertices i and k of the curves are projected directly from i' and 
lc\ the intersections of the outlines of both cylinders. When the cylinders are 
of unequal diameters, as in the present case, the curves of penetration are hy- 
perbolas. 

When the diameters of the cylinders are equal (Fig. 269), and when they 




Fig. 269. 



Fig. 270. 



cut each other at right angles, the curves of penetration are projected vertically 
in straight lines perpendicular to each other. 

To delineate the intersections of tivo cylinders of equal diameters at right 
angles^ when one of the cylinders is inclined to the vertical plane (Fig. 270). 

Suppose the two preceding figures to be drawn, the projection c of any 
point, as c', must be situated in the perpendicular c' c. Since the distance of 



ORTHOGRAPHIC PROJECTION. 



133 



this point (projected at c in Fig. 269) from the horizontal plane remains un- 
altered, it must also be in the horizontal line c c. Upon these principles all 
the points indicated by literal references in Fig. 270 are determined ; the 
curves of penetration resulting therefrom intersect each other at two points 
projected upon the axial line L K, of which that marked q alone is seen. The 
ends of the horizontal cylinder are ellipses. 

To find the curves resulting from the intersection of tiuo cylinders of un- 
equal diameters^ meeting at any angle (Fig. 271). 

Suppose the axes of both cylinders to be parallel to the vertical plane, and 
let A B E D and N Q P be their projections upon that plane. In construct- 
ing, in the first place, their 
horizontal projection, ob- 
serve that the upper end 
A B of the larger cylinder is 
represented by an ellipse 
A' K' B' M', which may easi- 
ly be drawn by the help of 
the major axis K' M' equal 
to the diameter of the cylin- 
der, and of the minor A' B', 
the projection of the diame- 
ter. The visible portion of 
the base of the cylinder be- 
ing similarly represented by 
the semi-ellipse L' D' H', its 
entire outline will be com- 
pleted by drawing tangents ^ 
L' M' and H' K'. The up- ^z- 
per extremity P jN" of the 
smaller cylinder will also be gtij 
projected in the ellipse p' W. rzi~[ 

Conceive a plane, as 
a' g', to pass through both 
cylinders parallel to their 
axes ; it will cut the surface 
of the larger cylinder in 
two straight lines, passing 
through the points /' and g' 
on the upper end of the cyl- 
inder ; these lines will be 
represented in the elevation 
by projecting the points/' 
and g' to /, g, and drawing 

«/and eg parallel to the axis. The plane a' g' will in like manner cut the 
smaller cylinder in two straight lines, which will be represented in the verti- 
cal projection by d 7i and e i, and the intersections of these lines with af 
and c g will give four points /, k, m, and n, in the curves of penetration. Of 
these points, one only, Z, is visible, Z', in the plan. 




Fig. 271. 



134 



ORTHOGRAPHIC PROJECTION. 



To find the curves of penetration in the elevation without the aid ofthejjlan 
(Fig. 271). 

Let the bases D E and Q of both cylinders be revolved parallel to the 
vertical plane after being transferred to any convenient distance, as D" E'' and 
Q'' 0% from the principal figure ; they will then be vertically projected in the 

circles D' W W and Q" G' 0^ Draw 
a^ c^ parallel to D E, and at any suitable 
distance from the centre I ; this line 
will represent the intersection of the 
base of the cylinder with a plane parallel 
to the axes of both, as before. The in- 
tersection of this plane with the base of 
the smaller cylinder will be found by 
setting off from E a distance R j9, equal 
to I 0, and drawing through the point j5 
a straight line parallel to Q 0. The 
intersection of the supposed plane with 
the convex surfaces of the cylinders will 
be represented by the lines af, eg, and 
d h, ei; and, consequently, the inter- 
sections of these lines indicate points in 
the curves sought. These points may 
be multiplied by conceiving other planes 
to pass through the cylinders. 

To find the curves of pe7ietration of 
a cone and sphere (Fig. 272). 

Let D S be the axis of the cone, 
A' L' B' the circle of its base, and the 
triangle A B S its projection on the ver- 
tical plane ; and let C, C, be the projec- 
tions of the centre, and the equal circles 
E'K'F' and EGF. those of the cir- 
cumferences of the sphere. 

This problem can be solved only by 
the aid of imaginary intersecting planes. 
Let a l represent the projection of a 
horizontal plane ; it will cut the sphere 
in a circle whose diameter is a ^, and 
which is partially drawn from the centre C in the plan, as a' f V . Its in- 
tersection with the cone is also a circle described from the centre S' with the 
diameter c t? as c'/' d' ; the points e' and/', where these two circles cut each 
other, are the horizontal projections of two points in the lower curve, which 
is entirely hidden by the sphere. The points referred to are projected ver- 
tically upon the line a h 2X e and/. The upper curve, which is seen in both 
projections, is obtained by a similar process ; but it is to be observed that the 
horizontal cutting planes must be taken in such positions as to pass through 
both solids in circles which shall intersect each other. In this respect it 
will be necessary, first, to determine the vertices m and n of the curves of 




Fig. 272. 



ORTHOGRAPHIC PROJECTION. 



135 



penetration. For this purpose, conceive a vertical plane passing through the 
axis of the cone and the centre of the sphere ; its horizontal projection will 
be the straight line C L', joining the centres of the two bodies. Suppose 
this plane to be turned upon the line C as on an axis, until it becomes 
parallel to the vertical plane ; the points S' and L' will now have assumed 
the positions S'' and L", and consequently the axis of the cone will be projected 
vertically in the line D' S", and its side in S^ L'', cutting the sphere at the 
points jt? and r. Conceive the solids to have resumed their original relative 
positions, the vertices or adjacent limiting points of the curves of penetration 
must be in the horizontal lines p o and r q^ drawn through the points deter- 
mined as above ; their exact positions on these lines may be ascertained by pro- 
jecting vertically the points m' and n'^ where the arcs described by the points jo 
and r, in restoring the cone to its first position, intersect the line S' L'. 

It is of importance, further, to ascertain the points at which the curves of 
penetration meet the 
outlines A S and S B 
of the cone. The plane 
which passes through 
these lines, being pro- 
jected horizontally in 
A' B', will cut the sphere 
in a circle whose diame- 
ter is i' j' ; this circle, 
described in the eleva- 
tion from the centre 0, 
will cut the sides A S 
and S B in four points, 
at which the curves of 
penetration are tangent 
to the outlines of the 




cone. 

To find the lines of 
j)enetration of a cylin- 
der and a cylindriccd 
ring, or annular torus 
(Fig. 273). 

Let the circles A' E' 
B', F' G' K', represent 
the horizontal, and the 
figure A C B D the ver- 
tical projection of the 
torus, and let the circle 
H'/' L', and the rectan- 
gle H I M L be the 
analogous projections of 
the cylinder, which 

passes perpendicularly through it. Conceive, as before, a plane, a J, to pass 
horizontally through both solids ; it will cut the cylinder in a circle which will 



136 ORTHOGRAPHIC PROJECTION. 

be projected in the base H'/' L' itself, and the ring in two other circles, of 
which one only, part of which is represented by the arc /' ¥ &', will intersect 
the cylinder at the points/' and Z>^ which, being projected vertically, will give 
two points / and If in the upper curve of penetration. 

Another horizontal plane, taken at the same distance below the centre line 
A B as that marked ^ ^ is above it, will cut the ring in circles coinciding with 
those already obtained ; consequently the points/' and Z>' indicate points in the 
lower as well as in the upper curves of penetration, and are projected vertically 
at d and e. Thus, by laying down two planes at equal distances on each side 
of A B, four points in the curves required are determined. 

To determine the vertices m. and n^ following the method explained in the 
preceding problem, draw a plane 7i , passing through the axis of the cylinder 
and the centre of the ring, and conceive this plane to be revolved about the 
point until it has assumed the position B', parallel to the vertical plane ; 
the point n\ representing the extreme outline of the cylinder in plan, will now 
be at r', and, being projected vertically, that outline will cut the ring in two 
points jt? and r, which would be the limits of the curves of penetration in the 
supposed relative position of the two solids ; and by drawing the two horizontal 
lines r n and p m^ and projecting the point n' vertically, the intersections of 
these lines, m and n^ are the vertices of the curves in the actual position of the 
penetrating bodies. 

The points at which the curves are tangents to the outlines H I and L M of 
the cylinder may readily be found by describing arcs of circles from the centre 
through the points H' and L', which represent these lines in the plan, and 
then proceeding, as above, to project the points thus obtained upon the eleva- 
tion. Lastly, to determine the points, as y, 2;, etc., where the curves are tan- 
gents to the horizontal outlines of the ring, draw a circle P' 5'/ with a radius 
equal to that of the centre line of the ring, namely, P D ; the points of inter- 
section z' and/ are the horizontal projections of the points sought. 

Required to represent the sectio?i which would he made in this rin^ ly a 
plane^ W T', parallel to the vertical plane. 

Such a section will be represented in its actual form and dimensions in the 
elevation. To determine its outlines, let two horizontal planes, g q and i k, 
equidistant from the centre line A B, be supposed to cut the ring ; their lines 
of intersection with it will have their horizontal projections in the two circles 
g' 0' and h' q'^ which cut the given plane W T' in 0' and q'. These points being 
projected vertically to 0, q, h, etc., give four points in the curve required. The 
line W T' cutting the circle A' E' B' at N', the projection N of this point is 
the extreme limit of the curve. 

The circle P' 5'/, the centre line of the rim of the torus, is cut by the planes 
N' T' at the point s\ which, being projected vertically upon the lines D P and 
C l^ determines s and I, the points of contact of the curve with the horizontal 
outlines of the ring. Finally, the points t and u are obtained by drawing from 
the centre a circle, T' v\ tangent to the given plane, and projecting the point 
of intersection v' to the points v and x^ which are then to be replaced upon C D 
by drawing the horizontals v t and x u. 

Required to delineate the lines of penetration of a sphere and a regular hex- 
agonal prism whose axis passes through the centre of the sphere (Pig. 274). 



ORTHOGRAPHIC PROJECTION. 



137 



The centres of the circles forming the two projections of the sphere being 
upon the axis C of the upright prism, which is projected horizontally in the 
regular hexagon D' E' F' G' H' I', and all the lateral faces of the prism being 
equidistant from the centre of the sphere, their lines of intersection with it will 
be circles of equal diameters. The perpendicular face, represented by the line 
E' F' in the plan, will meet the surface of the sphere in two circular arcs, E F 
and L M, described from the centre C, with a radius equal to c' b' or a' c'. 
And the intersections of the two oblique faces D' E' and F' G' will obviously 
be each projected in two arcs of an ellipse, whose major axis d g is equal to 
e' f, and minor axis the vertical projection of e' f . As it is necessary to 
draw small portions only of these curves, the following method may be em- 
ployed : Draw D G through the points E, F ; divide the portions E F and 
F G respectively into the same number of equal parts, and, drawing perpen- 
diculars through the points of division, set off from F G the distances from 





Fig. 275. 



the corresponding points in E F to the circular arc E F, as points in the 
elliptical arc required. The remaining elliptical arcs can be traced by the 
same method. 



138 



ORTHOGRAPHIC PROJECTION. 




Required to clraiu the lines of penetration of a cylinder and a spliere^ the 
centre of the sphere heing loithout the axis of the cylinder (Fig. 275). 

Let the circle D' E' L' be the projection of the base of the given cylinder, 
and let A B be the diameter of the given sphere. If a plane, as c' d\ be drawn 
parallel to the vertical plane, it will cut the cylinder in two straight lines, 

G G-', H H'. This plane wall also cut 
the sphere in a circle described from 
the centre C with a radius of half the 
line c' d' ; its intersection wdth the lines 
G G' and H H' will give so many points 
in the curves sought, viz., G, H, I, K. 

The planes a' V and e'/', w^hich are 
tangents to the cylinder, furnish respect- 
ively only two points in the curves ; of 
these points, E and F alone are visible, 
the other two, L and M, being concealed 
by the solid ; therefore the planes drawn 
for the construction of the curves must 
be all taken between a' V and e' f . The 
plane w^hich passes through the axis of 
the cylinder cuts the sphere in a circle 
whose projection upon the vertical plane 
will meet at the points D, N, and ^, /i, 
the outlines of the cylinder, to which 
the curves of penetration are tangents. 

To find the lines of penetration of 
a frustum of a cone and a. prism (Fig. 
276). 

The frustum is represented in the 
plan by two circles described from the 
centre C ; and the' horizontal lines M IS" 
and M' N' are the projections of the 
axis of a prism of which the base is 
square, and the faces respectively par- 
allel and perpendicular to the planes of 
projection. 

In laying down the plan of this solid, it is supposed to be inverted, in order 
that the smaller end of the cone and the lines of intersection of the lower sur- 
face, F G, of the prism may be exhibited. According to this arrangement, the 
letters A' and B' ought, strictly speaking, to be marked at the points I' and H', 
and conversely ; but, as the part above M' W is exactly symmetrical with that 
below it, the distribution of the letters of reference in the figures can lead to no 
confusion. 

The intersection of the plane F G with the cone is projected horizontally 
in a circle described from the centre C, with the diameter F' G'. The arcs 
I' F' A' and H' G' B' are the only parts of this circle which require to be 
drawn. In the vertical projection the extreme points K, L, A, B need only 
be found, for the lines of intersection are here projected straight. 




Fig. 276. 



ORTHOGRAPHIC PROJECTION. 



139 




To describe the curves formed hy the intersection of a cylinder with the 
frustum of a cone^ the axes of the tivo solids cutting each other at right angles 
(Fig. 277). 

The projections of the solids are laid down in the figure precisely as in the 
preceding example. The intersections of the outlines in elevation furnish four 
points in the curves of penetration. 
These points are all projected horizontal- 
ly upon the line A' B'. Now pass a 
plane, as a ^, horizontally through both 
solids ; its intersection with the cone will 
be a circle of the diameter c d, while the 
cylinder will be cut in two parallel 
straight lines, represented in the eleva- 
tion by a 5, and whose horizontal projec- 
tion may be determined in the following 
manner: Conceive a vertical plane, /^, 
cutting the cylinder at right angles to 
its axis, and let the circle g e/ thereby 
formed be described from the intersec- 
tion of the axes of the two solids ; the 
line j h will now represent, in this posi- 
tion of the section, the distance of one of 
the lines sought from the axis of the cyl- 
inder. Set o2 this distance on both sides 
of the point A', and through the points 
k and a' thus obtained, draw straight 
lines parallel to A' B' ; the intersections 
of these lines with the circle drawn from 
the centre C of the diameter c' d' will 
give four points m\p', n^ and o, which, 
being projected vertically upon a ^, deter- 
mine two points, m and p^ in the curves 
required. 

In order to obtain the vertices or ad- 
jacent limiting points of the curves, draw 
from the vertex of the cone a straight 
line, t e, touching the circle g ef and let a horizontal plane be supposed to 
pass through the point of contact e. Proceed according to the method given 
above to determine the intersections of this plane with each of the solids in 
question ; the four points i', r', g, and s, projected vertically upon the line e r, 
determine the vertices i and r required. 




Fig 277. 



THE HELIX. 



A helix is the curve described upon the surface of a cylinder by a point re- 
volving round it, and at the same time moving parallel to its axis by a certain 
invariable distance during each revolution. This distance is called the pitch of 
the helix or screw. 

Required to construct the helical curve described by the point A' upon a cyl- 



140 



ORTHOGRAPHIC PROJECTION. 



inder projected horizontally in the circle A' C F', the pitch being represented 
hy the line A' A' (Fig. 278). 

Divide the pitch A^ A^ into any number of equal parts, say eight ; and 
through each point of division, 1, 2, 3, etc., draw straight lines parallel to the 
ground line. Then divide the circumference A' C F' into the same number of 
equal parts ; the points of division. A', B', C, E', F', etc., will be the horizontal 

projections of the differ- 
ent positions of the given 
point during its motion 
round the cylinder. Thus, 
when the point is at B' in 
the plan, its vertical pro- 
jection will be the point of 
intersection B of the per- 
pendicular drawn through 
B' and the horizontal 
drawn through the first 
point of division. Also, 
when the point arrives at 
C in the plan, its vertical 
projection is the point C, 
where the perpendicular 
drawn from C cuts the 
horizontal passing through 
the second point of divis- 
ion, and so on for all the 
remaining points. The 
curve A> B C E F A^ 
drawn through all the 
points thus obtained, is 
the helix required. 

To draw the vertical 
elevation of the solid con- 
tained bettueen two helical 
surfaces and two concen- 
tric cyli.yiders (Fig. 278). 

A helical surface is 
generated by the revolu- 
tion of a straight line 
round the axis of a cylin- 
der, its outer end moving in a helix, and the line itself forming with the axis 
a constant and invariable angle. 

Let A' C F' and K' M' 0' represent the concentric bases of the cylinders, 
whose common axis S T is vertical ; the curve of the exterior helix A' E F A^ 
is the first to be drawn according to the method above shown. Then, having set 
off from A* to A' the thickness of the required solid, draw through A^ another 
helix equal and similar to the former. Now construct, as above, similar helices, 
K C and K^ C 0^ of the same pitch as the last, but on the interior cylinder. 





ORTHOGRAPHIC PROJECTION. 



141 




-\ 



The lines A' K', B' L', C M', etc., represent the horizontal projections of the 
various positions of the generating straight line, which, in the present example, 
has been supposed to be 
horizontal ; and these lines 
are projected vertically at 
A^ K, B L, etc. 

In the position A' K 
the generating line is pro- 
jected in its actual length, 
and at the position C M' 
its vertical projection is the 
point C. The same re- 
mark applies to the genera- 
trix of the second helix. 

To determine the verti- 
cal projection of the solid 
formed hy a sphere moving 
in a helical curve (Fig. 
279). 

Let A' C E' be the base 
of a cylinder, upon which 
the centre point C of a 
sphere whose radius is a' C 
describes a helix, which is 
projected on the vertical 
plane in the curve A C E J, 
determined as before. From 
the various points A, B, 

C, D , in this curve, 

as centres, describe circles 

with the radius a' C \ these 

denote the various positions 

of the sphere during its 

helical motion ; and, if lines 

be drawn touching them, 

the curves thereby formed will constitute the figure required. One of these 

curves disappears at 0, but reappears again at I. The exterior and interior 

circles of the plan represent the horizontal projection of the solid in question. 

The co?iical helix differs from the cylindrical one in that it is described on 
the surface of a cone instead of on that of a cylinder ; but the construction 
differs but slightly from the one described. By following out the same prin- 
ciples, helices may be represented as lying upon spheres or upon any other 
surfaces of revolution. 




Fig. 279. 



DEYELOPMEXT OF SURFACES. 



The development of the surface of a solid is the drawing or unrolling on a 
plane the form of its covering, the form that cut out of paper would exactly fit 
and cover the surface of the solid. Frequently, in practice, the form of the 



142 



ORTHOGRAPHIC PROJECTION. 



surface of a solid is found by applying paper or thin sheet-brass directly to the 
solid and cutting it to fit. 

To develop the surface of a cylinder formed by the intersection of another 
equal cylinder^ as the knee of a stove-pipe (Fig. 280). 

Let A B D be the elevation of the pipe or cylinder. Above A B describe 
the semicircle A' 4' B' of the same diameter as the pipe ; divide this semicircle 





^ 


/^__j 


1- ^' 


6 

/ 


y 








i 








V 

I 




into any number of equal parts, 
eight for instance ; through these 
points, 1', 2', 3', etc., draw lines 
parallel to the side A C of the pipe, 
and cutting the line C D of the in- 
tersection of the two cylinders. 
Lay off A'' B" equal to the semicir- 
cle A' 4' B', and divided into the 
same number of equal parts ; 
through these points of division 
erect perpendiculars to A" B", and 
on these perpendiculars lay off the 
distances A" C", Y 1", %" %\ ?>" 3", 
and so on, corresponding to A C, 

1 1, 2 2, 3 3, etc., in preceding figure. Through the points C", 1'', 2" , D", 

draw connecting lines, which gives but one half of the surface of the pipe, the 

other being exactly similar to it. 

To develop the surface of a cylinder intersected hy another cylinder, as in 

the formation of a T-pipe (Fig. 281). 

The construction is similar to the preceding. 

To develop the surface of a right cone (Fig. 282). 

From C as a centre, with a radius, 0' A', equal to the inclined side A C of 




Fig. 280. 



ORTHOGRAPHIC PROJECTION. 



143 



the cone, describe an arc of a circle, and on this arc lay off the distance 
A' B' A', equal to the circumference of the base of the cone ; connect A' C and 
C A'', and A' B' A' C is the developed surface required. 

To develop the surface of the frustum of a cone^ D A B E (Fig. 282). 
D' E' D" is the development of the cut-off cone C D E as shown by the 

preceding construction, and A' B' A' 
D'' E' D' the developed surface of the 
frustum. 

To develop the surface of a frus- 
ttim of a cone, ivhen the cutting i^lane 
a b is i?iclined to the base (Fig. 282). 

On A B, the base, describe the 
semicircle A 3' B ; divide the semicir- 
cle into any number of equal parts, 
six for instance ; from each point of 
division, 1', 2', 3', 4', 5', let fall perpen- 
diculars to the base at 1, 2, 3, 4, 5 ; 
^^ connect each of these last points with 




Fig. 282. 



the apex C. Divide now the arc A' B' A", equal to the circumference of the 
base A 3 B, into twelve equal parts ; each of these parts by the construction is 
equal to the arc A 1', 1' 2' ; connect these points of division with the point C ; 
on C A' take C a' equal to C a, a being the point at which the plane cuts the 
inclined side of the cone ; in the same way on C B', lay off C V equal to C l. 

All the lines connecting the apex C with the base, included within the two 
inclined sides, are represented as less than their actual length, and must be 
projected on the inclined sides to determine their absolute dimensions ; project, 
therefore, the points 1', 2", 3% 4', 5^ at which the cutting plane intersects the 
lines Cl, C 2, C 3, C 4, C 5, by drawing parallels to the base through these 
points to the inclined side C B. Now lay off C Y\ C 2"', etc., equal to C V ^ 

C 2' \ etc. ; connect the points a\ \\1\ V, a!\ and o! A' B' A" a!' V 

is the developed surface. 



144 



ORTHOGRAPHIC PROJECTION. 



To develop the surface of a sphere or hall (Figs. 283, 284). 

The surface can not be accurately represented on a plane, but only 
mately by gores. Let CAB (Fig. 284) be the eighth of a hemisphere : 
describe the quarter circle D A c ; divide this arc into any number of 
equal parts, six for instance; from the points of division 
1, 2, 3, . . . let fall perpendiculars on C D, and from the 
intersections with this line describe arcs 1' 1", 2' 2", 
3' 3^ . . . cutting the line B at 1\ 2", 3", . . . 
on the straight line CD' (Fig. 283), lay off 
C D' equal to the arc D A c, with as many 



approxi- 
on CD 




>1^ 




Fig. 284. 



equal divisions ; then from either side of this line lay off V" 1"", 2'" 2"" .... 

D' B' equal to the arcs 1' l^ 2' 2" D B (Fig. 284). Connect the points 

C, 1"\ %"\ .... and C A' B' is approximately the developed surface. 

In the preceding demonstrations the forms are described to cover the sur- 
face only ; in construction, allowance is to 
be made for lap by the addition of mar- 
gins on each side. And on account of the 
r i difficulty, in the formation of hemispheri- 
cal ends of boilers, of bringing all the 
gores together at the apex, it is usual to 
make them, as shown (Fig. 285), by cut- 
ting short the gores, and surmounting the 
centre with a cap-piece. 

For small boilers and air chambers the 
spherical ends are dished. 

SHADE LINES. 

The effectiveness of outline drawings is 
increased by the use of shade lines; the 
method is wholly conventional. The rule 
used in preparing drawings for the United 
States Patent Office is the simplest and the one generally used in this country. 
In this the light falls from the upper left-hand corner of the sheet of drawing- 
paper, and at an angle of 45° ; hence, the right-hand and lower edge of a 
projection (Fig. 286) and the left-hand and upper edge of a recess appear in 
heavy lines (Fig. 287). In the case of a circular object the shade is ter- 




FiG. 285. 



ORTHOGRAPHIC PROJECTION. 



145 





O 



Fig. 



Fig. 287. 



Fig. 288. 



Elevation. 




Fig. 289. 



n 



146 



ORTHOGRAPHIC PROJECTION. 



minated by a diameter inclined at an angle of 45°, the shade being a graduated 
one, as shown in Fig. 288. 

Fig. 289 is an example of this method. 

In a second method the elevation is shaded, as in the foregoing, but in the 
plan the light falls from the lower left-hand corner of the drawing, making the 
upper and right-hand edges of projections and the lower and left-hand side of 

Elevation. 




Fig. 290. 



recesses shaded. Examples of this method are shown in Fig. 290. In the 
orthographic projection of solids the boundary lines between surfaces in the 
light and shadow are made heavy. 

Still another method is described in the following chapter on " Shades and 
Shadows," where the light falls over the left shoulder, and this is the one gen- 
erally used in the casting of shadows and often in topographical drawings. 



SHADES AND SHADOWS. 

Rays of light are diffused through space in straight lines, and the direct 
rays of the sun may be regarded as parallel. The light on an object may come 
directly from the source of light, or by reflection from other objects or surfaces 
exposed to light. The surfaces of an object under direct light are the most 
strongly illuminated, while other surfaces, from their form or position receiv- 
ing less light, are in shade or direct shadow. Shadows are cast by an object 
upon another object by the interception of light, or upon any surface by pro- 
jections or undercutting. The limit of the line of direct shadow is called the 
line of shade. 

In the delineation of shadows, the most convenient mode of regarding the 
rays of light is, in all cases, as falling in the direction of the diagonal of a cube, 
of which the sides are parallel to the planes of projection. The projections of 
the ray form each an angle of 45° with, the ground line. This is not true of 
the ray itself in space, for that forms an angle of 54° 44' with the ground line, 
and an angle of 35° 16' with each of the planes of projection. 

To find the shadow of a point, as A, A' (Fig. 291), on either plane of pro- 
jection, the vertical, for instance, draw a line through the horizontal projection 




Fig. 291 



of the point A' at an angle of 45° with the ground line, L T, and at the point 
of intersection of those lines, a', erect a perpendicular to intersect the vertical 
projection of the ray through A, which will be at the point «, the shadow in 
question. 

The converse of this method determines the shadow of the point on the 



148 



SHADES AND SHADOWS. 



horizontal plane. The shadow thrown by B of the given line falls at J, and the 
straight line a h, which joins these' two points, is the shadow required. 

The line ah i^ equal and parallel to the given line A B ; this results from 
the circumstance that the latter is parallel to the vertical plane. 



IV 



c^ 



H 21 



\\ 



T- 



V 



^# 



\ 



\ 




A^^ W 3 ^ 




^^^^^^^^^ 




Fig. 293. 

The shadows of a rectangular slip of paper or wood, A B C D, cast upon the 
same vertical plane and parallel to it, is the rectangle A B D (Fig. 291). 

When the object is not parallel to the given plane, the shadow cast is no 
longer a figure equal and similarly placed, but the method of determining it is 
similar (Fig. 292). 

By a combination of the foregoing principles, the shadow of a slip of mould- 
ing placed on the vertical plane (Fig. 293) is determined. 



A c:bd 





Fig. 294 shows the shadow cast by a rectangular slip of cardboard at right 
angles to the vertical plane ; Fig. 295, the shadow cast by a slip parallel to the 
ground plane and at right angles to the vertical plane, which is itself set at a 



SHADES AND SHADOWS. 



149 



horizontal angle; Fig. 296, the shadow of the slip cast on a concave surface; 
Fig. 297, the shadow cast on a vertical plane by a circle parallel to it; Figs. 
298, 299, 301, the shadows on a vertical plane by circles in various positions 





Fig. 297. 



Fig. 298. 



relative to this plane, in all which the shadow assumes the form of an ellipse ; 
Fig. 300, the shadow cast by a circle horizontal to the ground plane on a verti- 
cal convex surface ; Fig. 302, the shadow cast by a circle parallel to the vertical 





Fig. 299. 



Fig. 300. 



})lane of the projection, the shadow being thrown upon two plane surfaces at 



an angle to each otl>er. 



150 



SHADES AND SHADOWS. 



In every drawing where the shadows are to be inserted, it is of the utmost 
importance that the projections which represent tiie object whose shadow is 
required, and the surface upon which this shadow is cast, should be exactly de- 







Fig. 301. 



Fig. 



fined by lines drawn lightly in India ink, and, to prevent mistakes, erase all 
pencil marks before proceeding to the operations determining the lines of 
shadow. 



JlITLO 




.<i> 


-^ 




\ 


iiiii 


^' ^ 


III III 


IjK, / 


||lj|}Ufl| 


1 llB ^ 


III 


1 M' 



t/l\r ,T 



Fig. 303. 



Fig. 304. 



In Fig. 303 the three sides of the hexagonal pyramid. A' B' F', A' B' C, and 
A' C D', alone receive the light ; consequently the edges A' F' and A' D' are 
the lines of shade. To determine the shadow cast by these two lines, draw 
from the projections of the vertex of the pyramid the lines A h and A' a' paral- 




SHADES AND SHADOWS. 151 

lei to the ray of light; then erect at the points a perpendicular to the ground 
line, which gives at a' the shadow of the vertex on the horizontal plane on the 
other side of the ground line ; and finally join this last point, a\ with the points 
D' and F' ; the lines D' o! and F' a! are the 
outlines of the required shadow on the 
horizontal plane. But, as the pyramid is 
sufficiently near the vertical plane to throw 
a portion of its shadow upon it, this por- 
tion may be found by erecting at the point 
c, where the line A' a! cuts the ground 
line, a perpendicular c a, intersecting the 
line Kh in a\ the lines a d and a e join- 
ing this point with those where the hori- 
zontal part of the shadow meets the ground 
line, will be its outline upon the vertical 
plane. 

Fig. 304 represents the shade on a cyl- 
inder placed vertically, and its shadow cast 
on two planes of projection. ' * 

Draw the tangents D' d' and C c' parallel to the rays of light ; these are the 
outlines of the shadow cast upon the horizontal plaue. Through the point of 
contact C draw the vertical line C C ; this line denotes the line of shade upon 
the surface of the cylinder. 

If the shadow of this cylinder were entirely cast upon the horizontal plane, 
it would terminate in a semicircle drawn from the centre o\ with a radius equal 
to that of the base ; but a part of the shadow of the upper part is thrown upon 
the vertical plane, and its outline is defined by an ellipse drawn in the manner 
indicated in Fig. 298. 

Fig. 305 represents the line of shade and the shadow of a horizontal cylinder 
inclined to the vertical plane. The construction in this case is the same as that 
explained by Fig. 304. Of the horizontal lines of shade, C D alone is visible 
in the elevation, while A B alone is seen in the plan, where it may be found 
by drawing a perpendicular from A meeting the base F' Gr' in A'. The line 
A' E', drawn parallel to the axis of the cylinder, is the line of shade required. 
Project the shadow of the line A B on the vertical plane, as in previous exam- 
ples, to define the outline of the shadow of the cylinder. 

The example here given presents the particular case in which the bases of 
the cylinder are parallel to the direction of the rays of light. In this case, to 
determine the line A' E' lay off the angle A' L A^ equal to 35° 16', so that the 
side A^ L shall be tangent to the circle F' A^ Gr', representing the base of the 
cylinder laid down on the horizontal plane ; through the point of tangency, 
A', draw a line. A' E', parallel to the axis of the cylinder, for the line of 
shade. 

Fig. 306 represents a cylinder upon which a shadow is thrown by a rec- 
tangular cap, of which the sides are parallel to the planes of projection. The 
shadow in this case is derived from the edges A' D' and A' E', the first of which, 
being perpendicular to the plane of projection, gives a straight line at an angle 
of 45° for the outline of its shadow, whereas the side A' E' being parallel to 



152 



SHADES AND SHADOWS. 



that plane, its shadow is determined by a portion of a circle, ai c^ described 
from the centre, 0. 

If the cap be hexagonal (Fig. 307), or circular (Fig. 308), the mode of con- 
struction is similar. Commence by finding the points which indicate the main 



J 



J) 



\ ^- 


--.1 ■-, 




E 


^^, 


' V 


\ 








C'\ 





a \ H 



pjiiiP'|>i 



-I 

c 




Fig. 306. 



Fig. 307 



Fig. 



direction of the outline. To ascertain the point a at which the shadow com- 
mences, draw from a! the line a! A' at an angle of 45°, and projected vertically 
to a A. Then the highest point h (Fig. 308) is determined by the intersection 
of the radius 0' B', drawn parallel to the ray, with the circumference of the 
base of the cylinder on which the shadow is cast ; the point c, where the outline 
of the cast shadow intersects the line of shade, is determined by a like process. 
In Figs. 309, 310, and 311 a hexagonal prism is substituted for the cylinder. 



4' B 


C 


rc !""- 


'S 


! ^^ 1 ^ 


X ' 1 \ 


i /' 


1 ^-^ 


A^A 


L ! -.. 


4--^ 


c\ 



C B 



llf'f I 'jlljjljjl 




Fig. 309. 



Fig. 310. 



D^^ 



G-^ 



4/ v-:r^' 



Iff' 



■\ 



\ A BiJDJE 



'^W 



I ' 



d '^iiiyil I 



Fig. 311. 



Fig. 312 shows the section of a steam-cylinder by a plane passing through 
its axis, with its piston and rod in full. To define its shadows, conceive the 
piston P to be removed ; the shadow cast into the interior of the cylinder will 
then consist of that projected by the vertical edge B C, and by a portion of the 
horizontal edge B A. To find the first, draw through B' a line, B' J', at an 
angle of 45° with B' A' ; the point Z*', where this line meets the interior surface 
of the cylinder, being projected vertically, gives the line hf as the outline of 



SHADES AND SHADOWS. 



158 



the shadow sought. Then, parallel to the direction of the light, draw a tangent 
at F' to the inner circle of the base ; its point of contact, being projected to F 
in the elevation, marks the commencement of the outline 
of the shadow cast by the upper edge of the cylinder. 
The point ^, where it terminates, will be the intersection 
of the straight line /^, already determined, with a ray, 
B ^, from the upper extremity of the edge B C ; and any 
intermediate point in the curve, as e, may be found in the 
same way. The outline of the shadow required will then 
be the curve Feb and the straight line b f. Insert the 
piston P and its rod T into the cylinder, as shown. The 
lower surface of the piston will then cast a shadow upon 
the interior surface of the cylinder, of which the outline 
D d h may be formed as above. The piston-rod T, 
being cylindrical and vertical, casts a shadow into the in- 
terior of the cylinder, consisting of the rectangle ij I k 
drawn parallel to the axis. 

In Fig. 313 is shown the interior of a cylinder closed 
at the top with the exception of a central aperture 

through which the light is admitted. Follow previous construction, but to 
determine what parts of the upper and lower edges of the central aperture 
cast their shadows into the interior of the cylinder, establish the position of 
the point of intersection, c, of the two curves b c f smd ace, shadows of these 
edges, which is the cast shadow of the lowest point, 0, in the curve D 0, pre- 
viously laid down in the circular opening of the cover. 

For the shadow cast in the interior of a cylinder, in section, inclined to the 
horizontal plane (Fig. 314), on a convenient part of the paper draw the diag- 




FiG. 312. 




Fig. 313. 



Fig. 314. 



Fig. 315. 



onal m o, parallel to the line of light A' E, and construct a square, mnop (Fig. 
315) ; from one of the extremities, o, draw the line o r, parallel to A' B', and 
through the opposite extremity, w?, draw a perpendicular, r 5, to this line, and 
set off on the perpendicular the distance r s equal to the side of the square, and 
join s 0. Now, draw through the point A', in the original figure, a line. A' a', 



154 



SHADES AND SHADOWS. 



parallel to s o, intersecting the cir- 
cle A' a' B' in the point a', which, 
being projected by a line parallel to 
the axis of the cylinder, and meet- 
ing the line drawn from A at an 
angle of 45°, gives the first point 
a in the curve C d a. The other 
points are obtained in like manner, 
by drawing at pleasure other lines, 
such as D' d', parallel to A' a'. 

For the shadow cast into the in- 
terior of a hollow hemisphere (Fig. 
316), let A B C D represent the 
horizontal projection of a concave 
hemisphere. Draw through the 
centre a line, A C, perpendicular to 
the ray of light ; the points B and 
D will at once give the extremities of the curves sought. On any point of B D 
produced, as 0', construct the semicircle A' a' C with a radius. A' 0', equal to 

A 0. At A' draw the line 




Fig. 316. 



,JB^ 




Fig. 317.- 



^ A' a', making an angle of 35° 
16' with A' C. The angle 
f. made by the ray of light in 

\ ''^, , space with the planes of pro- 

•, y'' N, jection, a\ the point of inter- 

A \ section of the line with the 

,- ' -——■'' \ semicircle, projected to a, gives 

cr- --'' ' yu a point of the outline of the 

----- --'''' shadow. Similar sections, as E F 

parallel to A C, will give other points. As this 
outline is an ellipse whose axes are B D and twice 
a, it may be constructed, when the point a is 
determined, by the ordinary methods for ellipses. 
In a niche (Fig. 317) the shadow of the cir- 
cular outline upon the spherical portion is part 
of an ellipse, e c D, found as in the previous 
example. The point e', where this ellipse cuts 
the horizontal diameter A F, limits the cast 
shadow upon the spherical surface ; therefore 
all the points beneath it must be determined 
upon the cylindrical part. Through A' in the 
plan draw the line A' a' parallel to the ray of 
light; project a' till it intersects the line of 
light A a in the elevation at a. The line of 
shadow below a is the shadow of the edge of 
the cylinder, and is a straight line. The line 
of shadow between a and e is the outline of the 
circular part falling on a cylindrical surface. 



SHADES AND SHADOWS. 



155 



The line of shade on a sphere (Fig. 318) in elevation and plan consists of 
two equal ellipses of which the major axes are the diameters D and C D' 
drawn at an angle of 45°. 





Fig. 318. 

To find the minor axes of these curves, assume any point, 0^ upon the pro- 
longation of the diameter of the perpendicular C D' ; draw through this point 
the straight line 0^ o\ inclined at an angle of 35° 16', to A' B' or its parallel, and 
erect upon it the perpendicular E'' F^ The projection of the two extremities 
E' and F' upon the line A' B' will give in the plan the line E' F' for the length 
of the required minor axis of the ellipse, i. e., of the line of shade in the plan ; 
and this line, being again transferred to the elevation, determines the minor 
axis E F of the line of shade in the elevation. 

The shadow cast upon the horizontal plane is an .ellipse of which the major 
axis is the transfer of the points E'' and F^ and the minor axis is on the line of 
the transfer of the point 0^ and is equal to the diameter C D'. 

The outlines of the shadows may be constructed by the aid of points. 

Draw the plan and elevation of a cylindrical ring with central lines 
(Fig. 319). 

On the elevation draw rays of light, a, J, to the exterior surface of the ring ; 



156 



SHADES ANP SHADOWS. 



the tangent points define the limit of shade ; draw a tangent at d at an angle 
of 35° 16', and through d a line parallel with the base ; transfer c d to C^ d^ in 
plan, and project d^ to d"^ ; its intersection with the parallel from d will be 
another point in the shade, as also the point c on the central line ; project F to 
/ on central horizontal line of elevation for another point. The lines of shade 
on both sides of the ring will be the same, and the extremities at a and h will 
be curves tangent to each other ; draw at these points short arcs of small radius 
and connect these arcs through the points/, c, d^, for the limit of shade. 




-Fig. 319. 

For the limit of shade on the plan, transfer C^ d'^ to the opposite side of C^ ; 
Q"^ d^ will be one half the minor axis and E F the major axis of an ellipse, which 
will define the line of shade for the exterior of the ring. Lay oif to g from the 
interior of the ring the distance G d^ ; C^ g will be half the major axis and 
E* F'* the minor axis of the ellipse of shade on the interior of the ring. 

For the shadow of the ring in plan, draw rays of light through E and F, 
and in elevation through/ to/^ ; project/' to F^ and draw through F^ a paral- 
lel to E F ; draw a diagonal ray tangent at h to the base at h\ transfer C^ It^ to 
C^ h^ which is one half the major axis for the line of the limit of shadow of the 



SHADES AND SHADOWS. 



15' 



exterior of the ring. Draw rays of light through E* F*, draw a diagonal ray 
tangent at e, transfer e* C^ to C e^ ; C^ e^ will be half the minor axis, and E'' F^ 
the major axis of the ellipse which defines 
the limit of shadow for the interior of the Ai 
ring. 

The shadow on the surface of a grooved 
pulley (Fig. 320) is cast by the circumfer- 
ence of the edge A' B'. Draw central lines 
through C of the plan and describe a circle 
C b with the radius of the least diameter of 
the pulley ; from i draw a line b a at an 
angle of 45° ; project a to a', and from a' 
draw a' b' as a limiting point in the line of 
shade, for another point draw a horizontal 
line from b' intersecting the centre line at 
b^ ; project c and d on the plan to the ele- 
vation, and intersect the projection of d at 
d' by a ray of light from c' ; d' is the high- 
est point in the curve. Take any horizon- 
tal line E F in the elevation and describe 
from C on the plan an arc with a radius 
equal to one half this line ; draw from C 
project to e\ and from e' as a centre describe an arc with a radius equal to C B ; 
the point of intersection of this arc with the circumference of the plan E F is 
projected to/'. The limit of shade is then drawn through the points b', d', b'^, 
/', and g. 




Fig. 320. 



ray intersecting E F at e, which 






z^\ 



.. x i 
\ 



CL 



V 



4^. 



\ 



/ 



— 7 
I ^\Ji'_ 

/ 



i 



¥■ 



/ 






- I 




Fig. 3:^1. 



Fig. 321 represents the projections of a screw with a single square thread, 
and placed in a horizontal position, A' o! being the direction of the ray of 
light. The shadow is simply that cast by the outer edge, A B, of the thread 
upon the surface of the inner cylinder ; its outline is delineated in the same 



158 



SHADES AND SHADOWS. 



manner as in treating of a cylinder surmounting another of smaller diameter 
(Fig. 308). 

The shadow cast by the helix ABO upon the concave surface of the square- 
threaded nut is a curve, a C (Fig. 322), determined in the same way as that 
in the interior of a hollow cylinder. The same rule applies to the edges A A" 




Fig. 322. 



and A' E, as well as to those of the helix F G H and the edge H I. The shadow 
of the two edges J K and K L, thrown upon an inclined helical surface, of 
which A L is the generatrix, follows the rules given in Fig. 323. 




Fig. 323. 



SHADES AND SHADOWS. 



159 



In the case of a triangular-threaded screw (Fig. 323) the outer edge, A' C D, 
of the thread projects its shadow upon a helical surface inclining to the left, of 
which the generatrix is known. 

Describe from the centre a number of circles representing the bases of so 
many cylinders, on the surfaces of which suppose helical lines to be traced of 
the same pitch as those which form the exterior edges of the screw. Draw any 
line parallel to the ray of light, as B' E', cutting the circles described in the 
plan in the points B', F', G', E', which are projected to their corresponding 
helical lines in the elevation at B^ F, G, and E. Transferring the point B' to 
its appropriate position B on the edge A' C D, and drawing through the latter a 
line, B Z>, at an angle of 45°, its intersection with the curve B^ G E will give one 
point in the curve of the shadow required. By constructing other curves, as 
H J K, the remaining points in the curve, as A, may be found. 



c- — 



\ 



\ 






\ 






K- 



\ 



>^ 



I 



^ 




The same processes are requisite to determine the outlines of the shadows 
cast into the interior surfaces of the corresponding nut (Fig. 324). These 
shadows are derived not only from the helical edge, A B D, but also from that 
of the generatrix, A C. 

The principles here laid down and illustrated are a sufficient guide for the 
delineation of the shades and shadows of nearly all ordinary forms and com- 
binations of machinery and architecture. Students should not copy the figures 
as here represented, but should adopt some convenient scale somewhat larger, 
and construct drawings according to the description. 



MAXIPULATIOX OF SHADIXG AXD SHADOWS, AXD METHODS OF TIXTIXG. 

The intensity of a shade or shadow is regulated by the forms of bodies, the 
position that they occupy in relation to the light, and the distance from 
the eve. 



160 SHADES AND SHADOWS. 

Surfaces in the Light. — Flat surfaces wholly exposed to the light, and at 
all points equidistant from the eye, receive a uniform tint. 

Of two parallel surfaces, the one nearer the eye receives a lighter tint. Every 
surface exposed to the light, but not parallel to the plane of projection, having 
no two points equally distant from the eye, receives unequal tints, gradually 
increasing in depth as the parts recede from the eye. Of two surfaces un- 
equally exposed to the light, the one more nearly perpendicular to the rays re- 
ceives the fainter tint. 

Surfaces in Shade. — When a surface entirely in the shade is parallel to the 
plane of projection, it receives a uniform dark tint. Of two objects in the 
shade parallel to each other, the one nearer the eye receives the darker tint. 
On a surface in the shade, inclined to the plane of projection, the parts nearest 
the eye receive the deepest tint. 

If two surfaces exposed to the light, but unequally inclined to its rays, have 
a shadow cast upon them, the part of it which falls upon the more lighted sur- 
face should be darker than where it falls upon the other surface. 

The methods of shading generally adopted are either by the superposition 
of any number of fiat tints, or by tints softened off at their edges. 

(See Plates I, II, III, IV, Y, XI, XII, and XV.) 

In the shading of a prism by flat tints (Plate I, Fig. 4), the face, ab c d^ 
being parallel to the plane of projection, receives a uniform tint usually of India 
ink or sepia. When the surface to be tinted is large, put on a very light tint 
first, and then go over the surface with a tint sufficiently dark to give the 
desired tone. The face, bghc, being inclined to the plane of projection, re- 
ceives a graduated tint from the line ^ c to the line g h. This is obtained by 
laying on a succession of flat tints. Divide the plan i' g' into equal parts, as at 
the points 1', 2', and from these points project lines upon, and parallel to the 
sides of, the face b gh c. These lines should b^ drawn very lightly in pencil, 
as they merely serve to circumscribe the tints. A grayish tint is then spread 
over the portion of the face between the lines b c and 1, 1 (Fig. 3). When this 
is dry, the same tint is laid on again, and extended over the space comprised 
within the lines b c and 2, 2 (Fig. 3). A third tint, covering the whole surface 
b chg (Fig. 4), imparts the desired graduated shade to that side of the prism. 
The number of tints in the graduated shade depends upon the size of the sur- 
face, and the depth of tint must vary according to the number used. The 
greater the number, the softer the appearance and the less harsh the lines which 
border the different tints. This method is preferable to that sometimes em- 
ployed of first covering the whole surface b ghc with a faint tint, then putting 
on a second tint b%% c, followed by a harrow wash bile, because the outline 
of each wash remains untouched and presents a prominence and harshness. 

The face a dfe, also inclined to the plane of projection, should, as it is en- 
tirely in the light, be covered by a series of much fainter tints than the surface 
b g he, which is in the shade, darkening, however, toward the line ef The 
gradation of tint is effected as on the face b g h c. 

In shading a cylinder by means of flat tints (Figs. 5-12), the line of separa- 
tion between the light and shade, a b (Fig. 6), is determined by the radius a' 
(Fig. 5), drawn perpendicular to the rays of light R 0. The part of the eleva- 
tion of the cylinder which is in the shade is comprised between the lines a b 



SHADES AND SHADOWS. 161 

and c d. This portion, then, should be shaded as a surface in the shade in- 
clined to the plane of projection. All the remaining part that is visible of the 
cylinder presents itself to the light ; but, in consequence of its curvature, the 
rays of light form angles varying at every part of its surface, which should re- 
ceive a graduated tint. Determine the part of the surface that is most directly 
affected by the light, situated about the line e i (Fig. 12). The visual rays are 
perpendicular to the vertical plane and parallel to V ; the part which ap- 
pears clearest to the eye may be limited by the line T 0, which bisects the 
angle V R. Project the points e' and m\ and draw the lines e i and m n 
(Fig. 12) ; the surface comprised between these lines will represent the lightest 
part of the cylinder. 

This part should have no tint upon it whatever if the cylinder is polished 
— as a turned iron shaft or a marble column ; but if the surface of the cylinder 
be rough, as a cast-iron pipe, then a very light tint, considerably lighter than 
on any other part, may be given it. 

Divide the half-plan of the cylinder/' ??2' a' c' into any number of equal 
parts by faint pencil-lines, and begin the shading by laying a tint over a c dh 
(Fig. 6). When this is dry, put on a second tint covering the line ah oi sepa- 
ration of light and shade, and extending over one division (Fig. 7). Proceed 
in this wa}^, as shown in Figs. 6-12, until the whole of that part of the cylinder 
which is in the shade is covered. Treat in a similar manner the part/e*^ 
(Fig. 12), and complete the operation by covering the whole surface of the cyl- 
inder, excepting the surface e m n ^, with a very light tint. 

In shading the frustum of a hexagonal pyramid (Plate II), the face ah c d 
should receive a uniform flat tint, as in Plate I, or the tint may be slightly deep- 
ened toward the top of the pyramid, as that surface is not quite parallel to the 
vertical plane. 

The face hglic, being inclined and in the shade, should receive a dark tint ; 
darkest where it meets the line h c, and gradually becoming lighter as it ap- 
proaches the line g h. To produce this effect, apply a narrow strip of tint at 
he (Fig. 6), and then, qualifying the tint in the brush with a little water, join 
another strip to this, and finally, by means of another brush moistened with 
water, soften off this second strip toward the line 1, 1, which may be taken as 
the limit of the first tint. 

When the first tint is dry, cover it with a second, which must be similarly 
treated, and should extend up to the line 2, 2 (Fig. 7). Proceed in this manner 
with other tints, until the whole face h g h c is shaded (Fig. 8). In the same 
way the face e a df is to be covered, though with a considerably lighter tint, for 
the rays of light fall upon it almost perpendicularly. 

The tint on these two faces should be slightly graduated from ea to fd, and 
from ch to h gi but this graduation may be disregarded until some proficiency 
in shading has been acquired. 

In shading a cylinder by means of softened tints (Plate II), the boundary 
of each tint being indicated, as in Plate I, the first strip of tint must cover the 
line of extreme shade a h, and then be softened off on each side. Other succes- 
sively wider strips of tint follow, and receive the same treatment as the one first 
put on. 

If, after shading a figure by the foregoing method, any very apparent ine- 
12 



162 SHADES AND SHADOWS. 

qualities present themselves in the shades, such defects may be remedied, in 
some measure, by washing oS. excesses of tint with a brush or a damp sponge, 
and by supplying a little colour to those parts which are too light. 

Dexterity in shading figures by softened tints is facilitated by practising 
upon large surfaces. 

Whatman's best rough-grained drawing-paper is better adapted for receiving 
colour than any other. Of this paper, the double-elephant size is preferable, as 
it possesses a peculiar consistence and grain. The face of the paper to be used 
is the one on which the water-mark is read correctly. 

The paper for a coloured drawing ought always to be damp-stretched 
(page 54). 

The size of the brushes used depends upon the scale to which the drawing 
is made. Long, thin brushes, however, should be avoided. Those possessing 
corpulent bodies and fine points are to be preferred, as they retain a greater 
quantity of colour, and are more manageable. 

Sable brushes are more durable and better than camel's hair, but more ex- 
pensive. Economy may be practised by using camel's hair for the larger sizes 
and red or black sable for the smaller. 

During the process of laying on a flat tint, if the surface be large, the draw- 
ing may be slightly inclined, and the brush well charged with colour, so that 
the lower edge of the tint may be kept moist until the Avhole surface is covered. 
In tinting a small surface, the brush should never have much colour in it, other- 
wise the surface will unavoidably present coarse, ragged edges, and an uneven 
appearance throughout. 

All objects with curved outlines have a certain amount of reflected light 
imparted to them. Bodies, whatever may be their form, are affected by re- 
flected light; but, with a few exceptions, this light is only appreciable on 
curved surfaces. 

In proportion to its degree of polish or brightness is the amount of reflected 
light which a body spreads over adjacent objects, and also its own susceptibility 
of illumination under the reflection from other bodies. A polished steam- 
cylinder or a white porcelain vase both receives and imparts more reflected light 
than a rough casting or a stone pitcher. 

Shade, even the most inconsiderable, ought never to extend to the outline 
of any smooth circular body. On a polished sphere the shade should be deli- 
cately softened off just before it meets the circumference, and, when the shad- 
ing is completed, the body-colour intended for the sphere may be carried on to 
its outline. This will give a clearness to the part of the sphere influenced by 
reflected light which it could not have possessed if the shade-tint had been ex- 
tended to its circumference. Very little shade should be suffered to reach the 
outlines even of rough circular bodies, lest the colouring present a harsh, 
unreal appearance. 

Shadows become lighter as they recede from the bodies w^hich cast them, 
and appear to increase in depth as their distance from the spectator diminishes. 
In Nature this increase is only appreciable at considerable distances. But it is 
important for the effective representation of machinery that the variation in 
the distance of each part from the spectator should strike the eye, and an exag- 
geration in expressing the var3dng depths of the shadows is one means of effect- 



SHADES AND SHADOWS. 163 

ing that object. The shadows on the nearest and most prominent parts of a 
machine should be made as dark as colour can render them, the colourist being 
thus enabled to exhibit a marked difference in the shadows on the other parts 
of the machine as they recede from the eye. The same direction is applicable 
to shades. The shade on a cylinder, situated near the spectator, ought to be 
darker than on one more remote. As a general rule, the colour on a machine 
should become lighter as the parts on which it is placed recede from the eye. 

Plates III and IV present some examples of finished shading and shadows 
of the solids given under the head of " Orthographic Projection." 

The direction of the shades and shadows in the elevation is from the upper 
left-hand corner, and in the plan from the lower left-hand corner. 

The shadow on a concave surface is darkest toward its outline, and becomes 
lighter as it nears the edge of the object. Reflection from the part of the sur- 
face on which the light falls causes this gradual diminution in the depth of 
the shadow, the greatest amount of reflection being opposite the greatest 
amount of light. No brilliant or extreme light should be left on concave sur- 
faces, as such lights tend to render it doubtful whether the objects presented 
are concave or convex. After the body-colour has been put on, a faint wash 
should be passed very lightly over the whole concavity. This will not only 
modify and subdue the light, but soften asperities in the tinting, which are 
particularly unsightly on a concave surface. 

The lightest part of a sphere is confined to a mere point, around which the 
shade gradually increases as it recedes. This point is not indicated on the 
figure because the shade-tint on a sphere ought not to be spread over a greater 
portion of its surface than is shown there. The very delicate and hardly per- 
ceptible progression of the shade in the, immediate vicinity of the light-point 
should be effected by means of the body-colour, either by lightening it toward 
the light point for polished or light-coloured curved surfaces, or deepening the 
body-colour for unpolished surfaces from the light point until it meets the 
shade tint over which it is spread uniformly. 

To shade a sphere effectively, put on two or three softened-off tints in the 
form of crescents converging toward the light-point, the first one being carried 
over the point of deepest shade. 

A ring (Plate IV, Fig. 7) is a difficult object to shade. To change with ac- 
curate and effective gradation the shade from the inside to the outside of the 
ring, to leave with regularity a line of light upon its surface, and to project its 
shadow with precision, requires attention and care. 

It should be noted that the depth of a shadow on any object is in propor- 
tion to the degree of light which it encounters on the surface of that object. 
In the plan (Fig. 6) the shadow of the apex of the cone falls upon the lightest 
point of the sphere and is the darkest part of the shadow. The deepest portion 
of the shadow of the cone on the cylinder in the plan (Fig. 4) is where it coin- 
cides with the line of extreme light. Flat surfaces are similarly affected, the 
shadows thrown on them being less darkly expressed according as their inclina- 
tion to the plane of projection increases. The body-colour on a flat surface 
should, on the contrary, increase in depth as the surface becomes more inclined 
to this plane. 

Reflected light is incident to shadows as well as to shades. This is observ- 



164: SHADES AND SHADOWS. 

able where the shadow of the cone falls upon the cylinder, though to a less ex- 
tent, on other parts of these figures. The reflected light on the cone from the 
sphere or cylinder adds greatly to the effect of the shadows and to the appear- 
ance of the objects themselves. 

The peculiarities and effects of light, shade, and shadow may be seen in the 
examples of screws (Plate V). 

In topographical and architectural drawing artistic effect may often be in- 
troduced, but in mechanical drawing distinctness of outline and accuracy of 
expression are essential ; though, to maintain harmony in the colouring and to 
equalize the appearance of the drawing, large shades should be coloured less 
dark than small ones, at equal distances from the eye, and no very dark shad- 
ing is permissible. 

In preparing colours for tints, great care should be used in grinding. The 
end of the cake should be slightly wetted and rubbed on a porcelain palette, 
then transferred by a wet brush to another saucer, and water added to bring 
to the required tint. Mixed colours should be intimately blended by the brush. 
Grind more than enough of the tint required, and let it stand in the saucer 
till the grosser particles have settled and the liquid is of clear, uniform tint. 
It is common to make little boxes or bags of waste drawing-paper to hold the 
colours instead of saucers; the gross matters^ settling on the bottom, are not 
then so readily disturbed. 

Instead of hard cakes of colour, moist colours are used, either in pans or 
tubes, which saves the trouble of grinding. For flat tints or washes, aniline 
colours, dissolved in water and kept bottled, are the readiest means of colour- 
ing, but are not applicable to finished work. 

If the surface of the paper is greasy and resists colours, dissolve a piece of 
ox-gall, the size of a pea, in a tumbler of water, and use this solution with the 
colours instead of plain water. 

When the brush is too full, as it comes toward the limit of the tint, take up 
the surplus moisture on a wet sponge or piece of cloth or blotting-paper. 

An expeditious way of shading a cylinder, or of delineating the shores of a 
stream or lake, is by drawing with a brush full of the darkest tint along the 
sides, and then, with a wet brush, modifying this tint toward the light from 
the sides, so as to give a shaded appearance. For this purpose, two brushes 
will be necessary — one with colour, the other with water ; also, a tumbler of 
water, and a piece of blotting-paper, to take up the .excess of moisture from 
paper or brush. Often a single line of dark colour blended this way will ex- 
press all that is necessary, but the effect may be improved by a sort of stippling 
with the colour-brush and by extending the line of shade. 

The same effect is obtained better by drawing two faint pencil-lines on the 
elevation of the cylinder, for instance, to indicate the extremes of light and 
shade on its surface and passing the brush, moderately full of the darkest tint, 
down the line of deepest shade, spreading the colour more or less on either side, 
according to the diameter of the cylinder ; then, before this layer of tint is dry, 
if possible, toward the line of extreme light, beginning at the top, and encroach- 
ing slightly over the edge of the first tint, lay on another not quite so dark, but 
about double its width. Put on the second tint before the first is thoroughly 
dry, that its edges may be softened by the application of the second. While 



SHADES AND SHADOWS. 165 

this second tint is still damp, with a much lighter colour in the brush, pro- 
ceed in the same manner with a third tint, and so on to nearly the line of ex- 
treme light. Eepeat this process on the other side of the first tint, approach- 
ing the outline of the cylinder with a very faint wash, so as to represent the 
reflected light which progressively modifies the shade as it nears that line. 
Then let a darkish narrow strip of tint meet and pass along the outline of 
the cylinder on the other side of the extreme line of light, after which gradu- 
ally fainter tints should follow, treated in the manner already described, and 
becoming almost imperceptible just before arriving at the line of light. 

But it is not possible, by the above-described means alone, to impart a suf- 
ficient degree of well-regulated rotundity to the appearance of such an object. 
It may be necessary to equalize the superfluities and deficiencies of colour to 
some extent by a species of gross stippling. This is done by spreading a little 
colour over the parts where it is deficient, and then passing the brush, supplied 
with a very light wash, very lightly over nearly the whole width of the shade. 
This process may be repeated to suit the degree of finish which it is desired to 
give the drawing. The shading of all curved surfaces is treated in the same 
manner. 

The shades having been put in, the shadows follow. Draw the outline of 
the shadow in pencil, and along its inner line, the line which forms a portion 
of the figure of the object whose shadow is to be represented, lay on a strip of 
the darkest tint, wide or narrow, according to the width of the shadow, and 
then, before it is dry, soften off its outer edge. 

The finish is made by a light wash or two of the body-colour, and in pass- 
ing over the shades and shadows care must be taken to manoeuvre the brush at 
such parts quickly and lightly. 

The shades and shadows of a machine being modified in intensity as their 
distance from the eye increases, its body-colour should be treated in a similar 
manner, becoming less bright as the parts of the machine which it covers recede 
from the spectator. 

When the large circular members of a machine have been shaded, the shad- 
ows, and even the body-colour on those parts farthest removed from the eye, are 
to follow, and the proportion of India ink in the tint used should increase as 
the part to be coloured becomes more remote. A little washing, moreover, of 
the most distant parts is allowable, as it gives a pleasing appearance of atmos- 
pheric remoteness, or depth, to the colour thus treated. 

The amount of light and reflection on the members of a machine should 
diminish in intensity as the distance of such objects from the spectator in- 
creases. As it is necessary, for effect, to render on the parts of a machine near- 
est the eye the contrast of light and shade as intense as possible, so, for the 
same object, the light and shade on the remotest parts should be subdued and 
blended according to the extent or size of the machine. 

To add to the definiteness of a coloured mechanical drawing, it is well to 
make the lines of light and shade distinct. 

After having marked in pencil the position of the extreme light, take the 
drawing-pen, filled with a just perceptible tint, and draw a line of colour on 
one side of the line of light, almost touching it ; then with the brush, filled 
with similar light tint, join this line of colour while still wet, and fill up the 



166 SHADES AND SHADOWS. 

space unoccupied by the shade-tint, within which the very light colour in the 
brush will disappear. Treat the part of the object on the other side of the line 
of light in the same way. The extreme depth of shade may, with great effect, 
be indicated by filling the pen with dark shade-tint, and drawing it exactly 
over the line representing the deepest part of the shade. On either side, join- 
ing this strip of dark colour, another, of lighter tint, is to be drawn. Others 
successively lighter follow, until, on one side, the line of the body is joined, and 
on the other the lightest part of the body is nearly reached. The line of light 
is then to be shown, and the faint tint used for this to be spread with the brush 
lightly over the whole of the part of the body that is situated on either side of 
this line, thus blending into smooth rotundity the graduated strips of tint drawn 
by the pen. 

In all tinted drawings the important parts should be more conspicuously 
expressed than the mere adjuncts. Thus, if the drawing be to explain the 
construction of the machine, the tint of the edifice may be more subdued than 
those of the machine ; and if the machine be unimportant, it may be repre- 
sented in mere outline, while the edifice is brought out conspicuously. 

With regard to washings, the soft sponge is an excellent means of correct- 
ing great errors in drawing or colouring, but care must be taken not to rub 
the surface. In removing or softening colour, for large surfaces, use the sponge ; 
for small spots, the brush. While colouring, keep a clean, moist brush by you 
to remove or modify a colour. 

The immediate effect of washing is to soften a drawing, an effect often very 
desirable in architectural and mechanical drawings, and the process is simple 
and easily acquired ; keep the sponge or brush and the water clean ; after the 
washing is complete, take up the excess of moisture with the sponge or brush 
or with a piece of clean blotting-paper. Where vigour is required, let the 
borders of the different tints be distinct. 

There are no conventional tints that draughtsmen have agreed upon to be 
uniformly used to represent different materials. India ink is not a black, but 
a brown, making with a blue a greenish cast, and with gamboge a smear. A 
coloured drawing is better without the use of any India ink at all ; any depth of 
colour may be as well obtained with blue as with black. There is the objection 
to gamboge that it is gummy, and does not wash well, and a better effect is ob- 
tained with yellow ochre. For the reds, the madder colours are the best, as 
they stand washing. For the shade-tint of almost any substance a neutral tint 
is required, such as Payne's gray, or madder brown subdued with indigo. 



MATERIALS 






Seetiort tArou^AAB 



Varied materials enter into the composition of structures and machines, or form 
their supports, which are to be represented by the draughtsman. That of the earths and 
rocks, in their natural position, are 
shown under the head of "Topo- 
graphical Drawing," or by a closer 
imitation of Nature, with or without 
colour. 

Fig. 325 represents a plan and 
section of an earth-bank of a canal, 
with a paved rock- slope. 

A base of rock may be represented 
by stratifications (Fig. 326). 

Rocks, gravels, sands, muds, etc., 
either in their natural or structural 
positions, are shown in ' ' Engineering 
Drawing." 

Earth., when first dug, occupies 
more space than when in its natural 
condition, but, after a time, it shrinks 
and becomes more compact. The 
earth dug out of a hole, when settled, 
will not fill the hole. Sand, gravel, 
loam, and clay, will occupy from 8 
cut. 

Loose, dry sand weighs from 90 to 100 pounds per cubic foot; compacted, 110; 
gravel, about the same ; clay, in the bank, 120 pounds. Sands and gravels are excellent 
material for embankments and fills. The slopes in cuts and fills are usually \\ horizon- 
tal to 1 perpendicular. Sands and gravels are readily drained, and, when dry, are but 
little affected by frost. The clays are hard to drain, heave with the 
frost when wet, and, under the influence of a thaw or excess of 
water, become fluid, but well rammed they are used as puddle walls 
in the centre of reservoir embankments for stanchness. In these 
positions it is recommended that the clay should be compacted 
dry. Very fine sand, with gravel, and perhaps some admixture of 
clay, a glacier till., is known as Tiard-pan by engineers, very difficult 
to be moved with the pick, and often requiring blasting. The same 
material wet, but without gravel, forms a quicksand — a jelly-like 
material — from which, if a spadeful be taken out, the hole closes up 
at once, and excavation shows but little visible sign of a depression, the space being 
made good from the entire mass. There is another material, called quicksand, which is 
rather a running sand — even when not wet, it rests with a very flat slope ; the particles 
are very fine, and flow like the sands in an hour-glass. 

167 



Fig. 325. 



to 12 per cent less space than when in the natural 




Fig. 326. 



168 



MATERIALS. 



Sands and gravels are large components of mortars, Utons^ and concrete ; and burnt 
with clay, of brick, tile, and pottery. 

BUILDING MATERIALS. 

The natural building materials of civilized communities are wood and stone, which 
are to be worked or fashioned to the purposes to which they are to be applied. 





■T 






4:: 










m 






^/-' 


1 
1 


-cn 












u^ 



Fig. 327. 



Fig. 328. 



Fig. 327 shows various sections of timber in which the rings or yearly growth are 
very strongly shown, and the effect of shrinkage by black margins and distortion, accord- 
ing to the form of cut. 

The strongest timber lies about one third the radius from the pith in the butt log ; 
in the top log the heart position seems strongest ; but in important bridge and floor tim- 
bers the heart should be excluded (Fig. 328) ; exterior rings or sap are soft and liable to 
decay. 

For beams or girders, the timber should be cut so that the stress will be parallel with, 

and not across, grain. For posts in 
compression, and lengthwise of the 
fibre, the section may be from any 
part. 

Figs. 329, 330, and 331 are draw- 
ings of wood, longitudinal and sec- 
tional, in which the grain of the 
wood is imitated, but wood is more 
often represented in plain outline, 
and the cross-section of a timber 
thus (Fig. 332), or by mere hatch- 
ing. When distinguished by col- 
our, burnt sienna is used commonly 
for wood, but sometimes the colour and grain of the wood is imitated. 

The draughtsman, for his designs, will probably have to confine himself to the timber 
within his reach. But he should know what is best for his purpose, reference being had 
to economy in cost and maintenance. For most purposes, wood should be seasoned, so 
that joints may not open under this operation after the material is in the structure. Bat, 
for work under water, wood should be but slightly seasoned, as a swelling of the wood 
may be disastrous. Seasoning of timber may be done by exposure for a time to outer 




MATERIALS. 169 

air-currents ; if in a kiln, it can be done speedily with heated air, or by steam. For 
beams, girders, and the like, there should be few knots, especially on the outer edges — 
for posts, small ones are not objectionable ; while for sidings and under-floors, firm, large 
knots do not impair the work ; but no smooth work can be made with knotty lumber. In 
most specifications, lumber is " to be square-edged, without sap, and large or loose knots." 

In selecting lumber for a permanent structure, the life and endurance of the material 
are to be considered. Most of the woods, sheltered from the wet and exposed to air- 
currents, will last for a very long time ; but many will check and warp and become dis- 
torted. All lumber in earth beneath the level of water will last indefinitely. In salt 
water, above the earth, all are subject to the attacks of the worm — the Teredo and Lim- 
noria — and, where the water is pure, the destruction is very rapid. Sewer-water and 
fresh water are both destructive to the worm. Green or wet timber, in positions from 
which the air is excluded, soon fail through dry rot, and even seasoned timber under un- 
favourable conditions. 

The life of timber exposed to wet or dry rot can be prolonged by filling the pores 
with creosote, pyrolignite of iron, solutions of chlorides of mercury or zinc and various 
other antiseptics. There are works in which the timber is first steamed in close cylinders 
to remove the sap and rarefy the air in the pores, and then injecting the preserving 
fluids. Open tanks of plank can be readily constructed, in which the soaking of lumber 
in cold solution, especially that of corrosive sublimate, is effective. 

CHARACTERISTICS AND USE. 

White Pine. — A wood of the most general application in the market; is light, stiff, 
easily worked, nails are easily driven into it, and takes paint well, warps and checks but 
little in seasoning, endures well in exposed situations; clear stuff, of best quality, useful 
for patterns and models, for interior finish of houses, doors, window sashes, furniture. It 
forms the base or inner core of the best veneered work, holds glue well, and the composite 
structure is better than single solid wood. The cheaper kinds of pine are used for frames 
of buildings, posts, girders, and beams. Even with large knots is well adapted for board- 
ings, and is extensively used for goods-boxes. 

Southern Pine. — A heavy, strong, resinous, lasting wood, clear and mostly without 
knots, hard to be worked by hand-tools, and when seasoned difficult to nail. The sur- 
faces, from their resinous character, do not hold paint well. It is used very largely for 
girders, beams, and posts of mills and warehouses, and for floors of the same, when ex-- 
posed to heavy work or travel. For the first, it can be obtained of almost any dimension 
to suit ; for floors, it is sold in long strips, from two to six inches wide, of varied lengths, 
tongued and grooved, and w^hen laid is blind-nailed, toeing the nail through the tongue, 
so that the nail-head does not show. 

Experiments of the Forestry Division of the United States Department of Agriculture 
prove that the extracting of the turpentine from the long-leaf yellow-pine trees does not 
in any material sense injure them for use as lumber. The bled timber is heavier in the 
bottom cuts by about two pounds per cubic foot. 

Canadian Red., Norway, and Silver Pines are resinous woods, like the Southern pine, 
and are used for similar purposes, but are not as valuable — woods less straight in the 
grain, and with more knots. 

Spruce. — A light, straight-grained wood, with but few knots, which are small and 
often decayed. It does not last well exposed to the weather, and checks and warps 
badly in seasoning. It is the most common wood here for floor-beams and common 
floors, but it must be well braced and nailed, and is not fitted for joiner- work. 

Hemlock is similar to the spruce, and, when selected, is less liable to check and twist 
in seasoning. It is often of a very poor quality, Vrash and shaky. Exposed, it is but 
little better, if any, than the spruce. For stables, it is well adapted for grain-boxes, as 
the fibre prevents the gnawing of rats. 



lYO MATERIALS. 

Ash. — Some of the ashes are of exceeding toughness. A straight, close-grained wood. 
It is used for carriage and machine frames, and for interiors, doors, wainscot, floors, 
when no paint is used. 

Chestnut. — Somewhat like the ash in appearance, but coarser- grained, and very en- 
during in exposed positions. It is most largely used for cross-ties of railways. As a 
roof-frame exposed in the inside, and in general interior finish without paint, the effect 
is very good. The closer-grained woods are very often thus used. 

Black Walnut is, in the trunk, a straight-grained, gummy wood, clogging the plane 
a little in its working ; the knots are useful for veneer. Were the wood cheap enough, 
it would undoubtedly make a good frame. It is used here for desks and counters, for 
furniture and interior finish, as an ornamental wood. 

Butternut. — Similar to the black walnut, less commonly used, but fully equal as an 
ornamental wood. 

Hickory. — A strong, tough wood; is used for cogs of mortise- wheels, handspikes, axe- 
helves, and wheelwrights' work. 

Beech. — A close-grained wood, but of little application in this market. Sometimes 
used for cogs of wheels, for small tool-handles, and in marquetry. 

Oak, Live. — A very strong, tough, enduring wood, used industrially almost entirely 
for ship-building. Ornamentally, in marquetry and panels. 

Oak, White. — A very valuable, strong, tough wood, with great endurance. It is 
heavy, and hard to work, and was formerly used largely for the frames of houses, but 
has been superseded by the white pine. It is used in ship-yards and in water-works — 
for the frames of flumes, penstocks, and dams, and for the planking of the latter, for 
dock-buffers and piles, and for railway and warehouse platforms. The red and black 
oaks may in general be considered a cheaper and poorer quality of the white oak. All 
have a handsome grain, that adapts them to ornamental work. 

Bass, Poplar, White-wood, are light woods, mostly used in the manufacture of fur- 
niture, for drawer-bottoms, cabinet-backs, panels; they are very clear stock, easily 
worked, and can be readily obtained in thin, wide boards. 

Cedar. — A straight-grained, light wood, of great endurance, valuable for posts, sills, 
shingles ; used for pails and domestic utensils. The red variety, from its odour, is ad- 
mirable for drawers and chests, preserving their contents from moths. 

Locust is in the market only in small sticks ; is of extreme endurance. It is used 
almost invariably here for the sills of the lowest floors of buildings, where there can be 
no ventilation, and for treenails of ship-planks. 

Elm. — Although a tree of wide diffusion, is but little used as lumber. It is kept for 
an ornamental tree, beyond its usefulness for any other purpose but fuel. Well selected, 
it is said to be an enduring timber, useful for piles and places exposed to wet. 

Maples are tough, close-grained woods, rather to be considered among the ornamental 
woods, for furniture and interior finish. The same may be said of the cherry, plum, and 
apple tree, of which the denser woods are admirably adapted for the handles of small 
tools, for bushings of spools and bobbins. 

The list of imported woods is extremely large, mostly for ornamental jiurposes; but 
the mahogany is one of the very best of woods for patterns and small models, as it 
changes but little in seasoning; and the lignum-vitse, a very hard and heavy wood, is 
used for pulley-sheaves, packing-rings of pumps, water-wheel steps, and shaft-bushings. 

Timbers of the same kind vary much in their weight, strength, and endurance, ac- 
cording to the localities in which they are grown, the season at which they are cut, and 
how seasoned. Tables are given in the Appendix in detail, their varied resistance under 
stresses and their specific gravities. 

Of late years paper in sheets and pulp has been used instead of woods, and serves 
well many purposes on account of its little shrinkage, incombustibility, strength, and 
endurance. 





Earth. 


p 


^W 


1 


» 


8 


^W 



MATERIALS. 

Concrete. 



171 



Brick. 






Rubble. 



Timber. 





STONES. 

In selecting the form of construction, and the stones of which it is to be composed, 
the draughtsman must be governed by the fitness for the purpose and the cost. He must 
select from what he can readily get, and arrange the form to suit the material. He must 
know what is to be the exposure, and what the effect will be on the stones. Almost any 
stone will stand in a protected wall, but many of the sandstones and slates disintegrate 
and exfoliate under the influence of the weather, heat, cold, frost, and moisture. Even 
the granites are liable to serious decomposition when the feldspars are alkaline ; and the 
limestones (dolomites), of which the English Houses of Parliament are composed, have 
failed in the sulphurous air of London smoke, while at Southwell Minster they have 
stood for over 800 years. Chemical tests of stone to determine endurance are decej^tive. 
The safe way is to see how the material has stood in like situations to the one in which 
it is to be employed, or go to the quarry, and see how the stones have weathered. 

The strength of stones to resist crushing, as determined by experimental cubes, is 
even in the weaker stones much in excess of what would be required in structures, but 
most stones are weak under cross-strains, and failures in construction are more likely to 
occur by faulty workmanship or design, by which the stones are subjected to unequal 
strains, and for which they are not adapted. The weight should not be brought on the 
outer edges or arrises^ as the faces will chip readily ; nor should most stones be used for 
wide-span lintels, unless relieved by the masonry above the opening. 

TECHNICAL, TERMS OF MASONRY. 

Agreeably to the nomenclature recommended in "Transactions of the American 
Society of Civil Engineers," November, 1877: 

RuhUe masonry includes all stones which are used as they come from the quarry, pre- 
pared at the work by roughly knocking off their corners., It is called uncoursed ruWe 
(Fig. 333) when it is laid without any attempt at regular courses; coursed rubble, when 
levelled off at specified heights to a horizontal surface (Fig. 334). 

Square-stoned Masonry. — Square stones cover all stones that are roughly squared and 
roughly dressed on bed and joints. 

Quarry-faced stones are those which are left untouched as they come from the quarry. 

Pitch-faced stones are those on which the arris is clearly defined beyond which the 
rock is cutting away by pitching-tool. 



172 



MATERIALS. 



Drafted stones are those in which the face is surrounded by a chisel-draft. 
If laid in regular courses of about the same rise throughout, it is range-work (Fig, 
335). If laid in courses that are not continuous, it is lyroken range (Fig. 336). 




Fig. 33;i. 



Fig. 334. 



Cut stones or ashlar covers all squared stones with smoothly- dressed bed and joints. 
Generally, all the edges of cut stone are drafted, if the face is not entirely fine cut, but 



'fill T-1,7. V- ^ ■■rv;riii'' {-"r— , \ :^ ' f 1. ' i 



^~"'M|| -i^J -^'Jdi't.- 1' ' I'll' 



?^H .....iui'-iU^*^"^ 



m 



^m^m 



Fig. 335. 



53E!J^V'7J' 



J,— ^."r^KuT^^. 



Wl 



iSIL 






IC« 



xzyi'^ 



juXtvrJlg^ 






■,:iyW\ 






Fig. 336. 



they may be quarry-faced or pitch-faced ; as a rule, the courses are continuous (Figs. 337, 
338), but, if broken by the introduction of smaller stones of the same kind, it is called 
lyrolcen ashlar (Fig. 336). If the courses are less than one foot in height, it is small ash- 
lar (Fig. 337). 



M 




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Fig. 338. 



Squared-stoned Masonry.— The joints in one course should not come directly over 
those of another; there should be a lap or l)ond, and, in connecting the front or face with 
the backing, headers must be introduced for bond. Headers are stones extending into 
the wall, stretchers running with the face. 

The backing is of rubble, sometimes laid dry, but as from its many and large joints it 
settles more than the face, it should be set in mortar to provide uniformity of support. 

In addition there is a class of ornamental stone work, specified as "close jointed, 
hammer-dressed rubble, " in which there are no courses and no pinners. The joint of 
each stone is carefully fitted to those beneath it. 

For rubble-work, all varieties of sound stone are used, and of almost any size. In dry 
work, for foundations and for heavy revetment-walls, the stones are laid with derricks, 
but they must have fair beds and builds. If boulders, they must be split, and cobbles 
in the filling are worse than useless, as they are unstable, and in settlement act as wedge 
to increase the movement. 



Drafted Quarry Face. 




MATERIALS. 

Bush Hammered. 



Axed. 




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mm ii 



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itolliiiiipi ilii'iiiii 



GRANITIC STONES. 

Granite and syenite are by builders classed as granites. The granite in general rifts 
in any direction, and works well under the hammer and points. From these circum- 
stances it is more desirable than the syenites, which are much harder to be worked. Both 
are admirable stones for heavy dock-walls, bridge -abutments, river-walls, either as 
rubble-squared stones or cut work, and are very enduring. They are also used for the 
faces of important buildings, either as fine-cut, quarry, or pitched-face. Ornamental 
work of the simpler kind is readily produced ; more elaborate is expensive, but it is about 
the only stone in this climate in which foliage and sharp undercut work will stand the 
weather without exfoliating. These stones, especially the syenites, admit of a high 
polish, and are used considerably for columns and panels in buildings, and in monumen- 
tal work. Gneiss is of the granitic order, but a cheaper, poorer stone. It splits with 
difficulty, except parallel with line of bed. It has a foliated structure, and is not adapted 
for ashlar, but is very good for squared-stone masonry and rubble-work, and often used 
for sidewalk-covers of vaults. 

ARGILLACEOUS STONES. 

The slates or stones thus designated by builders were formerly in very common use 
as roofing material, and were almost entirely from Wales, but latterly they are taken from 
Vermont and Pennsylvania, and other parts of the United States. They are also used, 
in thicknesses of one inch and above, for floors, platforms, facing of walls, mantels, and 
for wash-tubs by plumbers. Soap-stone maybe classed under the clay stones; also, used 
for tubs, for stoves, and for the lining of grates and furnaces. 

The Ulster, or North River blue stone of this market, is a coarser slate, a very strong 
and enduring stone ; it can be quarried of varying thickness up to twelve inches, and of 
any dimension that can be transported. It can be readily cut, hammer-dressed, axed, " 
planed, and rubbed. Is generally used for sidewalks under these various forms. It is 
used as bond-stones in brick piers, for caps, sills, and string-courses. 



THE SANDSTONES. 

Sandstones, called also freestones, from the ease with which they are worked ; and 
from their colours, are very popular for the fronts of edifices. In general, they are not 
very enduring stones, and when laid must be set parallel to their natural beds, as other- 
wise they flake off under the influence of the weather. The sandstones are not all of the 
same quality; those in which the cementing material is nearly pure silex, are strong, 
enduring stones, but not those in which the cementing material is alumina, or lime. By 
examining a fresh fracture, the character of the stone can generally be detected. A clay, 
shining surface with sharp grains indicate a good stone; while rounded grains, a dull, 
mealy surface, indicate a soft, perishable stone. None of the sandstones in this locality 
are used for heavy pier or abutment work and the like, but there are sandstones in other 
localities adapted to it. 

LIMESTONE. 

The coarser calcareous stones are of great variety; some are well adapted for 
building stones, being hard and compact, while others are soft and friable. They are 
more easily worked than granite, but are not considered as enduring. They are well 



174 



MATERIALS. 



adapted to the same class of lieavy work, and the locks of the Erie and Northern Canals 
and the dam across the Mohawk, at Cohoes, are built from limestone on the line of the 
canals. 

The finer kinds of limestones are classed under the head of marbles. They are easily 
worked, sawed, turned, rubbed, and polished. Marble is not popular as a building 
material, although more enduring than most sandstones, but is susceptible to the action 
of sulphurous gases in the smoky air of cities ; and it is said that the Capitol at Wash- 
ington, D. C, built of marble, is suffering from disintegration. But, for interior finish, 
as tiles, wainscots, architraves, mantels, linings of walls, it is admirably adapted, and 
from its richness, cleanliness, and variety of colour, it is very ornamental and effective. 



A.IITIFICIAL BUILDING MATERIAL. 





The most common and useful are bricks. They are generally made of clay, with an 
admixture of sand, well incorporated together, and mixed with water to the consistence 
of a smooth, strong, viscous mud, pressed into moulds, dried, and burned, the best quality 
being those in the interior of the kiln. The exteriors are light, friable bricks adajDted 
to walls supporting but little weight and not exposed to wet. The brick forming the 
arches are very hard-burned, dark in colour, often swelled and cracked ; but, by 23roi3er 
selection, they can be used for foot-walks. A good brick is well burned throughout; 
when struck, it gives a ringing sound, and is of uniform shape. 

Bricks vary somewhat in size and weight in different localities — from 8 to 8^ inches 
long X 3^ to 4 inches broad x 2 to 2^^ inches thick ; in general, the thickness of a wall 
with the joints is called some multiple of 4", as 8", 12", 16" . . . walls, and the num- 
ber of bricks in such wall is estimated by multiplying the number of brick in a square 
foot of face by 2, 3, 4, . . . In some cases bricks are laid by the thousand and there are 
custom allowances for corners, openings, and indents. The best face or front brick are 
pressed and are of great variety of colours, but uniform in tint. Of late there has been a 
class of face brick of which the edges are taken off by a set, leaving tlie face like rock- 
faced ashlar without draft. 

For variety, Pompeian face brick 1^" x 4" x 12", Roman 2" x 4" x 10", faces plain 
glazed and enamelled. Moulded brick for base, cornices, caps, sills, corners, and arches 
are in common use. 

Bricks are laid in mortar, of lime, lime and cement, or cement only — all with an ad- 
mixture of sand ; in common walls, in lime ; in walls of heavy buildings, above-ground, 
in lime and cement ; beneath, and in wet, exposed positions, in cement only. The com- 
mon bond of the different courses of brick is by header-courses every fifth or seventh 
course. When bricks are laid in arches they are set on edge, and turned in 4-inch rings, 
without any bond between the different rings; or with a bond of brick lengthways, 



MATERIALS. 175 

when two courses come on the same line, or with radial joints, or alternate 4" and 8" 
courses of brick work in masses laid header and stretcher; however laid, the strength 
depends on full joints in strong cement mortar. 

Bricks set on edge, as in arches or in a level course, are here termed rowlocks. 
Arch brick, between iron beams, to reduce the weight, are often made hollow, and 
laid in flat arches ; that is, the joints are radial, but the upper and lower surfaces are 
level. Hollow brick are also used for walls and partitions. 

Fire-briclc can be made of any size and pattern, but are usually 9 x 4^ x 2|. They 
are used for the lining of furnaces, flues, and cliimneys, exposed to the action of flame or 
great heat. Fire-clay, with an admixture of sawdust, which is burned out in the firing, 
leaves a light, porous, spongy mass, which can be sawed in sheets or strips, and is well 
adapted for covering the exposed parts of iron beams and girders, and, as it admits of 
naihng, is convenient for partitions. 

Enamelled Brick. — The English size is that of fire-brick — the American is that of com- 
mon brick. The brick, on the faces to be exposed, are covered with glaze of varied colors 
and designs, and fired. They make a handsome ornamental face for walls, do not absorb 
moisture, and can be washed. 

Tile are a species of brick, with or without enamel. The latter were originally used 
for roof-covering, but now are used in flooring walks and the like. The enameled or 
encaustic tile are generally in squares, 4:" x 4", 6" x 6", 8" x 8", but there are smaller 
ones for tessellation, and rectangular strips for borders. They can be obtained of any 
color or design, forming beautifully ornamented floors and wall-panels. 

Terra-cotta^ a kind of brick, is now largely used for exterior decoration. It is molded 
in every variety of capitals, cornices, caps, friezes, and panels. It is a good, strong brick, 
with all the good qualities of such a material. 

Mortars. — Brick are never laid dry, except in the under part of drains, to admit of the 
removal of ground-water. Stone-work, except in rough, heavy, rubble-work, is also gen- 
erally laid in mortar. Where cut-work is backed with rubble, the joints in the latter 
should be as close as possible, and full of mortar, that the settling of the wall in itself 
may not be more in the backing than in the face. Some lay the rubble dry, and fill in 
with cement grout, or cement mortar made liquid to flow into the interstices, but the sand 
is apt to separate and get to the bottom of the course. 

By mortar, is usually understood a mixture of quicklime and sand, but mortar may 
have an addition of cement to the lime, or it may be cement only with sand. 

Lime, or properly quicklime, is made by the calcination of limestone, shells, and sub- 
stances composed largely of carbonate of hme, carbonic-acid gas, water of crystallization, 
and organic coloring-matter. Quicklime, brought in contact with water, rapidly absorbs it, 
with a great elevation of temperature, and bursting of the lime into pieces, reducing it to 
a fine powder, of from two to three and a half times the volume of the original lime. This 
is slaked lime. It may be slaked slowly by exposure to the air, from which it will take 
the moisture. This is air-slaked lime. Barrels of lime exposed to rain often take fire 
from the heat caused by slaking. The paste of slaked lime may be kept uninjured for a 
considerable time, if protected from the air, and this may readily be done by a covering of 
sand, and it is customary, in some places, to hold it over one season, as an improvement 
to the uniformity of quality in the paste. But, in general, the lime is used soon after 
slaking, and is thoroughly mixed with sand, in various proportions, generally about two 
of sand to one of lime. The theory of the mixture is, that the lime should fill the void 
spaces in the sand, and the space occupied by the mortar is a little in excess of that occu- 
pied by the sand alone. 

The sand should be sharp, clean, silicious grains, from one twelfth to one sixtieth of an 
inch in diameter. Close brick-joints do not admit of as coarse sand as those of cut stone 
work, and, in rubble-work, sand coarser than the above can be used, and there will be 
considerable saving of lime in using a mixture of coarse and fine sand. 



176 MATERIALS. 

The hydraulic limes contain a small proportion of silica, alumina, and magnesia ; slake 
with but little heat, and small increase of volume ; are more or less valuable, accordino- 
to the property which they have for hardening under water ; but, in this particular, are 
not equal to the hydraulic cements. 

There are two great distinctions of cements — natural, as quarried from the rock and 
burnt, and artificial, like Portland, definite proportions from known materials, generally 
preferred from their uniformity of composition ; but in this country the natural cements, 
from old quarries and responsible makers, are satisfactory. 

Cement is used in all masonry in exposed and wet situations. With a small admix- 
ture of lime, it works better under the trowel, and for brick-work it does not sensibly 
impair its value. Cement adds to the strength of lime-mortar. 

The value of a cement depends very largely on its fineness ; the residue thrown out 
from a 2,500-per-inch mess should not exceed 10 per cent, the diameter of the wire is 
about one half the width of the mesh. This residue is reckoned as sand. The voids in 
the sand should be filled by the cement. To determine the amount of voids in the sand, 
fill a tight box of known capacity with the sand and then pour in all the water that it 
will hold. The whole may be considered as unity, and the quantity of water the per- 
centage of voids. In the same way the voids of gravel or broken stone may be deter- 
mine^ for concrete. In mixing cement mortar, it is important that it should be thorough, 
that the sand should be clean and damp, and that each particle should be covered with 
cement, and if to be used for concrete or Mton, that the stone or gravel should be clean 
and damp, and their surfaces should be completely covered with the mortar. Suppose 
the proportions be as below : 

1 part cement, without voids 1.0 

3 parts sand, 30 per cent voids 2.1 , 

6 parts broken stone, 50 per cent voids 3.0 

Parts in mixture 6.1 

The parts of sand and broken stone to cement are larger than in common use, or, say : 

Portland 1, 3, 5 

Natural 1, 2, 5 

But the increase is rather as an offset to coarseness of cement and defects in mixing. As 
a rule, from the time the water is added to the concrete, it should be kept damp for a 
month after it is laid. 

The Danish patent sand cement is sand ground with Portland cement to a uniform 
fineness, and then used like pure cement with great economy of construction and without 
impairing the strength of the mortar. 

Concrete is used for the base course or foundations of walls, and is formed in situ, 
that is, depositing and ramming it in the trench where it is to be left; or by forming in 
moulds, in immense blocks, for docks or break-water, or in the forms of brick. 

The bituminous cements are formed, of natural bitumens, or artificial from coal-tar 
mixed with various proportions of gravel and inert material. The mixture is usually 
heated, put down in layers, and rolled or rammed. It is used for roads and sidewalks, 
and for water-proof covering of vaults. For the covering of roofs, coarse paper, sat- 
urated with bitumen, is put on in layers, one over the other, breaking joints, cemented 
with the bitumen, the last coat being of bitumen, in which gravel is imbedded. For 
an anti-damp course in a wall, or for the joints in the bricks of a wet cellar-floor, or on 
top of a roof, hot bitumen is used as a cementing material with dry bricks. 

Plastering. — Coarse-stuff is nothing more than common brick-mortar, with an admix- 
ture of bullock's hair. When time can not be given for the setting it is gavged, that is, 
mixed with some plaster of Paris. Fine-stuff is made of pure lump-lime with an admix- 
ture of fine sand, and perhaps plaster of Paris. Hard-finish is composed of fine-stuff and 



MATERIALS. 



177 



plaster of Paris. One-coat work is of coarse-stuff, which may be rendered^ that is, put on 
masonry, or laid on laths. Tico-coat work is a coat of coarse-stuff, or scratch-coat ; that 
is, after the coat is partially dry it is scratched for a back for the fine coat. In tlirec 
coats, the first coat is a scratch coat, the second the brown-coat, and the third hard-finish. 
Keene's cement, for the last finish, gives a hard surface, which admits of washing. 

A single brick weighs between 4 and 5 pounds; but a cubic foot, well laid in cement, 
with full joints, will weigh about 112 pounds. They have resisted, in an experimental 
test, as high as 13,000 pounds to the square inch, but 12 tons should be the limit to the 
load per square foot ; and the brick should be uniform, well burned, and closely laid in 
cement. In lime mortar, the load should not exceed 3 tons per square foot. 

The granites weigh from 160 to 180 pounds per cubic foot; the limestones from 150 
to 175; the sandstones from 130 to 170; the slates from IGO to 180; mortar, set, about 
100 pounds ; masonry, laid full in mortar, according to the quality of the stone and the 
percentage of mortar, from 150 to 170 2:)0unds. But, for practical purposes, common 
mortar- rubble is not equal in strength to a brick wall, as it is seldom laid with equal care, 
with joints not as well filled or the load as evenly distributed; but cut stones will sustain 
more, and ashlar, up to 50 tons per square foot for sound, strong stones. 

METALS. 

Metals are often to be shown distinctively by the draughtsman. If he can use colour, 
he will in a measure imitate that of the material. For cast-iron, India-ink, with indigo, 
and a slight admixture of lake ; for wrought-iron, the same colours, with stronger pre- 
dominance of the blue; steel, in Prussian- blue; brass, in a mixture of gamboge and 
burnt sienna; copper, gamboge and crimson lake. In drawings where no colour is ad- 
missible as for photographing, or to be reproduced in printing, some conventional 
hatchings are used to represent sections of metals, but none have been so established as 
to have a universal application. The following are submitted to represent the most com- 
mon industrial metals : 



Brass or Bronze. 



Lead. 



Copper. 






1 


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Steel. 



Wrought Iron. 






Under the term iron maybe included cast-iron, wrought-iron, and steel, differing from 
each other in the percentage of carbon contained, and in the uses to which they are applied. 
Cast-iron contains more carbon than the others, sav from two to five per cent. It can be 
13 



1T8 



MATERIALS. 



cast in varied forms in moulds, but can not be welded or tempered. The usual moulds are 
in sand or loam, in whicli the pattern is imbedded, and when drawn out the space is filled 
with molten metal. The drawing of patterns for molding involves a knowledge of the art 
of founding. The shrinkage of the metal, usually about one per cent, for which provision 
must be made in increased size of pattern, is provided for by the pattern-maker, the 
draughtsman giving finished sizes, but the draughtsman must know whether the pattern 
can be drawn from the sand, and by what system of cores voids can be left ; or it may 
often happen that castings, designed as a whole, will have to be made in a number of 
pieces, involving fianges and bolts. In cooling, the shrinkage takes place the soonest in 
the thinnest parts, and, if great care be not taken by the molder in exposing the thicker 
parts to the air first, the parts will shrink unequally, and there will be a strain induced 
which will materially weaken the casting, and it may even break in the mold. The 
draughtsman, in his design, should make the parts of as uniform thickness as possible. 

Castings cool from the outside inward, in annular crystals perpendicular to the face, 
as in Figs. 339 and 340. Now, if the casting consist of a right angle (Fig. 341), there will 
evidently be a weak place along the line A B, but, if the angle be eased by a curve, the 





Fig. 339. 



Fig. 340. 



Fig. 341. 



Fig. 342. 



crystaUization takes place as in Fig. 343, and the line of weakness is avoided. This is 
eflfected by a very small easement of the angle, and a cove is almost invariably introduced. 
In castings, in almost all metals, the same efi'ects result from cooling, and therefore the 
changes of direction should not be abrupt. 

When castings are ordered for important structures, iron of certain tensile strength is 
called for, and specimens of the metal, in small rectangular bars, are required, cast at the 
same time and under as nearly the same conditions as the casting which may be subjected 
to test. 

If the casting be made in dry sand, it cools slowly, and the surface is comparatively 
soft ; if in greensand — sand somewhat moist — the surface becomes harder ; but if cast 
on an iron plate, or cliiU^ some irons become as hard as the hardest steel, useful in 
surfaces exposed to heavy wear, as the treads of railway-wheels. Cast-iron, in general, 
is brittle under the blows of a hammer, but some mixtures, under a process of annealing, 
become malleable iron, used largely for steam-fittings, parts of agricultural machines, forms 
requiring the toughness of wrought-iron, but difficult to forge. 

Wrought-iron is produced from cast-iron by removing the carbon and impurities by 
puddling, squeezing, heating, and rolling. As a material, it is sold in all sizes of wire, 
rods, shafts, bars, plates, shapes — girders and beams, chains and anchors. Its applica- 
tion industrially is well known. When hot, it can be welded, forged, drawn, and swaged 
into almost any required shape. Under the >team-hammer, the largest shafts, anchors, and 
cranks can be built, or by hand or by machinery it can be wrought into tacks, nuts, bolts, 
nails, or drawn into the finest wire. 

For shafts of mills it is generally turned in a lathe and polished, but of late it can be 
bought, up to six inches diameter, cold-rolled, which adds very considerably to the strength, 
and is ready for use. 

Bessemer and Siemens-Martin metals are made by burning out the carbon from a 
melted iron, and then reintroducing a known quantity, say from 0-03 to 0*6 per cent of car- 
bon. There are other patents covering somewhat different irons, but the above are the best 
known. All are commonly classed as steel, but by many are called homogeneous metal; 



MATERIALS. 179 

first-class iron, of very uniform texture and great strength, but not equal to that of the best 
steel. 

Steel is produced from pure wrought-iron by what is called cementation — heating the 
bars in contact with charcoal, by which a certain amount of carbon is taken up. The bars, 
when taken out, are covered with blisters, apparently from the expansion of minute bub- 
bles within ; hence called Uistered steel. From this shear-steel can be produced by piling, 
heating, and hammering, or cast-steel from melting in a crucible. 

Steel, when broken, does not show the fibrous character of wrought-iron. The frac- 
ture of shear-steel is fine, with a crystalline appearance. The fracture of cast-steel is very 
fine, requiring very close inspection to show the crystals or granulations ; its appearance 
is that of a fine, light, slaty-gray tint, almost without luster. Steel is stronger than any of 
the other iron products, and especially applicable for the piston-rods of steam-engines, and 
positions requiring great strength and stiffness, with the minimum of space. But it is the 
way in which steel can be hardened and tempered which adapts it to its peculiar appli- 
cations. 

When the malleable metals are hammered or rolled, they generally increase in hard- 
ness, elasticity, and denseness, and some kinds of steel springs are made by the process 
of hammer-hardening ; but the usual process of hardening and tempering is by heating 
tlie steel to a degree required by the use to which it is to be applied, and cooling it 
more or less suddenly by immersing in water or oil. The greater the difference between 
the heated steel and the cooling medium, the greater the hardness, but too much heat 
may burn the steel, and too sudden cooling make it too brittle. Steel, in tempering, is 
heated from 430° Fahr. to 630°. The temperature is shown by the color — from a pale 
yellow to deeper yellow, light purple to a dark purple, dark blue to a light blue, with a 
greenish tinge. 

Steel is used for the edges of all cutting-tools, faces of hammers and anvils, and is gen- 
erally welded to bodies of wrought-iron, but often composing the entire tool ; for saws, 
springs, railway tires, pins, and can be bought in the form of wire, rods, bars, sheets, and 
plates, in varied forgings and castings. 

All irons are very liable to rust, and must be protected where exposed to moisture. 
Polished surfaces are kept wiped and oiled, others painted, others galvanized or plated 
with some less oxidizable metal, generally tin, zinc, or nickel. Of late, a process has 
been introduced of coating them with black oxide, but is yet of no general application. 

Antimony, hismvth, copper, lead, tin, and zinc, are used more or less industrially, and" 
alloys of them are extremely useful. They may be hardened somewhat by the process 
of rolling and hammering, but can not be welded. Joinings are made by soldering or 
brazing or burning — that is, melting together. 

Antimony expands by cooling. With tin, in equal proportions, it makes speculum- 
metal, and is used, with lead, to make type. Type metal makes a very good bearing for 
shafts and axles. 

Bismuth is chiefly used as a constituent of fusible metal : 3 bismuth, 5 lead, and 3 tin, 
is an alloy which melts at 212°. Other mixtures are made, increasing the melting-point 
to adapt the metal for fusible plugs in boilers, or lowering the melting-point, so that, in 
case of fire in a building, a heat of say 140° melts the joint made by the metal, and lets 
water through sprinklers, to automatically put out the fire. 

Copper is very malleable and ductile. In sheets, it is used for the cover of roofs, gut- 
ters, leaders, lining of bath-tubs, kettles, stills, and kitchen' utensils. It is worked more 
easily than iron, and is stronger than lead or zinc, but it is much more costly than either 
of these metals, and its oxide is so poisonous that, without great care and cleaning, it can 
not be used to transmit or contain anything that may be used as food, without a cover of 
tin. It oxidizes slowly, and is used extensively for ships' fastenings and for bottom-sheath- 
ing. It is the most important element in all the brass and bronze alloys. 



180 MATERIALS. 

Brass, in common use, covers most of the copper alloys, no matter what the other 
components are, whether zinc, tin, or lead, or all three. 

Copper and zinc will mix in almost any proportions. The ordinary range of good 
yellow brass is from 4|^ to 9 ounces of zinc to the pound of copper. With more zinc it 
becomes more crystalline in its structure, but, as zinc is very much cheaper than copper, 
the founder is apt to increase the percentage of zinc, with the addition of a small per- 
centage of lead. Muntz metal, in its best proportion, contains lOf ounces of zinc to the 
pound of copper. 

Copper and tin mix in almost any proportion. The composition of ancient bronzes is 
from 1 to 3 ounces of tin to the pound of copper. Ten parts of tin to 90 of copper is the 
usual mixture for field-pieces, and this is used in steam-engine work, often under the 
name of composition. Bell-metal is from 4 to 5 ounces of tin to the pound of copper ; Bab- 
bit-metal, for journal-boxes, 90 of tin to 10 of copper. 

Copper and lead mix in any proportion up to nearly one half lead, when they separate 
in cooling. 

An addition of from one quarter to one half ounce of tin to the pound of yellow brass 
renders it sensibly harder. A quarter to one half ounce of lead makes it more malleable. 

German-silver is 50 copper, 25 zinc, and 25 nickel. 

Holzapfel gives the following alloys : 

1^ ounce tin, ^ ounce zinc, to 16 ounces copper, for works requiring great tenacity. 

1^ to If ounces tin, 2 ounces brass, to 16 ounces copper, for cut wheels. 

2 ounces tin, 1^ ounce brass, to 16 ounces coppe^, for turning-work. 

2^ ounces tin, 1^ ounce brass, to 16 ounces copper, for coarse-threaded nuts and bearings. 

2|- ounces tin, 2|- ounces zinc, to 16 ounces copper, Sir F. Chantry's mixture, from which 
a razor was made, nearly as hard as tempered steel. 

Professor R. H. Thurston, at the Stevens Technological Institute, tested various 
alloys of copper, tin, and zinc, and, by a graphic method (Fig, 343), exhibits the re- 
sults, enabling others to judge the probable strength of other mixtures. The apices of 
the triangle marked copper, tin, and zinc, represent the points of pure metal, 100 per 
cent. The lines opposite the apex of any metal represent the of such metal — thus the 
base opposite copper represents an alloy of tin and zinc only, without any cojDper, and 
every line drawn above this base, and parallel to it, will contain a percentage of copper 
increasing by regular scale, from the base to the apex, and so with lines opposite tin and 
zinc ; the first contains only copper and zinc, the latter tin and copper, and the percent- 
ages of tin and zinc increase with the distance from their opposite lines to their vertices. 
The intersections of these percentage parallels define the percentages of each metal, their 
sum always making 100 per cent. If the strength of such alloy, as obtained by test, rep- 
resent an ordinate or elevation, on any convenient scale, at its opposite intersection of 
percentage, a contour map, as in the figure, may be drawn and a model made from it. 
The summit, 65,000 on the figure, represents the position of the strongest alloy found: if 
through the scales marked copper on each side, we find the parallel to the base, which 
passes through this summit, it will be found to be about 55 — that is, 55 per cent copper. 
In like manner, the parallel to the o zinc base, intersecting this summit, will be about 43 
per cent zinc ; and, in the same way, tin is 2 per cent. 

To find the probable strength of any mixture, it is only necessary to find the contour 
intersected by the triple parallels representing the percentages. It is said probable 
strength, because the care and manipulation of the founder are such important factors in 
the result. 

Aluminum is about two and a half times the specific gravity of water. With the re- 
duction in the cost of manufacture, its uses have become more extended, and its alloys 
now occupy a high position in practical industry. With a few per cent of silver, 
titanium or copper aluminum wire can be made of a tensile strength of 80,000 pounds to 
the square inch, and an electrical conductivity, weight for weight with copj)er wire, of 



MATERIALS. 181 

170 to 100. A few per cent of aluminum added to other metals gives valuable proper- 
ties; with 8 to 12 per cent of copper, it makes one of the finest and strongest metals 



known; a lO-per-cent aluminum bronze can be made to fill a specification of 130,000 
pounds tensile strength and 5 per cent elongation in 8 inches ; and in the proportion of 
one third to three fourths of a pound to a ton of steel prevents blow holes and unsound 
tops of ingots. 

There are various other alloys, as phosphate bronze, aluminum bronze, Sterro-metal, 
of which the strength are given hereafter in the appendix. 

Lead is a very soft metal, that can be readily rolled into sheets and drawn into pipes, 
and is so flexible that it can be readily fitted in almost any position. It is, therefore, 
especially adapted to the use of plumbers, for the lining of cisterns and tanks, and for pipes 
for the conveyance of water and waste. For pipes for conveying pure water for drinking 
purposes, or for cisterns containing it, it is objectionable, as it oxidizes, and the oxide is a 
dangerous and a cumulative poison, but, in common waters which are more or less hard, 
the insides of the pipes become covered with a deposit which protects them. It is well, 
before drinking from a lead pipe in which the water has stood for a time, to draw off all 
the water, and, in lead-lined cisterns exposed more or less to the air, to protect them by a 
coating of asphalt varnish. Lead expands readily, and has so little tenacity that, in many 
positions, if heated, it has not strength in cooling to bring it back to its original position. 
It remains in wrinkles on roofs, and, for pipes conveying hot water, unless continuously 
supported, it will hang down in loops, continuously increasing under variations of tem- 



182 MATERIALS. 

perature, to rupture. But it makes a very good plating for sheet-iron for roofs, and its 
oxides are the most valuable of all pigments. 

Tin, in a pure state, is used for domestic utensils, as block-tin, and has also been used 
for pipes in the conveyance of water by parties who feared the poisonous qualities of lead 
pipe. But its chief use is for the covering of sheet-iron, which is sold under the name 
of tin or tin-plate, and is of universal application for architectural, industrial, and do- 
mestic purposes. It is so little affected by air and moisture that roofs, in many places, 
covered with it, need no painting, and oxidization takes place in the iron beneath only 
from deficiency in the plating, or from the abrasion or breaks in it. 

Zinc, in the pure form of spelter, is crystalline and brittle, but at a temperature be- 
tween 210"^ and 300° it is so ductile and malleable that it can be readily rolled into 
sheets, and of late has been used as a cheap substitute for sheet-copper ; but, under con- 
siderable variations of temperature, as for lining of bath-tubs, it takes permanent 
wrinkles, and, for coverings of roofs, suitable provision must be made for its expansion. 
But as a plating of iron, under the name of galvanizing, it affords an admirable protec- 
tion, cheaply, and extends the use of iron in sheets, bolts, and castings, where it would 
not otherwise be applicable. Zinc, as a pigment, does not discolour, like lead, under 
the action of sulphuretted hydrogen, but it is objected to by painters for its want of body 
or cover. 

Sulphur, when used in sufficiently large masses as to show on a drawing, may be rep- 
resented by a reddish-yellow tint, or some distinctive hatching. It melts at 248° Fahr., 
and, from its fluidity, answers admirably for the filling of joints between stones, beneath 
the base plates of iron columns, between wood and stone, and around anchor-bolts in stone, 
forming, when cold, a strong, uniform bearing, and adapting itself to the roughness of 
the material, and is detached with difficulty. It is used largely for the bases of engines, 
and for the joints of the cap-stones of dams. On the dam across the Mohawk, at Cohoes, 
N. Y. , many tons were used in these joints, the depth of sulphur being about 6 inches, and 
now, after about twenty years' use, it has been renewed, and there has been no injurious 
effect from the sulphur on the limestone, of which the apron or capping is composed. 
It is better for most of the above purposes than lead, being cheaper, more fluid when 
molten, shrinks less in cooling, is less affected by temperature, does not creep under 
pressure, and its crushing strength is adequate to any of the positions of use above, but 
it is brittle under blows. It sometimes rusts the bolts or iron with which it is brought 
in contact, but this is prevented by an addition of about 20 per cent of coal tar. This 
mixture is used as a cement to fasten lights in illuminating tile and vault covers. 

When heated to about 300°, sulphur begins to grow viscid, and at 428° it has the 
consistence of thick molasses. Above this, it begins to grow thin again. Heated to 
518°, and thrown into cold water, it becomes for a time plastic, and is used for taking 
moulds or casts. 

Sulphur, in powder, mixed in proportions of one sal-ammoniac, two sulphur, and 
fifty of iron-filings, makes a mastic which is used for calking the joints of iron pipes, 
especially gas-pipes. The joint is called a rust-joint. 

Pure silver is too soft for general purposes ; it alloys readily with lead, zinc, bismuth, 
gold, and copper. The last is the most important in an industrial point of view in its 
use for plate, coin, and ornaments, which invariably contain a certain amount of copper. 

Silver is used for plating by the electro-plate process, or by fire plating, in which the 
sheet is soldered or sweated to some other metal, as iron, German silver, composition, 
copper, etc. 

Gold is used industrially for chemical laboratories; sometimes as plate or for orna- 
ment, but mostly for gilding the baser metals by electro-plating or by fire gilt. As gold 
leaf, it is very largely employed for ornamental purposes ; leaf can be beaten beyond any 
requirements in the arts; a single grain of gold was spread to the extent of 75 square 
inches, and the same weight of silver to 98 square inches. Platinum is used largely for 



MATERIALS, 



183 



various apparatus in chemical laboratories, as it withstands high temperatures and is proof 
against a large number of chemicals. It is to be had in wire sheets, crucible and dishes, 
and in stiles of large capacity for the concentration 
of sulphuric acid. 

Glass, in drawing, is represented by a bluish tint 
or by different sliades or hatchings, expressive of the 
effect of light upon it, wiiether the light is reflected 
or transmitted. 

Fig. 344 represents a portion of a mirror when the 
light is reflected. The exterior of windows is often 
represented in the same way, but with deeper shades, 
and often with a piece of curtain behind in white 
with dim outline. A window viewed from inside 
is represented in shades less than in the figure, or as 
transparent, which is conveyed by the dimness of 
outline of figures or skies seen beyond. 

Fig. 345 represents a glass flask. 

Fig. 346 represents a glass box with glass sides. 

Fig. 347 represents a glass jar containing fluids of different densities. 

Figs. 348 and 349 represent spars, which may be taken for any transparent sub- 
stances, as glass, ice, and the like. 

Common window-glass is blown in the form of cylinders (hence called cylinder- 
glass), flatted out, and cut in lights of varying dimensions, from 6x8 up to 30 x 30 




Fig. 344. 





Fig. 345. 



Fig. 346. 




inches, and put up in boxes containing about fifty 
square feet. It is classed as single-thick (bout -^^ 
inch) and double-thick (^ inch). When the squares 
are large, or used for sky-lights, they should be the Fig. 347. 

latter. Plate-glass — polished plate is used for win- 
dows of stores and first-class buildings. It can be got of almost any dimensions, and of 
a thickness from y\ to f of an inch. Rough plate is largely used for floor-lights and 
sky-lights. It is cut to required sizes, and of a thickness from f to one inch. 

Single thick cylinder-glass cuts off from about 8 to 15 per cent of the light. 

Double-cylinder, from 12 to 20 per cent of the light. 

Polished plate, three sixteenths inch thick, from 5 to* 7 per cent of the light. 

Rough plate, one half inch thick, from 20 to 30 per cent of the light. 

Rough plate, one inch thick, from 30 to 40 per cent of the light. 

Ribbed glass, one eighth inch thick, known as ''factory glass," gives by diffusion a 
more effective illumination than clear, plain glass or the crystal-ribbed glass when either 
is screened with shades. On any exposure but the southern, the crystal-ribbed glass 
may be used without window-shades. 



184 MATERIALS. 

This is when the glass is clean; but there is always a film of moisture on its surface, 
which attracts dust, and impairs very much the transmitted light. Rough plate more 
readily retains the dirt, and, when it is used as floor-lights, becomes scratched. It is 
therefore usual, in the better class of buildings, to use a cast white glass, set in iron 
frames. In outer, or platform lights, these lights are in the form of lenses, set in cast- 
iron frames with an asphalt putty, or resting on iron frames and imbedded in Portland 
cement. 





Fig. 348. Fig. 349. 

Rubber, mixed and ground with sulphur, subjected to heat, becomes vulcanized, and 
is not affected by moderate variations in temperature. Soft rubber, most extensively 
used for industrial purposes, is subjected to a heat of from 265° to 300°, and for a time 
can withstand a temperature a little below this without losing its elasticity ; after a time 
it will harden. Soft rubber is classed as pure rubber, and fibrous rubber, or rubber with 
cloth. Pure rubber contains about fifty per cent of rubber and fifty per cent of com- 
pound, white lead and sulphur. It is used for the buffers and springs of railway- 
carriages, and for the faces of valves and seats of water-pumps, but it is not well Suited 
for the pumping of hot water, especially above 212°, as it is liable to lose its elasticity; 
and, although some valves may stand a considerable time, it is almost impossible to 
secure uniformity in the rubber. Fibrous rubber — rubber ground with cotton or other 
fibre, or spread on cloth, on more or less thicknesses — is used for the packing of faced 
joints of pipes and gaskets for water or steam. It makes a stanch joint, and, even when 
hardened under heat, it still preserves it. Rubber cloth is also used for belting and 
hose-pipes. When used for the conveyance of steam, the inner coat is the first affected, 
and it may be some time before the whole pipe suffers. In buying rubber, explain the 
purpose to which it is to be applied, and depend on the guarantee of the vender. Rubber 
is often to be designated by the draughtsman, which it may be by a bluish-black tint, or 
by lines across it parallel to its length. 

Paints are used for a twofold purpose —for covering and preserving the material to 
which they are applied, and for ornamentation. The best and the most general is white- 
lead ground with linseed-oil, either used by itself or mixed with various other pigments, 
as ochre, chrome, lamp-black, etc. It is often adulterated with barytes. For the cover- 
ing of iron, or for the packing of close joints in it, nothing is better than pure red-lead, 
but many of the oxides of iron, red or yellow, form good covers of iron, and, as cheap 
and good paints, are used on tin roofs. All the leads and pigments are ground in oil: 
if the oil is raw, it dries slowly; driers, as litharge, are added to hurry the process, but, 
with boiled oil, no drier is necessary. Almost any inert substance, as cement, chalk, or 
sand, if fine enough, can be ground with oil for a paint, and make a good cover, and for 
these fish-oil will answer. The general specification for painting is ' ' paint with — good 
coats of white-lead, of such colour as may be directed." The priming-coat of new wood- 
work requires more oil than paint. For the next coats, one-half pound of paint to the 
square yard would be considered a good coat. If the paint is on old work, or that 
which has been already painted, there will be a little less lead required. Wood should 
be fairly dry before the application of paint, so that it may properly adhere and not in- 



MATERIALS. 



185 



close moisture that may rot the wood. The knots should be Tcilled, that is, covered with 
shellac varnish or similar preparation, to prevent the exuding of the resin. The heads 
of nails should be sunk, and the holes and cracks filled with putty, and the surface of 
the wood smoothed. 

Coals and other minerals are represented like rocks or stones, in varied shades of 
tones and colours. Fig. 350 represents the fire-box of a locomotive, with coal in the 
state of ignition in its usual type. In colour, flame is represented in streaks of red- 
yellow, with dark tints for smoke. Water occupies the lower half of the boiler ; but, as 





Fig. 350. 



Fig. 301. 



steam under pressure is invisible like gas, the space occupied by it is shown as empty. 
If the direction of its movement is desired, it is indicated by arrows. Steam issuing 
into atmosphere, or boiling in an open kettle, has the appearance of a very light smoke 
or cloud (Fig. 351). 

There are many substances used in such masses in construction, or to be shown in the 
processes of manufacture, that must be, graphically represented by the draughtsman by a 
general imitation of their natural appearance, or conventionally with explanatory mar- 
ginal blocks and legends. 



MECHANICS. 



The draughtsman in designing a structure should be conversant not only with the 
nature of the material, but also with the forces to which it is to be subjected — their 
magnitude, direction, and points of application, and their effects; that is, he should 
know the first principles of mechanics, the science of rest, motion, and force — to wit, 



Statics, Dynamics, and Kinematics. 



dynamics, 



of unbalanced forces, where motion ensues ; and kinematics, of the comparison of mo- 
tions with each other. Considering statical forces simply in the abstract, the bodies to 
which they are applied are assumed to be perfectly rigid, without breaking, binding, 
twisting, or in any wise changing upon the application of such forces. 

Force is a cause tending to change the condition of a body as to rest or motion. Force 
is measured by weight. In England and the United States the unit of force is the pound; 
on the Continent, the gramme. All bodies fall, or tend to fall, to the earth. This force 
is called the attraction of gravitation. Its direction is that of a string from which a 
weight is suspended (Fig. 352). It is called a vertical line, and its di- 
■" _ rection is toward the centre of the earth. Practically, all such lines 

are considered parallels. Let a mass, P (Fig. 353), be suspended by a 
cord. Each particle is acted on by gravity, and the resultant of all 
these parallel forces is the force resisted by the cord, or the entire 
weight of the body. If a mass (Fig. 354) be suspended from two dif- 
ferent points, P and Q, the directions of the string will meet at a point 
C, which is called the centre of gravity, where all the weight may be 
considered to be concentrated. When a body of uniform density has 




cHf^^ 



k 





Fig. 352. 



Fig. 353. 



Fig. 354. 



Fig. 355. 



a centre of symmetry (a point which bisects all straight lines drawn through it), this 
point coincides with the centre of gravity. The middle of a straight line, the centre of 
a circle, the intersection of the diagonals of a parallelogram, the intersection of lines 
drawn from any two angles of a triangle to the centres of the opposite sides, are the cen- 
tres of symmetry; in solids, the centre of a sphere, the middle point of the axis of a 
cylinder, and the intersection of the diagonals of a parallelopiped. 

The centre of gravity of the triangular pyramid (Fig. 355) is in the straight line A E, 
connecting the apex A with the centre of symmetry of the base triangle BCD, and dis- 
tant \ of the length of the line A E from E. 

186 



MECHANICS. 



187 



The centre of gravity of solids which may be divided into symmetrical figures and 
pyramids, as for all practical purposes most may be, can be found by determining the 
centre of gravity of each of the solids of which it is composed, and then compounding 
them. The centre of gravity of bodies inclosed by more or less regular contours, as a 
ship, for instance, is determined by dividing it into parallel and equidistant sections, 
finding the centre of gravity of each, and compounding them. 

The centre of gravity of a body may be determined practically, as shown above, by 
its suspension from different points. It can be done generally more readily by balancing 
the body in horizontal positions on different lines of support ; the centre of gravity will 
lie in the intersection of planes perpendicular to these lines. A body, unless the vertical 
line from the centre of gravity falls within the base of support (Fig. 356), will fall over 
(Fig. 357). A person carrying a weight insensibly throws a portion of the body forward, 
backward, or laterally, to balance the load. Thus, in Fig. 358, the body is thrown 






Fig. 356. 



Fig. 357 



Fig. 358. 



back, so that the vertical from the centre of gravity g, compounded of the centre of 
gravity G of the woman and H of the load, falls within the base of the feet. 

When a figure rests in such a position that its centre of gravity is in its lowest posi- 
tion, it is said to be in stable equilibrium. A ball may rest in any position, as the centre 
of gravity is neither depressed nor raised by movement; but in the toy (Fig. 359) any 
movement tends to raise the centre of gravity, and, on the cessation of the force, the 
body returns to its original position. The ellipsoidal form (Fig. 360), placed on its 
pointed end, is balanced, but the slightest movement lowers the centre of gravity, and, 
without the application of an outside force, it can not be raised, and therefore falls. 




Fig. 359. 



Fig. 360. 



Fig. 361. 



This is called unstable equilibrium, while in the position shown in Fig. 361 it is in stable 
equilibrium. In the toy (Fig. 362) the body of the figure* is light, and the weight of the 
balls brings the centre below the point of support. This will admit of great oscillation, 
and return to its original position. 

When two parallel forces, F F', are applied at the extremities of a straight line (Fig. 
363), they have a resultant, R, equal to their sum, and acting at a point, C, which 
divides the line inversely in proportion to the forces. If the forces are equal, the point 
C will be at the centre of the line; if the force F is double that of F', C A will be equal 
to one half C B. This is called the principle of the lever. 



188 



MECHANICS. 



Levers, in practice, are called of the first (Fig. 364), the second (Fig. 365), and the 
third class (Fig. 366), according to the positions of the three forces, the weight, W, the 
power applied, P, and the fulcrum, or support or turning-point, F, of the lever. The 
two extreme forces must always act in the same direction; the 
middle one must act in the opposite direction, and be equal to 
the sum of the other two ; and the magnitude of the extreme 
forces is inversely proportional to their distances from the mid- 
dle one. Let the middle force, c, be measured by a spring-bal- 
ance (Fig. 367), it will mark the sum of the weights a and b. 





Fig. 363. 



Fig. 364. 




Call the distance from a to c, x, and from h to c, y, then the weight a will be to the 
weight d an y is to ic, or ax = dy. Suppose the weight a to be 6 pounds and at & 3 
pounds, at c it will be 9 pounds, and x will be to y,as 6 to 3, or, if the lever is 48 inches, 
5 c will be 16 inches and a c 32 inches. 



V^ 



W F 



m 



a 



Fig. 367. 



Fig. 365. 




y 



A 



w 



F 



oThi 



Fig. 366. 



Fig. 368. 



To find graphically the fulcrum, or point, at which a lever should be supported to 
sustain in equilibrium weights, or equivalent forces, acting at the extremities of the 
lever. Let A B (Fig. 368) be the lever. At A and B let fall and erect perpendiculars to 
the lever. Lay off from A, on any convenient scale, A B', corresponding to the weight 
applied at B; and at B, on the same scale, B A', the weight applied at A; draw the line 
A' B' ; its intersection, F, with the lever will be the position of the fulcrum. This is on 
the hypothesis that there is no weight to the lever, or that, after determining the posi- 



MECHANICS. 



189 



F ! 



Fig. 



tion of the fulcrum, the lever itself is balanced on the point by the addition of weight 
on the short arm F A, or the reduction of weight on the long one F B. If the lever is 
of uniform weight, on perpendiculars to C, the centre , 

of the lever (Fig. 369), and to F, the fulcrum, as before 1 

determined, lay off F C, the weight of the lever, and 
C F', the sum of the weights applied at A and B ; draw 
C F'. Its intersection, F", will be the actual fulcrum, 
taking into consideration the weight of the lever in ad- 
dition to the weights suspended at the extremities. 

The Wheel and Axle. — If a weight, P, be suspended 
from the periphery of a wheel (Fig. 370), while another 
weight, W, is suspended on the opposite side of a bar- 
rel or axle attached to the wheel, the principle of ac- 
tion is the same as that of the lever. P multiplied by 
its length of lever, the radius c a of the wheel, is equal 
to W multiplied by its length of lever, the radius of the — 
axle c d ; the axle c is the fulcrum. If a movement 
downward be communicated to P, as shown by the 
dotted line, a rotary motion is given to the wheel and 
axle; the cord of P is unwound while that of W is 
wound up, while P is still suspended from a and W from & ; the leverage, or distance 
from the fulcrum, of each is the same as at first. The wheel and axle is a lever of con- 
tinuous action. Since the wheel has a larger circumference than the axle, by their revo- 
lution more cord will be unwound from the former than is wound up on the latter; P 

will descend faster than W is raised in the proportion of 
the circumference of the wheel to that of the axle, or of 
their radii — that is, as cato ci. When P has reached the 
position P', W will have reached W. If c a be four times 
c 5, then P will have moved four times the distance that 
W has. The movement is directly as the length of the 
levers, or the radii of the points of suspension. Therefore, 
to move a large weight by the means of a smaller one, the 
smaller must move through the most space, and that the 
spaces described are as the opposite ends of the lever, or 
inversely as the weights. 

It is the fundamental principle of the action of all me- 
chanical powers, that whatever is gained in power is lost in 
space travelled; that, if a weight is to be raised a certain 
number of feet, the force exerted to do this must always 
be equal to the product of the weight by the height to 
which it is to be raised; thus, if 200 pounds are to be 
raised 50 feet, the force exerted to do this must be equal 
to a weight which, if multiplied by its fall, will be equal 
to the product 200x50, or 10,000; this force may be a 
weight of 10,000 pounds falling 1 foot, or of 1 pound fall- 
ing 10,000 feet. 

It is now common to refer* all forces exerted to a unit of 
pounds-feet (see p. 72, Fig. 181), that is, 1 jDound falling 1 
foot; and the effect to the same unit of pounds-feet, 1 jjound 
raised 1 foot. Thus, in the example above, the force exerted or power is 10,000 pounds- 
feet falling; the effect 10,000 pounds-feet raised. In practice, the pounds-feet of force 
exerted must always be more than the pounds-feet of effect produced ; there must be some 
excess of the former to produce movement and to overcome resistance and friction of parts. 




Fig. 370. 



190 



MECHANICS. 



The measure of any force, as represented by falling weight, is termed the absolute power 
of that force ; the resulting force, or useful effect for the purposes for which it is applied, 
is called the effective power. 

The Pulley. — The single fixed pulley (Fig. 371) consists of a single grooved wheel 
movable on a pin or axis, the strap through which the pin passes being attached to some 
fixed object. A rope passes over the wheel in the groove ; on one side the force is 
exerted, and on the other the weight is attached and raised. It may be considered a 
wheel and axle of equal diameters, or as a lever in which the two sides are equal, the pin 
being the fulcrum. P, the force exerted, must therefore be equal to the weight W, raised ; 
and, if movement takes place, W will rise as much as P descends. 

The fixed pulley is used for its convenience in the application of the force ; it may be 
easier to pull down than up, for instance ; but the pounds-feet of force must be equal 
to the pounds-feet of effect. The tension on the rope is equal to either the force or 
weight. 

Fig. 372 is a combination of a fixed pulley. A, and a movable pulley, B. The sim- 
plest way to arrive at the principle of this combination is to consider its action. Let P 
be pulled down, say, two feet ; the length of rope drawn to this side of the pulley must 
be furnished from the opposite side. On that side there is a loop, in which 
the movable pulley, with the weight W attached, is suspended. Each side 
of this loop, 2 and 3, must go to make up the two feet for the side or end 
1. Cords 2 and 3 will therefore furnish each one foot. ^ ^ ^ ^ 

As these cords are shortened one foot, the weight W is 



///////,///// 



^ ^>^\-^^^^-m^ ^\ ^ ^^\ 




Fig. 371. 




^^C 



^ 



(b 



(b 



y 



H a 



Fig. 373. 



Fig. 374. 



raised one foot, and, as the movement of W is but one foot for the two feet of P, W 
must be twice P. 

In the combination of pulleys (Fig. 373), let P be pulled, say, three feet; then this 
length of rope, drawn from the opposite side of the pulley, is distributed over the three 
cords, 2, 3, 4, and the weight W is raised one foot ; consequently, W is three times P. 
The cord 1 supports P, the cords 2, 3, 4, the weight W, or three times P ; consequently, 
the tension on every cord is alike. The same rope passing freely around pulleys must 
have the same tension throughout ; so that, to determine the relation of W to P, count 
the number of cords which sustain the weight. Thus, in Fig. 374, the weight is sus- 
tained by four cords ; consequently, it is four times the tension of the cord, or four times 
the force P. In order not to confuse the cords, the pulleys are represented as in the 
figures ; but, in construction, the pulleys, or sheaves, are usually of the same diameter, 
and when connected, as A and B, and C and D, they run on the same pin. 

The Inclined Plane. — To support a weight by means of a single fixed pulley, the force 
must be equal to the weight. Suppose the weight, instead of hanging freely, to rest 
upon an inclined plane b d (Fig. 375) ; if motion ensue, to raise the weight W the height 
a b, the rope transferred from the weight side of the pulley will be equal to b d, and P 
will have, consequently, fallen this amount ; thus, if 5 ^ be six feet, and a b one foot, 



MECHANICS. 



191 



while W is raised one foot, P has descended six feet ; and, as pounds-feet of power must 
equal pounds-feet of effect, P will be one sixth of W ; thus, P is to W as ah is to h d, or 
as the height of the incline is to its length. If the end of the plane d be raised, till it 
becomes horizontal, the whole weight would rest on the plane, and no force would be 
necessary at P to keep it in position ; if the plane be revolved on &, till it becomes per- 





'■y///////y/<V'^ 



Fig. 375. 



Fig. 376. 



pendicular, then the weight is not supported by the plane at all, but it is wholly depend- 
ent on the force P, and is equal to it. Between the limits, therefore, of a level and a 
perpendicular plane, to support a given weight W, the force P varies from nothing to 
an equality with the weight. 

The construction (Fig. 376) illustrates the principle of the wedge, which is but a 
movable inclined plane; if the wedge be drawn forward by the weight P, and the weight 
W be kept from sliding laterally, the fall of P a distance equal to ad will raise the 
weight W a height c I. P will therefore be to W as c & is to a d. For example, if the 
length of the wedge a ^ be ten feet, and the back c I two feet, then P will be to W as 
two to ten, or one fifth of it. 

Let the inclined plane aid (Fig. 376) be bent round, and attached to the drum A 
(Fig. 377), to which motion of revolution on its axis is given, by the unwinding of the 
turns of a cord from around its periphery, through the action of a weight P suspended 
from a cord passing over a pulley. If the weight W be retained in its vertical position, 

by the revolution of the drum it will be forced up 
the incline, and when the cord has unwound one half 
turn from the drum, and consequently the weight P 
descended a distance, c d, equal to one half the cir- 
cumference of the drum, the weight W has been 

raised to the height a & 
by the half revolution 
of the plane; P must 
therefore be to W as 
a 5 is to one half the 
circumference. Extend 
the inclined plane so as 
to encircle the drum 
(Fig. 378). The figure 
illustrates the mechan- 
ism of the screw, which 
may be considered as formed by wrapping a fillet-band or thread around a cylinder at a 
uniform inclination to the axis. In practice, the screw or nut, as the case may be, is 
moved by means of a force applied at the extremity of a lever; a complete revolution 
raises the weight the distance from the top of one thread to the top of the one above, or 
the 'pitch. If the force be always exerted at right angles to the lever (Fig. 379), the 
lever may be considered the radius of a wheel, at the circumference of which the force 
is applied. Thus, if the lever be three feet long, the diameter of the circle would be six 
feet, and the circumference 6 x 3-1416, or 18 ^V ^^^^5 if ^^ pitch be one inch, or one 




Fig. 377. 



Fig. 378. 



192 



MECHANICS. 



t-welfth of a foot, then the force would be to the weight as one twelfth is to 18-85; and 
if the force be one pound, the weight would be 326 "20 pounds. 

The resultant of two forces of exertion, as has been shown, is their sum, and counter- 
balances the force of re- 
sistance, which must be 
applied at a point inter- 
mediate between, and 
distant from each of 
them inversely as the 
forces exerted. 

The resultant of any 
number of parallel forces 
acting in one direction 
is equal to their sum act- 
ing in the same direc- 
tion at some intermedi- 
ate point; that is, the 
jPjg gr-g effect of all the forces 

is just the same as if 
there were but one force, equal to their sum, acting at this point, and is balanced by an 
equal force acting in the opposite direction. This central point may be determined by 
finding the resultant, i. e., the sum, and the point 
of application for any two of the forces, as shown 
graphically in Figs. 368, 369, and then of the other 
two, the resultants thus determined being again 
added together like simple forces. 

Inclined Forces are those whose directions are in- 
clined to each other. When two men of equal 
strength pull directly opposite to each other, the resultant is nothing. Let a third take 
hold of the centre of the rope (Fig. 380), and pull at right angles to the rope ; he will 
make an angle in the rope, and the other two now pull in directions inclined to each 
other. The less the force exerted at the centre, the less the flexure in the rope ; but 





Fig. 380. 




Fig. 881. 



MECHANICS. 



193 



when it becomes equal to the sum of the forces at the ends, the two, to balance it, 
must pull directly against it, bringing the ends of the rope together, and acting as paral- 
lel forces. Between the smallest force and the largest that can be exerted at the centre 
and maintain a balance or equilibrium, the ends of the rope assume all varieties of angles, 
which angles bear definite relations to the forces. 

Represent these forces by weights (Fig. 381). Let P and P' be the extreme forces 
acting over the pulleys M and N, and tending to draw the rope straight, which the 
weight P" prevents. Lay off 
the weight of P (90 pounds) Ci 

along A B, and the weight of 
P' (60 pounds) along A C. 
Draw B D parallel to A C, 
and CD parallel to A B. 
Connect D with A. If this 
is measured with the same 
scale that A B and A C were 
laid off with, it will be found 
that it equals 120 pounds, 
which will be found to be 




Y\a. 888. 





A' 



Fig. 382. 



Fig. 384. 



the same as the weight P". A D, therefore, gives the amount and direction of the re- 
sultant of the two forces P and P', which resultant is balanced by P". In the same 
way the resultant of any number of inclined forces (Fig. 382) may be found by com- 
pounding the resultant of any two forces with a third, and so on. 

As two forces may be compounded into a single resultant, so conversely one force 
may be resolved into two components ; thus, let the weight P (Fig, 383) be supported by 
two inclined rafters, C A and C B. Each resists a part of the force exerted by the weight 
P. To find the force exerted against the abutments A and B, in the direction of C A 
and C B, draw c k! (Fig. 384) parallel to C A, c B' to C B, and c 6Z, a parallel to the line 
C P, the direction in which the weight P acts ; lay off c <Z from a scale of equal parts, a 
length which will represent the number of pounds, or whatever unit of weight there may 
be in the weight P ; draw d a parallel to c B', and d 5 parallel to c A' ; c a, measured on the 
scale of equal parts adopted, will represent the pounds or units of weight exerted against 
A in the direction of C A, and cl the pounds or units of weight exerted against Bin the 
direction of C B. 

This method of finding the resultant of two forces, or the^ components of one force, is 
called the parallelogram of forces. If two sides of a parallelogram represent two forces 
in magnitude and direction, the resultant of these two forces will be represented in mag- 
nitude and direction by the diagonal of the parallelogram and conversely. 

The sum of a c and c & is greater than c d ; that is, the weight P exerts a greater force 

in the direction of the lines C A and C B, against A and B, than its own weight ; but the 

down pressure upon A and B is only equal to the weight of P and of the rafters which 

support it, which last, in the present consideration, is neglected. Resolve c b, the force 

14 



194 



MECHANICS. 



f ' f 



1} 

:0 



acting on B in the direction of c B', into gh or ce the downward pressure, and eg or eb 
the horizontal thrust on the abutment B, and c a into c/and/a. To decompose a force, 

form a triangle, with the direction of the other 
forces, upon the line representing the magni- 
tude and direction of the given force ; c e repre- 
sents the weight on B, c/the weight on A; cd, 
or ce + de, the whole weight P ; therefore, the 
weight upon the two abutments A and B is 
equal to the whole weight of P. 

The steelyard (Fig. 385) is a lever, from the 
short arm of which a dependent hook or scale 
supports the article to be weighed; while, on 
Fig. 385. the long arm, a fixed weight, P, is slid in cr 

out from the fulcrum till it balances the article ; 
the distance as marked on a scale on the long arm determines the weight. In plat- 
form-scales, when very heavy weights are balanced by small weights on a graduated arm^ 




(5= 



V 



F' 



Fig. 386. 



71" 



& 



combinations of levers are used, the principle of which can be understood from Fig. 
Thus, suppose P F to be 7", a F 2", a ¥' 9", l ¥' 2", b ¥" 11", F" W 3'^ 

P is to force a as a F to P F, or as 2 to 7 

Force a is to 5 as b¥' to a F, or as 2 to 9 

&istoWasF"Wto&F", oras 3 to 11 



P is to W as 



12 to 693 



The differential axle, or Chinese capstan, consists of an axle with two different diam- 
eters (Fig. 387), the weight W being suspended in the loop of a cord wound around 




Fig. 387. 




Fig 



these axles in opposite directions by a single turn of the axle. The weight is only raised 
or lowered by the difference between these two circumferences ; one takes up while the 
other lets out, and the P, to balance W, must be as these differences of circumference of 
axles IS to the circumference of the wheel from which P is suspended. 

The differential screw (Fig. 388) consists of an exterior screw. A, and an interior 
screw, B. By the revolution of the arm, the screw A is moved through the plate D in 



MECHANICS. 



195 



proportion to its pitch, but the interior screw B moves inward its pitch, and the move- 
ment of W is only the pitch of A less that of B, and the power applied is to the weight 
moved as the difference of these pitches is to the circumference described by the power. 
As the lever (Fig. 389) moves under the action of power or weight, the lever be- 
comes inclined to the direction of the forces, but the forces are still parallel. The rela- 
tions of the forces to each other are not changed, but the absolute action of each is only 
that due to the length a h and h c, to which the directions of the forces are perpendicular. 
In the bent lever (Fig. 390) the action of the forces is estimated on lengths of arms, 





The force is exerted in the 




Fig. 391. 



Fig. 389. Fig. 390. 

determined by the perpendiculars a h and & c let fall from the fulcrum on the directions 

of the forces. 

The toggle-joint (Fig. 391) is much used for presses. 

direction of the arrow at C, and the effective force is to 

separate the plates A and B. The action is as shown in 

Fig. 391a. Equal movements, as C-1, 1-2, 2-3, corre- 
spond to unequal movements at A and B, as A a', a' o?^ 

a? a?. The nearer the force C is to the line A B, the 

less the movement a?' a^ ; and, consequently, the force C 

exerts greater effects in intensity, but the latter is less in 

movement. 

Fig. 392 exhibits the principle of the hydraulic press. 

The small plunger or piston may be considered the application of the force, and the 

large one the weight to be raised to balance each other; the pressure per square inch of 

surface must be the same, 
f /K and the force must be to 

weight as the surface of 
its piston is to that of 
the w^eight - piston. If 
motion takes place, the 
force will move through 
space corresponding to 
the area of weight-pis- 
ton, while the weight will 
move that of the area of 

the force-piston. And this is the great principle of all mechanism in the transmission 

of force : there can be no total gain. What is gained in force is lost in movement, and 

in many complicated machines the theoretical comparison of force applied and resultant 

force may be ascertained by the measures of their movements. 




196 



MECHANICS. 



lib. 




The resultant effects of forces, as heretofore treated, 
16 lbs. have been without motion, or static. But when motion 
is produced, the forces are called dynamic. A weight sus- 
pended or supported exerts a force, which is balanced by 
the resistance of the suspending or supporting medium; 
but a falling weight acquires an increasing velocity with 
every unit of time or space passed. All bodies would fall 
with the same velocities were it not for the different re- 
sistances from the air due to their different bulk in pro- 
portion to their weight. Dense articles, as stones and met- 
als, acquire a velocity in this latitude of about 32 'S feet in 
each second, called the intensity of gravity, or g. The 
value of g at the equator is 32 '088; at the poles, 32*253. 
A body 



Starting with a velocity , 

Falls during the 1 st second 

Acquiring a velocity of 

Falls during the 2c? second 

Acquiring a velocity of twice 32, or... 

Falls during the Sd second , 

Acquiring a velocity of 3 X 32 = . .. , 

Falls during the 4:th second 

Acquiring a velocity of 4 X 32 = — 

Falls during the 5th second 

Acquiring a velocity of 5 X 32 = 



Ft. Tot. Fall. 

16\= 16 16 

32 feet per second 

32-fll6\= 48 64 

j 1\64 feet per second. 

32-|-;32-f 16\== 80 144 

feet per second. 

32-f|32-f 32-f;i6\= 112 ' 256 

128 feet per second. 

16\= 144 400 

160 feet per second 




Calling 8 the space passed over, v the terminal velocity in feet, t the time in seconds 
of falling, s = ^gt^, v =^ gt or = ^64. 4s. In determining the velocity of issuing water 
under a head h, corresponding to s in the equation, it is generally near enough to reckon 
V as eight times the square root of the head {^Jh). 

The motion of falling bodies is a uniformly accelerated one, but there are also uni- 
formly retarded motions in which the velocity is decreased by equal losses in equal times. 
There are also uniform motions when bodies are impelled by a constant force and op- 
posed by constant resistances. 

In Fig. 393, o s represents the trace of a body impelled horizontally by a uniform, 
but falling through the action of gravity with an accelerated, force. This curve, a 
parabola, represents approximately the. curve of the thread of stream issuing from an 
orifice, or flowing. 

It will be seen that to produce twice the velocity the body must fall through four 
times the space ; that there is four times the force stored in the body. But to maintain 
this velocity uniformly, only twice the force is necessary. The momentum of a body is 
its mass multiplied by its velocity, but its inertia is as the square of the velocity. It is 
an established principle of mechanics that the results must be proportional to the causes : 
if a body has to be raised four feet to obtain a double velocity in falling, the destructive 
result of that fall must also be four times. 

Under statics, it has been shown that forces may be resolved and compounded. The 
same may be done dynamically — that which has been treated as weight must now be 
considered as momentum. 



MECHANICS. 



h 



197 



In treating of dynamic forces the resultants have been considered as equal to the exer- 
tion, without any losses by resistances. This never happens in practice ; the resistances 
are a very large element. Resistances from the medium 
in which the bodies are moved are from the surfaces on 
which the bodies are supported ; resistances due to the 
displacement of the fluid in which the bodies move, and 
frictional resistances, or what is termed skin-resistances, 
of bodies moving through air or water ; and the surface- 
resistance of bodies sliding or rolling on each other. 
Suppose a weight to rest on a horizontal surface — it will 
take a certain force to move the insistent weight depend- 
ing on the amount of this weight and the kind of sur- 
faces in contact, and the force that will just cause motion 
overcomes the friction, or frictional force, and is equal to 
it. The frictional force is only a percentage of the in- 
sistent force of the body, and this percentage is called 
the coefficient of friction. If the horizontal surface of sup- 
port be raised at one end, so as to make the surface in- 
clined, it will after a time become so steep that the insist- 
ent body will slide down the surface. Thus, in Fig. 394, 

if the body Q is ready to slip on the surface A B, the angle BAG, which represents the 
angle of the surface with the horizontal, is called the angle of repose, or limiting angle 




of frictional resistance ; or thus (Fig. 395), if the force acting in the direction P"M is 





just sufficient to produce motion of the mass M along the plane F Q, the angle P M P'' 
is the limiting angle of resistance. 

General Morin has made an elaborate course of experiments on friction, some of the 
results of which are given in the table on the following page. 

In Morin's experiments the surfaces of the woods were first planed and those of the 
metals filed and polished with the utmost care. When the friction without lubrication 
was to be determined, any unctuosity was especially provided against. For unctuous 
surfaces, the unguent was carefully wiped off, so that no layer of it should prevent their 
intimate contact. 

When lubricated, the resistance from the viscidity of the lubricant may be overlooked, 
compared with the friction. As respects the nature of the substance used in lubrication, 
it was observed, by comparison of the coefficient of the friction of motion, that with 
hog's lard and olive oil surfaces of wood on metal, wood on wood, metal on wood, and 
metal on metal, had all very nearly the same friction — between 0-07 and O'OS. With tal- 
low the coeflScient was the same except in the case of metals upon metals. 

Practically the sliding of wooden surfaces on each other or on metal surfaces is con- 
fined within small limits. As far as possible, sliding surfaces in most machines or me- 
chanical appliances are of metals, and when surfaces are liable to be affected by rust and 
adhere, they are made of brass or bronze. But in the moving of houses or the launching 
of ships the ways are of wood, and in this country of Southern pine, as being without 
knots and extremely stiff. 



198 



MECHANICS. 



Sliding Friction of M. Movin's Experiments on Plane Surfaces. 



Sliding 
surface. 



Oak 

Oak 

Oak 

Oak 

Elm 

Beech.. . . 
Cast-iron. 
Oak 

Cast-iron. 

Wrought- 
iron. 

Wrought- 
iron. 

Cast-iron. 



Cast-iron , 



Wrought- 

iron. 
Bronze.. . 

Cast-iron. 

Bronze.. . 

Bronze.. . 

Steel 



Surface 
at rest. 



Oak 
Oak 
Oak 
Elm 



Oak.. 

Oak 

Oak 

Cast-iron . 

Elm 

Wrought- 
iron. 

Cast-iron . 



Wrought- 
iron. 



Cast-iron . 



Bronze . . 

Wrought- 

iron. 
Bronze . . 

Cast-iron 

Bronze . . 

Cast-iron 



State of the Surfaces. 



Fibres s s' parallel to 
motion. 

Fibres s perpendic- 
ular to motion.. . 

Fibres s s' perpen- 
dicular to motion. 

Fibres s s' parallel j 
to motion. ( 

Fibres s s' parallel j 
to motion. ] 

Fibres s perpendicu- 
lar to motion. 

Fibres s s' parallel ( 
to motion ] 

Fibres 5 s' parallel j 
to motion } 

Fibres of the wood 
perpendicular to 
motion. 

Fibres of the wood 
parallel to motion. 

Fibres s s' parallel j 
to motion ( 

r 

Fibres s s' parallel J 
to motion j 

Fibres s s' parallel \ 
to motion 1 



Fibres s s\ parallel \ 
to motion 1 



Fibres s s' parallel \ 

to motion } 

Fibres s s' parallel j 

to motion ( 

Fibres s s' parallel \ 

to motion } 

Fibres s s' parallel ] 

to motion ( 

Fibres s s' parallel j 

to motion '. . { 

Fibres s s' parallel to 

motion. 



Without lubrication 

Without lubrication 

Unctuous 

Without lubrication 

Without lubrication 

Unctuous 

Without lubrication 

Unctuous 

Without lubrication 

Without lubrication 

Unctuous 

Without lubrication 

Unctuous 

Without lubrication 



Without lubrication 
Surface unctuous. . . 
Without lubrication 
Surfaces unctuous.. 
Without lubrication 
Surfaces unctuous.. 
Lubricated with 

olive oil . 

Surfaces unctuous.. 
Without lubrication 
Surfaces unctuous. = 
' water 



0-478 

0-324 
0-143 
0-336 

0-246 
0-136 
0-432 
0-119 
0-450 

0-360 
0-330 
0-490 
0-107 
0-372 



Lubri 

cated ^ 
with I 

I 
Without 
Surfaces 
Without 
Surfaces 
Without 
Surfaces 
Without 
Surfaces 
Without 
Surfaces 
Without 



soap 

tallow 

lard 

olive oil. : 
lard and 
plumbago 
lubrication 
unctuous., 
lubrication 
unctuous., 
lubrication 
unctuous., 
lubrication 
unctuous,, 
lubrication 
unctuous., 
lubrication 



friction of 
motion. 



195 
125 
138 

177 
194 



066 
143 
152 
144 
314 
197 
100 
070 
064 

055 
172 
160 
161 
166 
147 
132 
217 
107 
201 
134 
202 



h-l 03 0) 



25°33 

17 58 
8 9 

18 35 

13 50 
7 45 

23 22 
6 48 

24 16 

19 48 
18 16 
26 7 

6 7 

20 25 



11 3 

7 8 

7 52 

10 3 

10 59 



8 39 
8 12 



5 43 



9 46 
9 6 
9 9 
9 26 
8 22 
7 22 
12 15 

6 7 
11 22 

7 38 
11 26 



friction of 
quiescence. 



£•= 



0-625 

0-540 
0-314 



0-376 

0-694 
0-420 
0-570 

0-530 
0-100 



0-137 

0-194 
0-118 

0-100 

0-162 



0-100 
0-100 



0-164 



loi 



bCM 
Am 
d 0) 



32° 1' 

28 23 
17 26 



20 37 

34 46 
22 47 
29 41 

27 56 



5 43 



10 59 
6 44 

5 43 

9 13 

5 43 



9 19 



In the launching of a vessel, the width of the ways must be proportioned to its 
weight, not to exceed three tons per square foot. A slope of f " to the foot permits the 
control of the vessel if necessary. On a slope of |" to the foot, a vessel will move 
steadily and gently down without attaining a high speed, and is the one adopted where 
other circumstances do not affect the choice. A slope of |" to the foot is often used 
for large vessels; the speed attained, however, is very high, and in narrow water both 
dangerous and inconvenient. A slope of 1 in 12 may be used where the distance to be 
traversed is short, and the ship launched broadside in. 



MECHANICS. 



190 



Before striking the dog-shore, which prevents the ship from sliding down the ways, 
they are thoroughly slushed with some greasy mixture, like tallow and soap. 

It was formerly held that friction was directly as the weight, without regard to the 
amount of surface or velocity of movement, and Morin's experiments, referred mostly to 
the friction of quiescence and slow movements, come within this rule ; the results give 
coeflBcients that may be considered maxima, but in practice it has been found that the 
coefficient of friction with unguents is reduced by increase of velocity and of tempera- 
ture, that extent of surface may be prejudicial, and that careful selection of unguents, 
according to the work to be done, will reduce friction. 

Axle and Rolling Friction. — Axle friction has been generally supposed to follow the 
laws of sliding friction, with the exception that its coefficient is a smaller fraction of the 
total pressure applied. There are but few experimental data relating to this branch of 
the subject. The results of some experiments by Morin are given in the following table : 



Ratios of Friction to Pressitre for A 



Motion in their Bearings. 



I.- 


-ACCORDING TO MORIN'S EXPERIMENT. 










State of surfaces and nature of lubrication. 




It 

ft 


1. 
If 


1| 

n 


Oil, tallow, or 
hogs' lard. 


H 

Is 


il 


0/ o 


Designation of Surfaces 
IN Contact. 


Supplied 

in the 
ordinary- 
manner. 


The 
grease 
coiitinu- 

ally 
renewed. 




r.ronze on bronze 








0-079 

6' 075 
0-075 
0-075 
0-075 
0-125 
0-100 
0-116 










lU'onze on cast-iron 








0-049 
0-054 
0-054 
0-054 
0-054 








Iron on bronze. 


0-251 


0-189 





0-090 


0-111 




Iron on cast-iron 




Cast-iron on cast-iron 




0-137 
0-161 


0-079 








Cast-iron on bronze 

Iron on lignum-vitse 

Cast-iron on lignum-vitae 

Lignum-vitae on cast-iron . . . 


0-194 
0-188 
0-185 


0-065 




0-137 
0-166 






0-92 





0-109 


0-140 






0-153 


Lignum-vitae on lignum-vitae.. 









0-170 
























It is well known that the obstruction which a cylinder meets in rolling along a smooth 
plane is quite distinct in its character, and far less in amount, to that which is produced 
by the friction of the same cylinder drawn lengthwise along a plane. 

In the composition of machines attrition should be avoided as much as possible, and 
rolling motions substituted. 

On this principle depend the advantages of the application oi friction-wheels 2indi fric- 
tion-rollers. The extremity of an axle c, Fig. 395a, instead of 
resting in a cylindrical socket, is made to rest on the circum- 
ferences of two wheels, A and B, to the axles of which, a and &, 
the friction is transferred, and consequently diminished in the 
ratio of the radius of the wheel A to the radius of the axle a. 

At speeds and pressures usual in machinery, the resistance 
from friction decreases as the journals and bearings heat up to 
limits which the engineer and mechanic would consider safe. 

With very heavy pressures and slow speeds, the lubricant 
may be forced out and journal and lubricant be brought into 

close bearing, while with light pressure and low speeds the journals float on the film of 
fluid, and the frictional resistance is independent of the materials of which journal and 
bearing are composed. 

Mr. C. J. H. Woodbury, in his experiments on the driving of cotton spindles, found 
the coefficient of friction to be from 7 to 20 per cent, the load being from 1 to 5 pounda 




Fig 395a. 



200 MECHANICS. 

per square inch, while Prof. Thurston, with heavy loads of 1,000 pounds per square inch, 
as on the crank-pins of the North River steamboat engines, found the coefficient of fric- 
tion was one half of one per cent, the unguent being sperm oil. Practically, it may be 
said that the coefficient of friction for light-running spindles should not exceed 10 per 
cent, and for the usual work in shops, of say 100 to 200 pounds, should not exceed from 
2 to 3 per cent. 

For lubricants under heavy pressure and slow speeds, use graphite, soapstone, tallow, 
lard, and greases. For the journals of calender rolls in paper mills, it is common to lay 
on the top of the journals a large piece of salt pork, skin up. 

Cast iron holds oil better than any other metal or alloy, and is the best metal to use 
for light bearing, perhaps for heavy. 

It has been proved by Mr. Waite's experiments that a highly polished bearing is 
more liable to friction than any surface finely lined by filing. The lines left by the file 
serve as reservoirs for the oil, while the high polish leaves no room for the particles be- 
tween the metal surfaces. 

Mr. Waite's experiments on very heavy bearings at Manchester, N. H., go far "to 
prove that a considerable quantity of thin, fine oil keeps the bearing much cooler, and 
requires less power than a smaller quantity of thick, viscoas oil. No vegetable oil is fit 
to use as a lubricant, and castor oil is the worst of all, because the most viscous, and all 
vegetable oils in connection with fine vegetable fibre, like cotton, are liable to spontaneous 
combustion. 

' ' The rule of best lubrication is to use an oil that has the greatest adhesiveness to metal 
surfaces, and the least adherence as to its own particles. Fine mineral oils stand first in 
this respect, sperm second, neat's-foot third,* lard fourth." 

Experiments on rolling friction usually include that of the axles. The resistance 
of a wheel rolling on a smooth and resistant plane is very different, and much less 
than that of the same wheel fixed and sliding on the same plane; a moving railroad 
train is brought to a stop by the brake reducing or stopping the rotation of the 
wheels. 

Between the usual diameters of wheels the resistance has not been found to increase 
inversely as the diameter, but rather as their square roots of the diameter, and less on 
hard and well-graded roads. 

Of the resistance dependent on the material and character of the roads there have 

been many experiments. The following formula and table is from Prof. Thurston on 

" Rolling Friction," 

W 
R=/_ in which R = resistance, W the total weight, and r the radius of the wheel: 
r 

Kind of road. - Value of friction. 

Well paved 0'02 

Hard, smooth ground 0-02 

Well macadamized and rolled 0-015 

Smooth wooden pavement 0-01 

Ordinary railroads '. 003 

Best possible railroad 001 

" On railway trains a minimum resistance is reached usually at a speed between 10 
and 15 miles per hour, but the increase is not great at higher speeds where the common 
system of lubrication is practised ; in ordinary work, the resistance varies as low as from 
4 pounds per ton of train up to 25, and sometimes above 30 pounds. " 

At a speed of 25 miles per hour, Chanute makes the increase of resistance due to 
curvature about 0*4 pound per degree per ton. 

The amount of resistance is measured by the weight resting on the axles, multiplied 
by c, which is dependent on the condition of the surface of the rails : 



MECHANICS. 201 

Perfectly dry c= f 

Average condition ^ ^^ j 

Damp in rain, fog, or tunnel j'2^ 

Greasy or iced ^-V 

With head winds the resistance is increased with the square foot of front exposed and 
as the square of the velocity in miles per hour. 

Side winds, by forcing the flanges of the wheels against the rails, adds very seriously 
to the resistance of draught. 

On street railways the resistance to the movement of cars is greater than upon rail- 
roads, and may be considered from 3 to 5 times as much. 

From his experiments in 1840, Morin states the resistance applied at the circumfer- 
ence of the wheel on pavements and macadamized roads to be inversely proportional to 
the diameter of the wheel independent of the breadth of the tire and increasing with the 
velocity. 

By the Studebacker experiments in South Bend, Ind., it was found that there was no 
reduction in resistance on hard roads in increasing the width of the tire, but rather the 
contrary, nor in soft mud or slush ; but on sandy roads or across fields the resistance is 
very much less with a broad tire. 

In many States there are laws regulating the width of tire in proportion to the load, 
and even on the harder roads it is supposed that the broad tire deteriorates the track 
less than the narrow one, and in fact acts as a roller and improves the roadway, and for 
the same purpose the front wheels are of less gauge than the hind ones, that they may 
not track in the same rut. 

It is of importance that the line of draught should be horizontal, as with an oblique 
pull the effort of the animal may either be exerted in carrying the load or by increasing 
the resistance of it on the roadway. 

MECHANICAL WORK OR EFFECT. 

Mechanical work is the effect of the simple action of a force upon a resistance which 
is directly opposed to it, and w^hich it continuously destroys, giving motion in that di- 
rection to the point of application of the resistance ; it is therefore the product of two 
indispensable qualities or terms: 

First. — The effort, or pressure exerted. 

Second. — The space passed through in a given time, or the velocity. 

The unit of force in England and here is represented by the pound, and the unit of 
space by the foot. 

The amount of mechanical work increases directly as the increase of either of these 
terms, and in the proportion compounded of the two when both increase. If, for 
example, the pressure exerted be equal to 4 pounds, and the velocity one foot per second, 
the amount of work will be expressed by 4 x 1 = 4. If the velocity be double, the work 
becomes 4x2 = 8, or double also ; and if, with the velocity double, or 2 feet per second, 
the pressure be doubled as well — that is, raised to 8 pounds — the work will be 8 x 2 = 16 
pounds feet. It is more usual to write foot-pounds ; but as explained before the Conti- 
nental idiom of Tcilogrammetre is followed, in which the unit of force, kilogramme, pre- 
cedes that of space, the metre, it should be pounds-feet. 

In comparison of motors with each other, it is usual to speak of them as so many 
horse-power equivalent to 550 pounds-feet per second, or 33,000 pounds-feet per minute. 
The Continental horse-power is equal to 75- kilogrammetres or 542*48 pounds-feet per 
second. 

It is very common to use other units of force and space, as tons-miles ; and train- 
miles, in railway practice. 

The time must also be expressed or understood. It is impossible to express or state 



202 MECHANICS. 

intelligibly an amount of mechanical effect without indicating all the three terms — force, 
space, and time. 

The motors generally employed in manufactures and industrial arts are of two kinds 
— living, as men and animals ; and inanimate, as water and steam. 

"What may be termed the amount of a day's work, producible by men and animals, is 
the product of the force exerted, multiplied into the distance or space passed over, and 
the time during which the action is sustained. There will, however, in all cases be a 
certain proportion of effort, in relation to the velocity and duration, which will yield the 
largest possible product or day's work for any one individual, and this product may be 
termed the maximum effect. In other words, a man will produce a greater mechanical 
effect by exerting a certain effort at a certain velocity than he will by exerting a greater 
effort at a less velocity, or a less effort at a greater velocity, and the proportion of 
effort and velocity which will yield the maximum effect is different in different indi- 
viduals. 

In the manner and means in which the strength of men and animals is applied there 
are three circumstances which demand attention : 

1. The power, when the strength of the animal is exerted against a resistance that is 
at rest. 

2. The power, when the stationary resistance is overcome, and the animal is in mo- 
tion. 

3. The power, when the animal has attained the highest amount of its speed. 

In the first case the animal exerts not only its muscular force or strength, but at the 
same time a very considerable portion of its weight or gravity. The power, therefore, 
from these causes must be the greatest possible. In the second case some portion of the 
power of the animal is withdrawn to maintain its own progressive motion ; consequently 
the amount of useful labour varies with the variations of speed. In the third case the 
power of the animal is wholly expended in maintaining its locomotion; it therefore can 
carry no weight. 

Weisbach calls the mean effort of an animal one fifth its weight, which may serve as 
a general rule, but, in practice, will be considerably modified, when applied to the indi- 
vidual, depending upon the exertions, and the conditions and circumstances under which 
it is made. A man-power is usually estimated at one sixth of a horse-power (H. P.); 
yet, if the muscular force of a man be required for an effort of short duration, it will ex- 
ceed one horse-power. Thus, a horse-power is equal to 33,000 poands-feet per minute, 
or 550 pounds-feet per second; and, if a man weighing 150 pounds move upstairs at the 
rate of four feet per second, he exerts a force of 600 pounds-feet, which he can readily 
double for a few seconds. 

The force of a man is utilized mechanically through levers, as in pumping or rowing, 
or at a vertical capstan, or at a crank, carrying or dragging loads, shovelling, etc. In 
continuous work at the lever he will exert from 25 to 30 pounds; at the crank, from 15 
to 20 pounds. 

The muscular force of horses is utilized in the draught of carriages, in hoisting, and 
in horse-powers, either moving in a circle round a central shaft or on a revolving plat- 
form, or on an endless belt. The draught of a horse varies with the speed of movement 
and its duration. Trautwine gives the draught of a horse at two and a half miles per 
hour for 10 hours per day, 100 pounds; 8 hours, 125 pounds; 6 hours, 166f pounds; 5 
hours, 200 pounds. The omnibus -horses here average nearly six miles per hour, and 
make 16 to 24 miles per day; the average will not exceed 16 miles. At the Manhattan 
Gas Works a span of horses hoist from the lighter 200 tons gross in 10 hours to the 
height of say 25 feet, with charges of 6 to the ton, in a bucket weighing 150 pounds, the 
rope passing over a single block and through a snatch-block. On a horse-power, the 
force exerted by a single horse is from 125 to 175 pounds, at an average speed of about 
three miles per hour, and for eight hours per day. Beyond a speed of four miles per 



MECHANICS. 



203 



hour the pounds-foot of work of a horse will decrease in an increasing ratio up to the 
limits of his speed, when the whole work done will be used up in locomotion. In pro- 
portioning levers, cranks, traces, chains, through which animal force is transmitted to 
machines, or for mechanical purposes, it is not safe to estimate the stress as the average 
force ; there are impulses and stresses in action which will exceed the weight of the 
animal. 

Water-Power. — Water, used for the purposes of power, moves machinery either by its 
weight, by pressure, by impact, or by reaction, and is applied through various forms of 
wheels. 

Fig. 396 is what is termed a tub wheel with a vertical shaft, the wheel running in a 
bottomless, wooden case or tub to which the water is conveyed by a wooden trunk or spout 

and acting on the floats or buckets by im- 
pact. The wheel was commonly used for 
grist mills, and the power was applied di- 
rectly to the stones through the vertical 
shaft. The same wheel on a horizontal 





Fig. 39G. 



Fig. 397. 



shaft, without the tub, was called a flutter wheel, and the power was transferred by 
crank on the shaft through a wooden connecting rod or pitman to the saw frame of 
.saw mill. A similar wheel, but of 
larger diameter, w^as suspended over 
the surface of a stream, the floats be- 
ing dipped into the water suflflciently 
to give motion and power. 

Fig. 397 is the section of the up- 
per part of a breast wheel, in which 
the water is admitted through the 
gates g g g, acting after its delivery 
into the buckets through gravity ; the 
power is transferred through the cir- 
cumferential gear to a jack shaft, usu- 
ally placed below the gates ; a plank 
case called the breast is set outside 
the wheel with but little clearance 
from the gates to within a few feet 
of the bottom of the wheel. Wheels 
of this class, where water is brought 
over the top of the wheel and dis- 
charged into the buckets without a 
breast, is called an overshot wheel, 
and when the water is discharged be- 
neath the wheel, an undershot. The 
overshot and breast, when properly Fig. 398. 




204 



MECHANICS. 



proportioned, give a good percentage of effect, but occupy considerable space, and the 
speed of the gear is slow. 

Fig. 398 is one of the earliest improvements of the reactor, the Scotch wheel ; the 
principle is that of the sky-rocket. It is very simple in construction; the central curve 
of the hollow arm or adjutage is constructed like a cam, in which the horizontal move- 
ment is a percentage of the radial velocity due to the head, and the cross sections of the 
arm a contracted vein. 

The above wheels belong rather to history, but there are positions and circumstances 
which make them the most available. 

The wheels now in use are mostly of cast iron or bronze, occupying small space, and 
the shafts giving a velocity nearly proportioned to the speed of the machinery which it 
is to drive. 

Fig. 399 is a Fourneyron, called in this country a Boyden wheel, from the improve- 
ments which he made upon it. The water flowing downward through a pipe is diverted 
by guides at the bottom, which give it an outward direction with a tangential whirl as it 
strikes the buckets of the wheel, which are formed to give a reactive impulse. 

In Fig. 400, the Jonval, there are fixed guides in the tube that give motion to the 
water against guides in the wheel beneath and a resulting reaction. 




-'1[~^ ^ -' 








Fig. 399. 



Fig. 400. 



Fig. 401. 



Fig. 401 is the type of wheel commonly used ; the fixed guides are at the outside of 
the wheel and the motion of the water is inward and downward against the buckets. 
The shaft of this wheel is generally vertical, and the power transmitted generally through 
bevel gears, but it is often preferable to set the shaft horizontally and transmit the power 
through belting. These wheels, whether horizontal or vertical, can be set above the tail 
race and the entire fall utilized through draught tubes below the wheels, and admit of 
the use of belts. The greatest length of draught tube from the centre of horizontal 
shaft to tail water at Manchester, N. H., is 26 feet. 

Wheels can be furnished by many makers from stock from 6 to 84 inches in diameter, 
the smaller ones for very extreme heads of water, and the larger to the limit of 100 feet. 
The power for the different wheels depends on the head, the speed of the shaft on the 
size of the wheels. For the best percentage of effect, the wheel must be of good de- 
sign, material, and workmanship, and the makers will give their opinion as to which of 
their wheels they consider best adapted for any given position. 

Fig. 402 is the elevation of a Pelton wheel, in which the action of the water on the 
bucket is by impact, and Fig. 403 a section of the bucket showing the action of the 
water upon it; they work under heads as high as 1,000 feet and to 2,000 H. P., giving a 
large percentage of efficiency. 

However used, the mechanical effect inherent in water is the product of its weight 
into the height from which it falls; but there are many losses incurred in its application, 



MECHANICS. 



205 



so that only a portion of the mechanical effect becomes available ; and the comparative 
efficiency of any water-wheel or motor is represented by this percentage of the absolute 
effect of the water applicable to power. 

The watershed of the Merrimac River at Lowell is 4,085 square miles; and the per- 
manent water equal to one cubic foot per second per square mile of shed during working 




Fig. 402. 



hours ; gross fall, 34^ feet ; loss in canal, say 1^ foot ; and in flumes and races, 1 foot ; 



net fall, 32 feet; 



4,085 X 62-4 pounds x 32 feet 



= 14,830 H. P. 



550 pounds 

Taking the effective power on the wheel at 80 per cent, which is obtained from the 
wheels at full gate, 14,830 x SO = 11,864 effective H. P. A very close rule to deter- 
mine the E. H. P. is, multiply the number of cubic feet per second by the fall in feet 

and divide by 11, thus: ^^^^^ ^ ^^ = 11,884. 
J , 11 

Wind is applied for the purposes of power ; but, as there is no constancy in its action, 
its use is mostly confined to the purpose of raising water by means of pumps into cisterns 
or reservoirs. 




Fig. 403. 




Steam is the elastic fluid into which water is converted by a continuous application 
of heat. It is used to produce mechanical action almost invariably by means of a piston 
movable in a cylinder. Thus, in Fig. 404, the steam entering through the lower 



206 



MECHANICS. 



channel-way, or port, presses against the under side of the piston in the direction 
of the arrow, the piston is forced upward, the steam above the piston escaping 
through the exhaust-channel o. When the piston reaches the top of the cylinder, 
the valve is changed by mechanism, the steam enters above the piston, and the 
steam below it escapes through the exhaust ; in this way a reciprocating motion is es- 
tablished. 

It is not practicable at a single instant to let the whole pressure of the steam in the 
boiler into the cylinder, nor maintain it uniform during the whole stroke ; there are 
losses of pressure due to friction through the pipes, valves, and channel-ways, and back 
pressure from the same causes in the exhaust, condensation from exposed surfaces, and 
consequent reduction of pressure and volume of steam, and there are gains of effect by 
cutting off the introduction of steam to the cylinder at some point of a partial stroke, 
which is completed ,by the expansion of the inclosed steam, but with a constantly di- 
minishing pressure. 

Under expansion, the volume of a confined gas is inversely proportional to the pres- 
sure to which it is exposed. This is called the law of Mariotte, or the law of expansion, 
under equal temperatures for all gases, and is shown graphically in Fig. 405. 



Vol. Recip. 




Fig. 405. 



To determine the action of the steam within a steam-engine cylinder, an indicator is 
used. It consists of a small cylinder connected by a steam pipe with the main cylinder, 
with its piston controlled by a graduated spring, and recording by a pencil the varying 
pressures in the main cylinder on a paper card wrapped around a reciprocating cylin- 
drical tube ; to this, movement is given by a cord attached to some mechanism connected 
with the steam-engine piston, but with a reduced motion. 

Indicator cards show the efficiency of a steam engine by a comparison with theoreti- 
cal ones, the mean effective power exerted (M. E. P.), the volume of steam expended, 
losses of pressure by imperfect passages or channels, leaks in valves and around pistons 
and by radiation. 

Fig. 406 is an indicator card from a non-condensing engine. The steam exhausts 
directly into atmosphere, and the back pressure, 3 to 3 pounds, is shown by the line just 
above that of the atmosphere line. 



MECHANICS. 



207 



In Fig. 407 the exhaust is into the condenser, where a vacuum is maintained by the 
air pump of from 2 to 3 pounds. The M. E. P. of the condensing engine is greater than 























13. 
17. 


A 


2 c 


^ 


%_ 


1 










36 10. 
35.5 11.5 
35.5 11.5 
80.5 10.5 
26. 10. 
.,. 15. 9. 
>. 10.5 8. 
1\ 6.5 7. 5 
1 \ 4.5 6. 

\. 3.5 4. 20.3 
^O ''■^^^03.5 = 20.3 SS.= 8.8 
"^^ ir^ Tn^"--~>^^^_M. E. P. 29. 1 


25. 

35. 

48. 

64. 

B5. 
118. 
122. 

120. M.E.P. 
647 = 64.7 




a 








in 


in ^ 
^ % 

A:mospher 

iS ^~ 
— ■ o 


C't J- 


/ 


V. 


- f -^— 






Atmospheric Line 
Fig. 406. 


















Fig. 407. 



that of the non-condensing, but this is not obtained without expense of power in running 
the air pump, and more condensation in the cylinder due to the lower temperature at 
which the steam leaves it. See Table of Temperatures of Steam, Appendix. 

The ends of both cards are rounded by the early opening of the steam valve in the 
out stroke, and by the earlier closing of the exhaust valve in the return stroke. This 
last shuts up the balance of steam in the cylinder, as shown by the curve of compression, 
and retains a volume of some importance in the next stroke, especially in quick-running 
engines regulated by movable eccentrics, and cushions the piston at the end of the 
stroke. 

Both cards are divided into ten equal spaces, and subdivided for the average pres- 
sures, which are given in figures on the scale of pounds of the indicator. The sum of 
the pressures are then divided by 10, which gives the M. E, P. , which, multiplied by the 
area in square inches of the piston by the travel in feet per minute and divided by 33,000, 
gives the H. P. 

Assume the diameter of the cylinder in Fig. 406 
to. be 15" (area, 176-7); stroke, 3 feet; revolutions, 
90 per minute. 90 x 3 x 2 = 540 feet travel per 
minute. 



Then, 



64-7 X 176-7 X 540 



= 187 H. P. 



33,000 

The indicator card may be divided into twenty 
equal spaces, and the first, third, fifth, . . . nine- 
teenth taken as subdivision ordinates, or it may be 
divided by a flexible grid ; but where ordinates are 
not required the M. E. P. may be taken by plani- 
meter. 

The M. E. P. of a steam cylinder can be esti- 
mated approximately from the initial pressure and 
the cut-off. The reduction of pressure by the cut- 
off is shown in the diagram (Fig. 408) constructed 
from the formula of Rankine for dry saturated 
steam. Multiply the initial pressure by the decimal 
on the vertical line of the diagram at its intersection 
by the curve of cut-off, and the result is the M. E. P. 
of the entire card to 0; from which to find the 
effective pressure as given by the indicator card 
there must be subtracted the loss of pressure be- 
tween the lower line of card and the line. Assume the initial pressure in Fig. 406 
to be 124 pounds above atmosphere, and the vacuum 14*7, or, together, 138*7 cut-off 




208 



MECHANICS. 



1.00 
1.00^ 



o 

C/5 O.J 



§ 0,70 
en 



en 

t- 

< 0.50 

CL 



2 

o 

UJ 
Q 

? 0.40 
cc 

CO 

en 

HI 



u 0.30 

3 



0.20 



ZERO 
LINE 



1.11 

0.90 



EXPANSIONS 
1.25 1.43 

0.80 0.70 



t 



I 



t 



UT^OFF- 



1.67 

0.60 



2. 

0.50 
1.00 



0.90 



0.70 



0.60 



0.20 



0.10 
10 


0.20 0.30 
5 3.33 
EXPANSIONS 
Fig. 408. 


0.40 
2.5 


0.50 
2. 



at J, or -25 of the stroke, 4 expansions by diagram -582 x 138"7 = 80-7 pounds, 

80-7 

17"7 
3 pounds above atmosphere and 14-7 below, --— 



MECHANICS. 



209 



In the appendix will be found a table of both dry and moderately moist steam from 
the same authority. 

At the commencement of each stroke there is a space between the piston and the 
cylinder head which, together with the space between it and the valve, are called clear- 
ances, and, as it causes an expenditure of steam, is reckoned in percentages of the 
stroke. 

To enable one to judge of the economy of the steam engine, it is necessary to know 
how much weight of steam is used. In the example the pressure at cut-off is taken at 
139 pounds, and the weight of a cubic foot of steam at this tension, by tables of satu- 
rated steam in appendix, is -3092 pound ; the area of cylinder = 1 -227 square feet. 

Stroke 3 x '25 cut-off = -75 

Clearance, 3 per cent of stroke = "09 

•84 foot. 
1-227 X -84 X -3092 = -319. '319 x 180 strokes x 60 minutes = 3,445 pounds per 
hour. If the evaporation be 8 pounds of water per pound of coal, then the consump- 
tion of coal would be 431 pounds, and -— = 2*30 pounds of coal per H. P. per hour. 

187 

Of late years, the principle of expansion has been very much extended by the con- 
struction of compound engines. Fig. 409 shows the general arrangement, without valves, 
of a simple compound engine of two cylinders — a 
high-pressure (h. p. c.) and a low-pressure (1. p. c.) 
one. The h. p. c. (ABC D) draws its steam from 
the boiler and exhausts into the 1. p. c. (A', B', 
C, D') ; the top of the h. p. c. into the bottom 
of the 1. p. c, and vice versa, so that the pressure 
on the pistons of the two cylinders is in the same 
direction. 

To determine whether a steam engine is work- 
ing properly, it is necessary to compare the abso- 
lute card with the theoretical one. 

Figs. 410 and 411 represent indicator cards, 
taken from a condensing and non-condensing engine. On these are shown the con- 
struction of the isothermal curve. It will be observed that there is a line, A B, to the 
top of the card. The space between this and the card represents the clearance, which, 
estimated in percentages of the capacity of the cylinder, is plotted on the indicator card. 
On the indicator card, as taken by the instrument, the absolute can not be taken, but 
only that of the atmosphere, the will be at a distance below this, corresponding to the 






Fig. 410. 



Fig. 411. 



barometric pressure, usually 14*7 pounds. Draw the line parallel to the atmospheric 
line, the clearance line perpendicular to it, a line parallel to the line, at the height of 
the initial pressure, and a line parallel to the clearance line at the point of cut-off on the 
initial pressure line. Any point on the expansion line, as la, 22, 3a, may be determined 
15 



210 MECHANICS. 

by drawing lines B 1, B 2, B 3, and then horizontal lines la li, 2a 2i, Sa 3i from their in- 
tersections li, 2i, 3i. With the cut-off line, parallel to the line, and perpendiculars 
from 1, 2, 3, the intersections of these two lines, la, 22, 32, will be the points in the 
curve. Inversely, the indicator card may be tested by the construction of parallelo- 
grams on the curve, and if their diagonals intersect at a point on the line it may be 
considered that this represents the amount of clearance. The curves in the outline of 
the cards, at the times of admission, cut-off, and exhaust, show the action of the valves 
and time occupied in change of condition. The stroke commences at A, cuts off at C, 
commences to exhaust at E ; about D the exhaust valve closes. 

To enable a draughtsman to comprehend the action of the steam in multiple cylinders 
and calculate approximately the diameter and capacity of the different cylinders, a curve 
of expansion is constructed. Fig. 405. The ratio of expansion is on the Mariotte curve 
and is as the reciprocal of the pressures. Taking as the unit the abscissa of the pressure 
of 100 pounds, at 120 it is -833, at 40 pounds 2-50, and on this principle the curve is 
drawn, taking cross-section paper, for the ease with which it may be laid down and as 
more intelligible in its explanation. 

In Fig. 405 is illustrated a triple compound with an initial pressure (I. P.) of 120 
pounds and a final expansion of twenty-one times. To divide the expansions between 
the three cylinders, V^l = 2"76 expansions in the first cylinder, 2 '76 x •833 = 2-30 
abscissa at end of stroke of first cylinder. 

120 ri P ) 

(1) — ^^-^ — — = 43*48 final pressure, ordinate corresponding to an abscissa of 2*30. 

(2) 2-76^ = 7-617. 7-617 x -833 = 6-345 i^ = 15-76 pounds. 

120 

(3) 2-76^ = 21. 21 X -833 = 17-5 —- = 5-71 pounds. 

With a cut-off at -833, and an expansion of 2-76, the stroke will be 2-3, which is the 
uniform stroke in the three cylinders. Calling the diameter of the H. P. cylinder 15" 
A 176-7 n", the area of the 1. P. cylinder will be 176-7 x 2-76 = 487*69 square inches 
= 25" diameter, and that of the low pressure 487-69 x 2*76 = 1,346 square inches = 41^" 
diameter. Taking the M. E. P. of the different cards by averages or by planimeter, in 
which the area of the card in square inches is divided by the length of card in inches 
and multiplied by the vertical scale, we find the M. E. P. for first cylinder 42-2, second 
cylinder 15-4, third cylinder 5-6. The pounds-feet per stroke will be: 

First cylinder, 176-7 x 2-3 x 42-2 = 17,150 
Second " 487-69 x 2-3 x 15-4 = 17,274 
Third " 1,346- x 23 x 56 = 17,336 

51 332 

The M. E. P. of the whole card was 16-6, stroke 17 5, area 176-7 = -—- = 17,110 pounds- 

o 

feet, a result very nearly that of the single cylinder, but as the areas measured by the 

planimeter includes only that between the lines of final pressure, while the absolute card 

in the low-pressure cylinder should be carried to the line of exhaust, or say 3 pounds 

above 0, the pounds-feet of effect should be more than in either of the others, which it 

would be impossible to equalize with the same stroke and the same rates of expansion. 

All these results are obtained from the plotted isothermal curve, but in expanding steam 

does not maintain the same temperature, and occupies less space than shown by the 

above curve, and making allowance for this a curve is developed which is called the 

adiabatic curve. 

To plot this on the diagram take the abscissa at 120 as equal to 3*65 (or the volume 

of steam at this pressure), construct a scale taking the volumes at the different pressures 

from the table in the Appendix ; but if the stroke and the areas of cylinders is considered 

the same as in the previous calculations, although the area of the cards is less, yet as the 



MECHANICS. 211 

length of card is less, the M. E. P. remains nearly the same, and consequently the pounds- 
feet of results, estimating pounds-feet of work done in the several cylinders by the mean 
pressures as taken from Rankine's tables in the Appendix. In these cases the average 
pressure is taken from the 0, from which has been subtracted the initial pressure in the 
next cylinder. 
Thus: 



Average pressure in first cylinder 88 

Initial pressure in second cylinder 43 

M. E. P. in first cylinder 44 

Average pressure in second cylinder 31 

Initial pressure in third cylinder 15 

M. E. P. in second cylinder 16 

Average pressure in third cylinder 11 

Pressure at end of expansion 5 

M. E. P. in third cylinder 5 



86 



For dry steam the results are very nearly the same as by the Mariotte curve. In none 
of the calculations is the difference as great as will be found in practice, where it is 
found desirable to jacket the steam cylinders and heat the steam in the intermediate 
chambers to prevent condensation from the walls of the cylinders and passages, and to 
restore the heat which has been converted into work. 

The above card refers to an engine in which there is an intermediate chamber between 
the cylinders. 



In the designing of machines it is often important to show the changes in the moving 
parts, that they may not conflict with each other in the practical working, and to obviate 
the effect of dead-points through which motion may have to be transferred. 

To describe the path of the crosshead of the piston of the steam engine, its connect- 
ing-rod, and crank, Fig. 412, draw the path of the crosshead which, controlled by 
guides, is a straight line ; divide into equal parts to 6 ; on the same line lay off the 
length of the connecting-rod from to 0', and the length of the crank to the centre C ; 
from C as a centre with a radius equal to the length of the crank describe a circle which 
will be the path of the crank-pin. From the points 1, 2, 3, '4, 5, and a radius equal to 
that of the connecting-rod, describe arcs cutting the crank path at V, 2', 3', 4', 5', 0' 
and 6' on the line of the crosshead path, the commencement and end of the strokes. 
The path of the crosshead is divided into equal spaces, but that of the crank-path is not. 
The point 3' corresponding to the mid stroke 3 of the crosshead is not that of the half 
circumference of the crank-path. These irregularities are due to the angularity of the 
connecting-rod, which is here made less than its usual proportion to that of the crank. 



212 



MECHANICS. 



Moreover, when the crank-pin and the axle-centre are in the line with the connecting- 
rod, as at 0' or 6 6', the driving force passes through the fixed axis and no motion is 




5 4 '3210 



Fig, 412. 



possible. Some other mechanism is necessary to pass over the dead-points ; usually this 
is by means of the fly-wheel, in which the force stored in the mass by rotation continues 
the motion, and rightly proportioned nearly with uniformity, and the irregularities are 
transferred to the stroke, Fig. 413. 




Fig. 413. 



If the crank is the driver there will be no dead-point ; the circular movement of the 
crank -pin will be converted into the rectilinear and reciprocating one of the crosshead. 

In locomotives the cranks from the cylinders are put at right angles, that there may 
be no dead-point. 

STANHOPE LEVERS. 

In the Stanhope hand press (Fig. 414) the extreme power is obtained by a combina- 
tion of levers in which the greatest pressure is exerted when the platen has reached the 
type. A is a fixed point on which the bell-crank lever B revolves, and to the extremity 
of which the power is applied, and which describes the circle designated by equal arcs, 
0-10 ; at the angle & of B there is a connection C with the lever D revolving on a fixed 
centre, d\ under this action the ])oint of the lever D, at which the pressure is exerted, 
passes through the small arc 0-10, corresponding to the arcs of the extremity of the 



MECHANICS. 



213 



lever B, but always with decreasing lengths, as shown on the figure, and consequently 
increasing pressure. 

To obtain the positions of the lever from the path of the lever B, from A as a centre, 
and with a radius equal to A 0, describe an arc the path of the extremity of B, and 




Fig. 414. 

divide into equal arcs 0-10 ; on A as a centre describe another arc, A &, and from any 
point, say 5, with a radius equal to 6 0, describe an arc 5", intersecting the arc &; from 
d asa. centre, with a radius equal to d c, describe an arc, and from 5", with a radius equal 
to 6 c, intersect the previous arc, and through this point draw a radial line from d ; with 
a radius equal to d 0, describe an arc for the path of the extremity of the lever D ; the 
intersection of the radial with this arc will give the point 5 on the smaller arc, corre- 
sponding to 5 of the larger. In the same manner other positions can be determined. 

whitworth's quick return motion. 

Fig. 415 is known as Whitworth's Quick Return Motion, and consists of a driven 
crank, a ; moving at a uniform speed, to the end of the crank is a block, d, sliding in a 
slotted link; this link is fastened to a fixed centre, e, and has a vibrating motion. A 




Fig. 415. 



tangent drawn from each side of the crank-path to the point e will give the extreme 
movements of the link e, and a line at right angles to this line and from the centre of the 
crank-shaft on each side will divide the crank-path in two parts. The tool-holder, /, or 
planer platen, travels over an equal space while the crank moves from d' to d as from d to 
d' ; it follows, therefore, as the crank is moving uniformly, the motion of the tool-holder 
while cutting is slow and the return quick. 



214 



MECHANICS. 




Fig. 416, 




Fig. 417. 



MECHANICS. 



215 



watt's parallel motion. 

Watt's parallel motion is shown in Fig. 416, the 
object of this motion being to obtain a rectilinear mo- 
tion of the piston-rod and air-pump rod under the 
varying angularity of the beam. 

In the figure the line C D indicates the centre of 
the beam ; from the point H, situated midway between 
C and D, and from D, are suspended two links, H I 
and D E, of equal length. Connect E and I by a rod 
equal in length to D H ; the point I is then attached 
to the fixed centre at O, and is equal in length to E I, 
with an angle E I O equal to the angular motion of the 
beam. By the movement of the beam the point H is 
thrown outward from C and I inward an equal amount ; 
the centre point, K, connected with the air pump, takes 
a nearly vertical movement, and the same may be said 
of the point E ; the heavy lines illustrate the position 
of the various levers when the beam is in the middle 
of its travel. 

It is the practice in this country to use crossheads 
and guides for the piston rather than parallel motions. 

Fig. 417 represents another form of parallel motion 
to preserve the perpendicularity of the piston - rod 
against the varying angle of the connecting-rod. 

This motion consists of two pairs of equal radial 
bars, O I and O' I', moving in planes parallel to that of 
the circle of revolution of the crank, and on opposite 
sides of the piston-rod and connected by a link IF, 
while the centres O and O' are fixed at points at equal 
distances from the centre of motion and on opposite 
sides ; the communication with the piston-rod is at C, 
which point moves nearly perpendicularly. 

The dotted lines show the positions of rods and 
levers when the crank is at the extreme point of its 
revolution. 

JANNEY CAR COUPLER. 

Fig. 418 is a drawing of the Janney car-coupling 
device, the lower portion being in section to explain 
the internal mechanism, and the upper portion a top 
view, showing the exterior appearance. 

The section and top view of the coupler, in dotted 
lines, represent the couplers approaching each other 
for coupling, and the section and portion in solid lines 
show the coupling completed. 

The knuckle B represents a pinion with two teeth 
B' B^ and the drawhead A and tooth or nose, B^, of 
the other coupler representing the rack. When the 
couplers are brought together the teeth engage each 
other, the hub revolves, and the long tooth B' is carried 
around to a locking position, the catch C being forced 
back by the circular end of tlie tooth B' in passing, 
after which the catch is returned to its locking position 
by the catch spring F. 



irr 




216 



MECHANICS. 



The uncoupling is effected by throwing over a platform lever, which in turn forces 
around the coupler lever D and catch C, allowing the tooth B' to revolve outward. 

VALVE MOTION. 

To establish the reciprocating motions of the piston, valves must be moved so as to 
alternately let the steam into one end of the cylinder and permit it to escape at the other. 
The mechanism by which the valves are moved are usually by means of an eccentric on 
the crank-shaft, and a strap and rod connecting it with the valve rod. 

The motion of the rod is the same as if the eccentric were a small crank. 










° 


^ 


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MjJ 


KV^^'> 




' .( 










^ \ 


■ 









Fig. 419 



Fig. 419 shows six positions of one of the old slide valves and piston, together with 
the position of the crank and eccentric for each movement of the valve. 



MECHANICS. 



217 



In Fig. 419 the valve is merely suflficient to cover the ports, and at the slightest 
movement in either direction passages veill be opened for steam to the cylinder, and the 
escape of the exhaust from it ; under these conditions there can be no cut-off, and con- 
sequently no economy from expansion of steam. 



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1 




f 

1 


/■~-\ 






\ 
\ 
\ 


>A' 



^ 




A'- 



i 




Fig. 420. 



For common engines the cut-off is effected by the lap and lead of the valve (Fig. 
420), When the valve is placed centrally over the ports, the portion of the valve over- 
lapping the steam ports is known as lap ; when on the steam side, it is designated as 
outside lap, and as inside lap when on the exhaust side. In quick-running engines, both 
steam and exhaust ports are opened before the completion of the stroke ; on the steam 
side there is a cut-off or closing of the valve before the completion of the stroke to ad- 
mit of expansion, and before the completion of exhaust for compression, thus saving heat 
and relieving the pressure and, consequently, the friction of the slide valve. 

The channels, usually three in number, alternately exposed and covered during the 
movement of the valves, are called jiorU. The ones admitting steam to the ends of the 
cylinder are the steam 'ports ; the central one giving exit of the steam from the cylinder is 
the exhaust port ; the spaces between the ports are called bridges. The working surfaces 
on valve and cylinder are valve and valve seat faces. 

The width of opening of the steam ports at the beginning of the stroke for the ad- 



218 



MECHANICS. 



mission or release of steam is termed lead ; on the steam side outside lead ; on the ex- 
haust side inside lead. When the valve is placed at half stroke over the ports, the 
amount which it overlaps each port, either internally or externally, is the lap ; on the 
steam side outside lap ; on the exhaust side inside lap. Laps and leads by themselves 
refer to outside laps and leads. The amount by which the valve has travelled beyond 
its middle position when the piston is at the end of the stroke is the linear advance. 

The proper understanding of the positions of valve under the different positions 
during the stroke are of great importance to the draughtsman. It is very common in a 
shop to have a model of an eccentric in which the throw can be readily changed and 
applied with a small rod for connection to a simple section of valve and ports. But the 
valve motion may be illustrated by diagram. 



VAJ.YE DIAGKAMS. 

The separate drawings of the movements of a valve may be shown in one general 
diagram containing the continuous movement of the valve ; for illustration, the valve of 
the last engraving is taken. 

Draw a perpendicular line (Fig. 421), E D, called the datum line ; from the centre, C, 
of this line describe a circle equal in radius to that of the eccentric ; for the first position 




Fig. 421-. 



of the eccentric draw a line perpendicular to D E of one inch and five sixteenths (one 
inch lap and five sixteenths lead) till it intersects the path of the eccentric at 1. Draw 
a line from C to 1 ; this is the first position of the eccentric ; from this point divide half 
the circle into six equal parts, representing six positions of the eccentric; from each of 
these points draw a horizontal line till it intersects the datum line ; these lines give the 
linear movement of the eccentric, and therefore the travel of the valve. From the centre 
C draw a circle equal in radius to that of the crank; commencing at 1', this being the 
first position of the crank, divide half the circle into six equal parts, the positions num- 
bered V 2' 3' on the crank-path corresponding to 1, 2, 3 of the eccentric path ; on the crank 



MECHANICS. 



219 



circle construct a square, F, G, H, I, and through each of the points of the crank-path 
draw lines parallel to the side of the square. Draw a horizontal dotted line A B through 
C, and from A as the centre of the exhaust port lay off the ports and bridges. Above 
and below this draw parallel lines alcdef across the square, indicating the limits of 
the exhaust opening and ports on both sides of the drawing, also horizontal lines g and^' 
to define the position of the valve when placed centrally over the ports, and draw a sec- 
tion of the valve according to the dimensions given. Lay off the distance from D E to 
the first position of the eccentric below g' on the line F H, and draw an outline of the 
valve as moved into this position. Lay off on each successive perpendicular line 3', 3', 
etc., from g'^ the corresponding positions of the eccentric as measured from D E, and 
draw a curve through these points. Lay off the position of the edges of the valve h ij h 
on the lines 3', 3', etc., above the determined points 2^^, 3', etc., and draw curves through 
these points. 

In this position of the valve the steam port has been opened by a distance equal to 
plc\ through^ draw a horizontal line intersecting the elliptical curve at a', draw shade 
lines from a to the curve below ; this shade represents the continuance of the steam in 
the cylinder ; the intersection a' is the point of cut-off and commencement of expansion. 
On the other side the cylinder is wide open to the exhaust, as shown by M, and is closed 
where the elliptical curve intersects the line e. The waste steam becomes compressed and 
is shown at N, and is utilized on the return stroke, as shown at L. The period of admis- 
sion against the piston is shown where the line of the curve intersects a at o, and is 
shown by the small space O at the commencement of the back stroke and at P for the 
forward stroke. 

This diagram entirely disregards the angularity of the connecting-rod. 

With a single valve it is difficult to secure economy in the cut-off; it is usual in 
the larger sizes of stationary engines to have steam and exhaust valves moved by separate 
mechanisms, and independent of each other, and to regulate the engine by a direct con- 
nection of the steam valve wiih the governor. 

Among this class of engines, the widest known is the Corliss, of which Fig. 423 is 
a side elevation of one of the simplest and earliest forms. 




Fig. 422. 



The exhaust valves at the bottom of the cylinder are connected positively with the 
wrist-plate w, vibrated by a hooked connection with an eccentric on the engine shaft. 
Connected with the wrist plate are two vibrating levers, R R', to the upper ends of which 



220 



MECHANICS. 



lever pawls, pp^ are attached, which rest on the stems, s, of the steam valves. On the 
stems are notches against which the pawls strike, push back the stems, compress the in- 
closed spring, and open the valves, and this continues till the outer end of the pawl 
lever, coming in contact with the head of the lever a, controlled by the governor, releases 
the spring which closes the valve. The cases, &, are cylindrical, with air cushions at the 
ends. 

Fig. 813 shows sections of the valves of which the ports are very long and narrow. 
In their construction, the valves may be considered cylindrical plugs, of which portions 
near the ports are cut away for the prompt admittance and exhaust of steam ; the valves 
are fitted on the lathe and the seat by boring. The motion given to the valves is rock- 
ing, but the valves are not firmly connected to the rocking shaft ; in the figure the valves 
are shown shade lined, and the shaft or stem plain ; the valves are not affected by the 
packing of the valve stem, but always rest upon the face of the ports. 







Fig. 4->3. 



Since the lapse of the Corliss patent, it may be considered the most popular form of 
design, and its manufacture has been taken up by many shops, which, while in the 
matter of valves and cut-off coming within the claims of the old patent, have been much 
improved in the details of mechanism. The dash-pot is now set vertically; the plunger 
acts without springs by gravity. 

Fig. 423 is the side elevation of a Corliss engine of the Fishkill Landing Machine 
Company, of which the details of the dash-pot are given in Fig. 424. It consists of a 
cylinder. A, of two different diameters, to which is fitted the double-diameter plunger, 
with grooved air packing, the one in the cylinder, the other on the lower plunger. At 
the commencement of the lift the plunger is at the bottom ; as it is raised, a vacuum is 
formed beneath the plunger, partial, as air is supplied from the annular space x x through 



MECHANICS. 



221 



the channelways e e', but the vacuum increases with the increase of the space y at the 
cut-off. 

The plunger's descent is rapidly retarded by a partial vacuum in e e\ and at the end 
of its stroke by the compression of the air in y, and seats without pounding. By the 




Fig. 434. 

valve 1) in the passage e e' the flow of air between the upper and lower end of the cylinder 
is controlled to produce this effect. 

Figs. 425, 426, and 427 are details of the releasing mechanism of the same engine. 

To the valve stem A is attached a single-armed lever, to which is suspended the 
dash-pot connection Y, and at the extremity the steel catch-plate c. The double crank 




Fig. 425, 



C C rocks on the valve stem ; to its lower end there is a connection X with the wrist- 
plate, from which it receives motion ; at its upper extremity C there is a small rocking 



222 



MECHANICS. 



lever and hook E which is pressed inward by the spring /, and the hook E, engaged 
with the catch-plate c, gives the motion of the wrist-plate to C C, opens the valve, and 




jji^^W 






Fig. 427. 

raises the piston of the dash-pot. The governor-rod Z moves the triple crank H H' H^, 
rocking on the valve stem A ; at the extremity of H' there is a roller R which is thrown' 
by the governor into such a position that it comes in contact with the roller R' on the 
hook E in its motion upward, and is thrown outward, disengaging the hook E from the 
catch c ; this arm, which is connected with the dash-pot, instantly falls, the valve closes, 




Fig. 428. 



MECHANICS. 



223 



and steam is cut off sharply; the return stroke again 
engages the catch and hook, and the release is again 
effected by the position of the governor. 

On the arm H^ there is an adjustable cam W, 
which serves as an automatic safety stop-motion. 
When the engine is at its lowest normal speed, and 
the hook E is at the point of engagement with the 
valve lever B, the roller R' comes nearly in contact 
with the camW. Should the balls fall below the 
point corresponding to the lowest normal speed, the 
bell- crank H will move in the direction of the arrow; 
the cam W will come in the way of the roller R', 
which will ride on the top of it, thus preventing the 
hook E from engaging with the end of the valve 
lever B, and the valve will remain closed. No steam 
being admitted, the engine will stop. 

Linic motion (Fig, 428) is a mechanism by which 
the travel of the valve is changed and the motion of 
the piston reversed at the option of the engineer. 
It consists of two eccentrics at nearly opposite points 
on the crank-shaft, each of w^hich is connected by 
rods to the opposite ends of a shifting link A ; with- 
in the link is a sliding block B ; the block B is at- 
tached to a rocker R. The link is suspended from a 
bell-crank C, controlled by the engineer through the 
rod a. As the link A is raised or lowered it slides 
on the block B, of which the movement becomes 
more or less, or is changed in direction according to 
its position in the link, and this motion is transferred 
to the valve through the rod r. 

This is a common form of link motion, but the 
same effect is obtained by a fixed link and a movable 
block without a rocker shaft connected by a link to 
the valve rod. 



DIAGRAM OF LINK MOVEMENT. \ 

The horizontal and vertical movement of the dif- " 
ferent positions of the sliding block of the stationary 
link in connection with the eccentrics is shown in 
Fig. 429. 

The link is attached to a radius rod attached to a 
centre O, which compels the centre of the link to vi- 
brate in an arc c c'. The crank-path is divided into a 
number of equal parts, say 12, commencing at its first 
position, and the forward and backwarji eccentric 
paths are similarly divided, also commencing at the 
first position. The length of the eccentric rod is 
then taken in the compasses and an arc described , 
from the point 1 of the fore eccentric, and another 
from V of the back eccentric. The arcs for the fore 
eccentric are struck above the centre horizontal line, 
and for the back eccentric are struck below this line. 
An arc is now struck from the centre of the link, 



224: 



MECHANICS. 




MECHANICS. 



225 




16 



226 MECHANICS. 

with a radius equal to the height at which the sliding block is in the link; where this 
arc intersects that struck from the fore eccentric wdll indicate the point at which the 
sliding block will be when the gear is full forward, and the same arc described, cutting 
the arc from the back eccentric, will give the point of the sliding block in the link 
when in full gear backward; and an arc described through these two points, with a 
radius equal that of the link, will give the centre line of the link when the eccentrics 
are in the position indicated. 

The other positions of the link are obtained in a similar manner. 

In describing tlie centre line of the link, numerous trials are necessary to get the 
proper centre of the arc passing through the two points, and where many positions of 
the link are necessary it will expedite the work by making a templet of the link in card- 
board, which can be readily applied to the several series of points. 

The upper line on the link movement connecting the series of points indicates full 
forward gear. The arc c c\ mid-gear. The lower line, full gear backward. 

This diagram also shows the position of the valve in forward and backward stroke. 

joy's valve gear. 

Figs. 430 and 431 are drawings of Joy's valve gear in different positions. This gear 
differs from the link motion in that the valve motion, instead of being given by means of 
eccentrics, is imparted directly from the connecting-rod. 

At a point A of the connecting-rod a link B is attached, the movement of this link 
being controlled by the radius rod C attached to a stationary point I of the engine ; from 
a point D of the link, movement is given to the lever E;- from the upper end E' of this 
lever, motion is given to the valve spindle G. The centre F has also a vertical movement 
due to the vibration of the connecting-rod at A; the centre or fulcrum F of the lever 
E is therefore carried in blocks sliding in slots of the link K, which has a radius equal 
to the length of the valve spindle G. In Fig. 431 the link is shown at mid-gear ; this 
link can be partially rotated by a point on the outside of the link corresponding to the 
point F of the lever E, shown in Fig. 430. When the link is thus inclined, as shown at X 
and Y, the vertical movement of E causes the blocks of the link and (he centre F to trav- 
erse a path inclined to a vertical line. The centre F has therefore a horizontal move- 
ment, tlie amount of which depends on the obliquity of the link. It is by this means 
that the cut-off of steam and the forward and backward movement of the engine is con- 
trolled. 

The dotted ellipse A N indicates the path of the point A of the connecting-rod, and 
the dotted curve beneath shows the path of the pin D, which partakes of the motion of 
the point A of the connecting-rod and of the extremity of the radius rod E. 

WALSCHAERT VALVE GEAR. 

Figs. 432, 433, 434, 435 are drawings of the Walschaert valve gear. In this gear 
the valve derives its motion partly from the piston-rod crosshead.and partly from a single 
eccentric moving a vibrating link. 

To the crosshead A is attached a fixed arm B ; to this arm is attached the link C, 
which communicates its motion to the combination arm D. To the upper end of this 
arm is connected the valve stem d-^ just below this connection the combination arm is 
pivoted to a centre e ; the valve derives the other element of its motion from the radius 
rod E attached to the centre e and to the slider in the vibrating slotted link F, which is 
hung externally at its centre/; the link receives its motion from the eccentric rod G 
attached to its lower end and connecting with the eccentric g. 

The sliding of the rod F in the slotted link by means of the levers, shown in dotted 
lines, is the means adopted for giving an earlier or later cut-off and forward or back- 
ward gear. 

Skeleton diagrams (Figs. 433 to 435) illustrate the movement of this gear : 



MECHANICS. 



227 




228 



MECHANICS. 



7/ 

V///////// 







\ / If 



MACHINE DESIGN AND MECHANICAL 
CONSTRUCTIONS. 

In the designing of new machines and mechanical constructions, the draughtsman 
must draw from his knowledge of well-known forms and parts, and combine them ; but, 
to proportion them properly, and adapt them to the purposes required, he must under- 
stand the stresses to which they are to be subjected, and the action and endurance of the 
material to be used, to withstand these stresses. 

In the present technical application x)f the term, stress is confined to a force exerted 
between two bodies or parts of a body, such as a pull, push, or twist. Strain is the 
alteration produced by a stress. Stress is the cause, strain the effect ; the first is meas- 
ured by the load, the latter by the deformation of the body produced by the first. A 
stress, not greater than the elastic limit of the material acted upon, produces a strain 
which disappears as soon as the load is removed : up to this limit the strain is propor- 
tional to the stress; beyond, the strain increases faster than the stress, up to the point 
of rupture. The elastic limit is a percentage of the breaking strain, varying with the 
kind of material and application of stress. Stress is usually designated as load, meaning 
thereby the sum of all the external forces acting on the member or structure, together 
with its weight. 

Dead load^ or weight, is a steady, unchangeable load. Live loads are variable, alter- 
nately imposed and removed, or varying in intensity or direction. It is usual, in design- 
ing constructions, to proportion the parts to resist a much greater load than will be 
brought on them in the structure ; the load is multiplied by a factor termed factor of 
safety, as a security against imperfections in material and workmanship, contingencies of 
settlement, and other incidental stresses. But it must be observed that these imperfec- 
tions are such as can not be seen and met ; there can be no factor of safety to provide 
for poor and unknown material and defective workmanship. 

The factor of safety adopted for dead loads varies but little with the same kind of 
material; but for live loads the factor varies not only with the material, but with the 
character of the stresses, whether they are applied and relieved gradually or suddenly ; 
whether they only vary in intensity, or also in direction, alternately compressive or ten- 
sile. In this latter case the load should never be considered less than the sum of the 
stresses, with a large factor of safety. Vibrations, shocks, and changes in the direction 
of stresses concentrate the strains at the weakest point of the construction, and rupture 
takes place at these points, which would be adequate to the strain if the form through- 
out were uniform with that at these points. Thus, boiler-plates show wear just at the 
edge of the lap of the sheets, and car-axles (Fig. 436), with sharp angles at the journals, 
are known to break after a time, while under the same stresses an axle of uniform size 
with the journal would not break; nor if a slight cove J inch radius (Fig. 437) be made 
in the angle to distribute stress. 

Besides provisions for strength, the draughtsman should understand the necessities 
of the construction, and the character of the material to be used. He should know 
what parts of the design are to be forged, cast, framed, and how it is to be done. He 
should know what wear is to be met, and what waste, as rust or rot, to be provided for. 



230 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



This knowledge can only be arrived at by reference to examples of practice and by ob- 
servation of results under similar conditions of use and time. 





■ ■■ A 

k 


1 


^ «-m 





J : % 



err 



Fig. 436. 



Fig. 437 



The stresses to which constructions and parts of constructions are subjected are the 
tensile or stretching stress, tending to lengthen a body in the direction of the stress ; the 
compressive or crushing stress, tending to shorten a body in the direction of the stress ; 
the shearing or cutting stress, tending to elongate, compress, and deflect ; the torsional or 
twisting stress, the effect being an angular deflection of the parts of the body ; and the 
transverse or lateral stress, tending to bend the body or break it across. 

In Appendix is given a table of the strength of various metals to resist compression 
and tensional stresses, and examples will hereafter be given of varied constructions, with 
their usual or required factors of safety ; but, for a practical rule for the common neces- 
sities of the above stresses, under dead loads, 10,000 pounds per square inch for wrought- 
iron and 12,000 for steel may be considered perfectly safe. 

Posts in structures are subjected to compressive stresses ; but, as the action is modi- 
fied somewhat by a tendency to bend, depending on the proportion of the length to the 
diameter, and the material of which they are composed, the usual tables of crushing 
strength are not generally applicable, and the formulae to be depended on are those de- 
duced from practical tests. The best tests of wooden posts are those made by Professor 
Lanza, for the Boston Manufacturers' Mutual Fire-insurance Company, and the following 
are the results : 

"That the strength of a column of hard pine or oak, with flat ends, the load being 
uniformly distributed over the ends, is practically independent of the length, such 
columns giving way by direct crushing, the deflection, if any, being very small. Tests 
were on columns 6" to 10'' diameter x 12 feet. The average crushing strength of very 
highly seasoned, hard pine was 7,386 pounds per square inch. Some very slow-growth 
and highly seasoned, 9, 339 pounds ; very wet and green, 3,015 pounds; seasoned about 
three months, 3,400 pounds; not very well seasoned and not very green, 4,400 to 4,700 
pounds. The average of two specimens of thoroughly seasoned white-oak, 7, 150 pounds; 
for green and knotty, average, 3,200 pounds. Spruce, nearly 5,000 pounds. White- 
wood, 3,000 pounds. 

"That it is a mistake to turn columns, taper, or even turn them at all, square col- 
umns being much stronger, cheaper, and better, and that accuracy of fitting is of great 
consequence, that the stress may be directly vertical." The professor recommends that 
longitudinal holes be bored through the centre of columns to allow of the circulation of 
air (in the experiments the holes were 1*7'' diameter), and that iron caps be used instead 
of wooden bolsters, as the wooden bolster will fail at a pressure far below that which 
the column is capable of resisting, and the unevenness of pressure brought about by the 
bolster is sometimes so great as to crack the column. He also recommends horizontal 
holes in the iron caps to connect the longitudinal ones in the column with the outer air. 

From the whole of the experiments, we estimate the safe load, for fair-grained, well- 
seasoned oak or yellow-pine columns, to be from 1,000 to 1,500 pounds per square inch; 
for the more imperfect and green specimens, from 300 to 500 pounds ; for good speci- 
mens of whitewood, about 300 pounds ; and of spruce, about 500 pounds. 

Cast-iron. — For the columns of buildings where the load is dead, cast-iron is very 
generally used. They are, in interiors, mostly of circular section, but for outer columns 
forms are used suited to the necessities of their position or style of architecture. Thej^ 
admit of considerable ornamentation and finish direct from the mould ; but, as they are 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



231 



liable to defects not readily detected in the process of casting, the factor of safety is 
usually taken as high as 5. To protect them against the effects of fire and water in con- 
flagrations, they should be covered with a shell of light refractory material, as porous 
brick or tile. 

The experiments of Hodgkinson are the usual basis of all formulae on the strength of 
circular cast-iron columns, and the ends of all columns are now required to be faced by 
architects and by the rules of building departments, since Mr. Hodgkinson states this 
rule, that "in all long columns, of the same dimensions, the resistance to fracture by 
flexion is three times greater when they are flat and firmly bedded than when they are 
rounded and capable of moving." 

Table of the safe load of solid cylindrical columns, with flat ends calculated with a 
factor of safety of 5. 



TABLE OF SAFE LOADS FOR SOLID CAST-IEON COLUMNS, WITH FLAT ENDS. 





8' 


9' 


10' 


11' 


12' 


13' 


14' 


15' 


16' 


17' 


18' 


19' 


20' 


21' 


22' 


23' 


24' 


Diam. 


1,000 


1,000 


1,000 


1,000 


1,000 


1,000 


1,000 


1,000 


1,000 


1,000 


1,000 


1,000 


1,000 


1,000 


1,000 


1,000 


1,000 




lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


Ibi. 

5- 


lbs. 

5- 


lbs. 


3' 


29- 


23- 


20- 


17- 


14- 


13- 


Il- 


10- 


9- 


8- 


7- 


7- 


6- 


6- 


4- 


8i" 


40- 


31- 


2e- 


22- 


19- 


17- 


ls - 


13- 


12- 


11- 


10- 


9- 


8- 


7- 


7- 


e- 


6- 


3t" 


50- 


41- 


34- 


29- 


25- 


22- 


19- 


17- 


15- 


14- 


12- 


Il- 


10- 


10- 


9- 


8- 


8- 


3i" 


63- 


54- 


43- 


37- 


32- 


23- 


24- 


22- 


19- 


18- 


16- 


ls- 


13- 


12- 


11- 


11- 


10- 


4" 


77- 


es- 


54- 


46 


40- 


35- 


81- 


27- 


24- 


22- 


20- 


18- 


17- 


15- 


14- 


is- 


12- 


4i" 


9-2- 


se- 


70- 


57- 


49- 


43- 


38- 


34- 


30- 


27- 


25 


23- 


21 


19- 


18- 


le- 


15- 


4i" 


110- 


96- 


84- 


74- 


61- 


53- 


47- 


41- 


37- 


33- 


30- 


28- 


25- 


23- 


22- 


20- 


19- 


H" 


130- 


113- 


99- 


88- 


73- 


64- 


se- 


50- 


45- 


41- 


37- 


34 


31- 


28- 


26- 


24- 


23- 


5" 


152- 


133- 


117- 


103- 


92- 


77- 


es- 


69- 


54- 


49- 


44- 


4(1- 


37- 


34- 


31- 


29- 


27- 


5i" 


176- 


154- 


136- 


121- 


lOS- 


97- 


81- 


72- 


64- 


58- 


53- 


48- 


44- 


40- 


37- 


35- 


32- 


5i" 


201- 


177- 


157- 


14>- 


1-25- 


113- 


95- 


85- 


76- 


68- 


62- 


57- 


52- 


48- 


44- 


41- 


38- 


5i" 


230- 


203- 


ISO- 


161- 


144- 


130- 


118- 


99- 


89- 


80- 


73- 


66- 


61- 


56- 


52- 


43- 


45- 


6' 


260- 


280- 


205- 


183- 


165- 


149- 


135- 


115- 


103- 


93- 


84- 


77- 


71- 


65- 


60- 


56- 


52- 


6J" 


292- 


260- 


232- 


203- 


187- 


169- 


154- 


140- 


119- 


103- 


98- 


89- 


82- 


75- 


69- 


64- 


60- 


el" 


327- 


292- 


2»il- 


284- 


212- 


192- 


174- 


159- 


146- 


124- 


112- 


102- 


94- 


86- 


80- 


74- 


09- 


6i" 


364- 


326- 


292- 


263- 


2:38- 


216- 


197- 


180- 


165- 


141- 


128- 


117- 


107- 


99- 


91- 


85- 


79- 


T' 


404- 


362- 


3-25- 


293- 


266- 


242- 


221- 


202- 


186- 


171- 


146- 


133- 


122- 


112- 


104- 


96- 


90- 


li" 


445- 


401)- 


361- 


326- 


296- 


269- 


.246- 


226- 


208- 


192- 


177- 


151- 


138- 


127- 


113- 


109- 


101- 


li" 


489- 


441- 


3 8- 


361- 


328- 


299- 


274- 


251- 


231- 


214- 


198- 


170- 


156- 


143- 


138- 


123- 


114- 


li" 


536- 


434- 


43S- 


398- 


362- 


331- 


303- 


278- 


257- 


237- 


220- 


294- 


175- 


161- 


149- 


133- 


129- 


8" 


58f 


529- 


43 J- 


436- 


393- 


364- 


334- 


308- 


2S4- 


263- 


244- 


227- 


196- 


180- 


167- 


155- 


144- 


8i" 


639- 


626- 


571- 


521- 


477- 


437- 


402- 


371- 


343- 


318- 


296- 


275- 


•257- 


241- 


207- 


192- 


178- 


9" 


802- 


733- 


670- 


614- 


564- 


519- 


479 


442- 


410- 


381- 


3c4- 


331- 


309- 


290- 


272- 


235- 


218- 


H" 


92G- 


849- 


730- 


717- 


66)- 


603- 


563- 


522- 


484- 


451- 


420- 


393- 


3G7- 


345- 


824- 


305- 


•265- 


W 


105S- 


975- 


898- 


829- 


765- 


70S- 


656- 


6)9- 


566- 


! 528- 


493- 


461- 


432- 


400- 


382- 


360- 


340- 


lOi" 


1U»5- 


iios- 


1026- 


957- 


892- 


823- 


779- 


740- 


693- 


, 653- 


610- 


530- 


546- 


511- 


485- 


459- 


433- 


11" 


]:359- 


1264- 


1159- 


103^3- 


1017- 


950- 


889- 


846- 


793- 


1 751- 


703- 


665- 


627- 


5SP- 


661- 


542- 


513- 


Hi" 


1517- 


1413- 


1319- 


1226- 


1147- 


lOSO- 


1018- 


956- 


904- 


i 852- 


810- 


758- 


727- 


691- 


655- 


613- 


587- 


12" 


1674- 


loS3- 


1470- 


1380- 


1289- 


1221 • 


1142- 


1074- 


1018- 


i 973- 


916- 


871- 


746 


701- 


667- 


645- 


611- 



Solid columns are very seldom used in constructions; they are almost invariably made 
hollow, the shell being y to 2" thick. To determine the safe load of a hollow column, 
it will be sufficiently accurate to take from the table the safe load of a column equal to 
that of the exterior diameter, and subtract from this the safe load of a column of a 
diameter equal to the core. 

Example. — To find the safe load of a column 12 feet long, 8" exterior diameter, 
shell I". 



Safe load of 8" column 398,000 lbs. 

" " 6V' •' 212,000" 

" " required column 186,000 " 

For square box-columns, it will be safe to estima'te that a square column will su]iport 
as much as a round one, the side of the one being equal to the diameter of the other, 
and the thickness of shell the same. 

For a star-cohimn (Fig. 438), the load should be about i less than on a cylindrical 
column of same diameter and same area of section. 

There is a convenience in the use of cast-iron that the brackets for the support of 



232 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



beams and girders can be readily cast on, but it must be done with care in the design 
and in the moulding. It will be seen (Fig. 341) that weak places occur in the cooling 
when the junctures are at right angles, which must be avoided by easements, or coves, 
in the patterns, and by intelligence in the moulding, pouring, and cooling. For many 
years cast-iron was the only metal used for posts, and with but few accidents from im- 
perfect construction or from conflagrations. 

WrougTit-Iron Columns. — With the decrease in the cost of the manufacture of shapes 
in wrought-iron, columns of this material have largely superseded those of cast-iron in 






Fig. 438. 



Fig. 439. 



Fig. 440. 



constructions liable to varying loads and shocks. 
Phoenix column. Fig. 440 of the Keystone. 



Fig. 439 shows the section of a 



TABLE OF PHCENIX COLUMNS. 



MAEK OF COLUMN. 


Thickness in 
inches. 


Area in square 
inches. 


Weight in pounds 
per foot. 


Internal diam- 
eter. 


A 


t 

A- 

i 
f 
i 

i 
f 


2-8 
5-8 
5-0 

]4-8 
5-8 

IT- 
8-8 

40- 

14-0 

26- 

16- 

60- 

24-5 

36-4 

24- 

80- 


9-3 
19-4 
16-Y 
51. 
19-4 
58-6 
30-3 

138. 
48-2 
89-Y 
55-2 

207- 
84-5 

125-6 
82-8 

276- 




4 segments 


H 


B 




4 segments 


4if 


B^ 


5H 


4 segments 




Vi\ 


4 segments 


D 




5 segments 


9i 


E 




6 segments 


11 


F 




V segments 


13 


G 


14f 


8 segments 







BUILT COLUMNS. 

Open columns should be used in positions exposed to dampness and rust on account 
of their accessibility to painting and inspection. Built columns present advantages in 
the facility with which connections can be made to floor beams or bracing rods. 

In determining upon the proper sections for these columns, the material should be so 
disposed that the tendency to yield will not be greater in one direction than in the other 
to secure the fall strength of the column. 

The rivets at the ends should be pitched not more than three inches apart, and the 
maximum distance between rivets in the line of stress should not exceed sixteen times 
the thickness of the plate. 

Figs. 459 and 460 are plan and elevation of a latticed column. 

Spacing of the Lattice or Lacing Bars. — The object of these bars is to join the two 
channels composing the post or chord, and thus cause them to act together; they should 
be attached at intervals so close that there shall be no danger of failure of the channels 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



233 



between the points of attachment, which never should be more than 0*6 of the interval, 
and lacing bars are not allowed to make an angle of more than 60° with each other, or 
less than 60° with the flanges. 



Fig. 441. 




V2^ "H^ ^^ 



— ; 



>^^ h. >rfM 



Fig. 442. 



-x:? o 

Fig. 443. 




Fig. 444. 



Fig. 445. 



-D--^ i._-D --! 

L L J 

Fig. 446. Fig. 447. 




Fig. 454. 



Fig. 455 



Fig. 456. 



Fig. 457. 




Fig. 458. 



On the Strength of Wrought- Iron Columns.— In the 
former editions of this work the strength of wrought 
columns was shown by curves of the average breaking 
loads (Fig. 461), as determined by experiments on the 
Phoenix, Keystone, Piper, and open columns with flat 
ends. Vertical distances represent the pounds of load 
per square inch, the horizontal the proportion of the 

length of the columns to the diameter-^ ; D is taken as 

the least outside diameter as marked on the varied sections above. The lower curves 
represent the safe loads, under factors of safety of 3, 4, and 5. In looking at these 
curves, it will be observed that, within the common limits of prac- 
tice, of 15 to 35 ~ — ^-- — , these lines may be considered straight ; that 

with iron of a breaking strength of 53,000 pounds per square inch, 
and within the above limits, and a factor of safety of 3, the safe load 
may be taken at 11,000 per square inch; with a factor of safety of 4, 
at 8,000 pounds; with a factor of safety of 5, at 6,500 pounds; and 
that for common and usual purposes 10,000 pounds per square inch 
is a safe load. 

At present there ar6 few wrought-iron columns 
manufactured; they are almost invariably steel, but 
the diagram still represents in their working propor- 
tions the action of columns under stress. The steel 
Fio. 459. Fio, 460. column is about 20 per cent stronger. When, as ob- 




=^ 



234 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



served above, the common and usual safe load on iron is 10,000 pounds per square inch, 
that on steel is 12,000 pounds. 

For struts, angle irons, or a combination of them forming an angle or cross (Figs. 441 

and 442), with or without separators, are generally used, and in these cases for D in :^ 

take D equal to 0-8 of the shortest leg or legs. 

It has generally been considered that columns with pin or cylindrical ends had about 



1 1 1 1 


. T-i-t-i — r r 1 1 r 1 r r 






it : : : :: ' :" : 




















SQ.IN. 




s. It it 




50000^+ ± : : ::_:: :±: _ 




^ -^ 








\ 




12 X It 












T"^. 








: :: ^^: : :" " ' :it 


~ 


40000 ^ 












*■ . 




" ' s iii[ :ei ir 


JJl^ 






E :: : : ::^s _: : 






\ 


T'T — 


n ^H--H44-l. 


30000 _ " " "T 




1 


- - - -4--'^aJ-■4--- 


1 1 


-t^^ 


1 1 






1 






















?oooo : zi" _± : I'l" : 








I I It: " :it:^;i^±^. 




k ! kK'v: .hn 


ii: ' ip ■ j - - 


■^ ^ 1 






:: : : jiii ^ -'-' ^i 






- 3::-^ ±- — - 










: X i±±- - -'--'- 




^MmJ 


i = = i== = '|=--:::i: = ^ = H! 






















1 1 -1 L .!,L. ... L 



— iO 

D 



20 30 

Fig. 461. 



three fourths of the resisting strength of flat ends, but if the pin ends are closely fitted, 
so that the strains are uniformly in the direction of the length of the column, the differ- 
ence is but little between the two kinds of ends. 

Shearing Stresses. — Parts of machines and of constructions subjected to these stresses 
have often the resistances modified by friction, combined with other stresses. The sizes 
of parts necessary to resist such stresses practically, as in the cases of bolts, rivets, and 
the like, will be hereafter illustrated by examples and determined by particular rules. 
In general, the strength to resist shearing stress is, in wrought-iron and steel, from 70 to 
80 per cent of its tensile strength; in cast-iron, about 40 per cent of its crushing strength. 
The softer woods, as spruce, white pine, hemlock, resting on walls or girders, will safely 
sustain a load of 200 to 300 pounds per square inch of bearing surface, and the harder 
woods, as oak and Southern pine, 300 to 500 pounds. By experiment, oak treenails, 1" 
to If" diameter, were found to have an ultimate shearing strength of about two tons per 
square inch of section ; but, according to Rankine, the planks thus connected together 
should have a thickness of at least three times the diameter of the treenails. In 3" planks. 
If" treenails bore only 1-43 tons per square inch of section; in 6" plank, 1-73 tons. 

Torsional Stress.— Bybtj shaft through which power is transmitted, whether through 
gears, cranks, or pulleys, is subjected to a torsional stress, of which the power acting 
tangentially to the shaft in one direction is resisted by the load in an opposite direction. 
When this stress exceeds a certain limit depending on the material, the fibres are twisted 
asunder, but much below this limit the elasticity of the shaft may be too great to trans- 
mit power uniformly. 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



235 



The length of the axle subjected to torsion does not affect the actual amount of pres- 
sure required to produce rupture, but only the angle of torsion which precedes rupture, 
and therefore the space through which the pressure must be made to act. 

A practical limit of torsional deflection is 1° in a length equal to twenty diameters 





Fig. 462. 



Fig. 463. 



of the shaft — or ^\-^ part of a full turn. D. K. Clark gives the following rule : "To 
find the diameter of a shaft capable of transmitting a given torsional stress within good 
working limits. Divide the torsional stress in foot-pounds by 18-5 for cast-iron; 27*7 
for wrought- iron; and 57"3 for steel. The cube root of the quotient is the diameter of 
the shaft in inches. 

Example. — On the teeth of a 4-|-foot gear, the force exerted is 2,800 pounds. What 
should be the diameter of a wrought-iron shaft to transmit this force safely ? 

The torsional stress will be 2, 800 pounds multiplied by the radius of leverage, 2^ feet, 

or 6,300 foot-pounds = |?^ = 228, ^^228 = 6-1. 

BEAMS. 

Transverse Stress. — The strength of a beam is influenced by the manner in which its 
ends are supported. Where the ends are simply supported — that is, resting upon the 
abutments — and the beam loaded with a weight W (Fig. 462), the beam is subjected to a 
bending movement, or transverse stress, composed of a tensile stress on the lower part of 
the beam and compressive on the upper part. In addition, the weight of the beam and 
its supported load act on the abutments as shearing stresses. 

If the ends of a beam are fixed in the wall, however, the transverse stresses arc con- 
siderably relieved throughout the beam, which is thereby capable of sustaining a heavier 
load. Figs. 464 to 471 are examples of beams with both ends simply supported and 
both ends fixed, or one end supported and one end fixed, and a comparison of their 
strength for a centre load and a load uniformly distributed. 

The strength of a square or rectangular beam to resist transverse stress is as the 
breadth and the square of the depth; and inversely as the length, or the distance from or 
between the points of support. Thus a beam twice the breadth of another, other pro- 
portions being alike, has twice the strength; or twice the depth, four times the strength; 
but twice the length, only half the strength. 

It is evident, therefore, that, with the same area of section, the deeper a beam the 
stronger it will be, if the breadth is sufficient to prevent lateral buckling. 

To cut the best beam from a log, Fig. 463, the section of which is a circle : draw a 
diameter, divide it into three equal parts, erect perpendiculars at the points of division 
1, 2, and they will intersect the circumference at the^corners of the beam, of which the 
extremities of the diameter are the other two. 

For the transverse strength of rectangular beams the general formula is W = — j— , in 

wliich W is the breaking weight ; S, a number determined by experiment on different 
materials; 5, the breadth, and d, the depth in inches; and Z, the length in feet. 

Figs. 464 to 471 represent the usual methods of loading beams, and the loads as 



236 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



drawn represent the comparative strength of beams under these different conditions. 
Thus, in Fig. 464, the beam supports but one unit of load, while Fig. 465 supports twice as 



'^^W?^ 



''y/^//////, - 







Fig. 464. 






^^ 



Fig. 465. 



much. The formulae given represent the safe dead loads with a factor of safety of 6, 
deduced from experiments of Mr. C. J. H. Woodbury on Southern pine. For spruce the 






^ 



Fig. 466. 









y/////yy 



Fig. 467. 






coefficient would be about \ less, and for live loads the factor of safety should be 12. 
Beams fixed at one end and loaded at the other (Fig. 464). 

Safe load = 30 ^'. 

Beams fixed at one end and load distributed uniformly, not as represented in the 
figure, as the two units of weight would be spread over the whole length of the beam 
(Fig. 465). 

Safe load = 60 ^. 

Beams supported at the extremities and loaded at the middle (Fig. 466). 

Safe load = 120 ^. 

Beams supported at the extremities and the load uniformly distributed (Fig. 467). 

Id'' 
Safe load = 240 -^. 









m 



M 



Fig. 468. 







/0^ 
-<^-^^ 






Fig. 469. 



Beams, one end firmly fixed, the other supported, and loaded at the middle (Fig. 468). 
Safe load = 160 -y-. 

Beams with one end fixed, the other supported, and load uniformly distributed 

(Fig. 469). 

Id? 



Safe load = 240 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



237 



Beams with both ends fixed, and loaded at centre (Fig. 470). 

Id'' 
Safe load = 240 ^• 













Fig. 470. 



Fig. 471. 



Beams with both ends fixed, and load uniformly distributed (Fig. 471). 

Id? 
Safe load = 360 -y-. 

If the loads on a beam be neither at the centre nor uniformly distributed, 
but at intermediate points, it is important to determine the load which placed 
at the centre will produce an equivalent stress. 

Thus on a beam of 30 feet span, if a weight of 800 pounds be placed at 10 
feet from an end. Lay oS on any convenient scale (Fig. 472) a horizontal line 




Fig. 4' 



of 30 feet, and at a point 10 feet from one end, draw a vertical or ordinate from 
this point, and at the ends A and B. 

From any convenient point on the ordinate beneath A draw a line parallel 
to A B and set off to 0, a distance equal to \ of the span for the pole distance 
of the force polygon about to be constructed, which is established at \ of the 
span, in order to determine readily the equivalent central load. From the 
point a in the ordinate lay off on any scale a a' ^ 800 pounds, draw lines a 
and «', and the force polygon is complete. 

From a extend the line a till it intersects the weight ordinate from D at 
E. Draw E F parallel to a' to intersect the ordinate B ; connect F with a ; 
F a is called the closing line of the equilibrium polygon. 

The weight 800 pounds is supported by the abutments A and B. Draw a 
line c in the force polygon parallel to F a ; the distance above this line in 



238 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



pounds will be the amount of the load on A, 533 pounds, c a\ below the line, 
267 pounds will be that on B. 

If the weight be placed centrally (Fig. 473) and its material sufficiently 
elastic to be considered uniformly distributed for its whole length ; to determine 
its effect under these conditions, draw the equilibrium polygon a E F as if the 




Fig. 475. 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



239 



weight of 800 pounds were suspended from a single central point; divide the 
weight into any number of equal parts (say 8, of 100 pounds each), and draw 
ordinates through the centre of these parts. Draw through 1' a line parallel 
to 1 and consecutively through 2' 3' 4' 5' 6' T 8' lines parallel to 2, 3, etc. 
Tlie central weight as measured on the longest ordinate is 690 pounds. 

If the weight 1,200 pounds (Fig. 474) be distributed on a beam of 40 feet — 
40 -^ say 8 = 5. Lay off at each extremity one half part or 2^ feet, and for the 
intermediate lengths, 7 parts of 5 feet each, and draw ordinates through these 
divisions ; follow the diagram construction as in the preceding, each weight 
being 150 pounds, the longest ordinate is 600 pounds, or one half the total 
weight of 1,200 pounds, and each abutment load is 600 pounds. 

In Fig. 475 the weights are many and unequally distributed; construct dia- 
gram as before, always making the pole distance equal to a quarter of the span ; 
measure the longest ordinate, which is 595 pounds, the equivalent central load. 
Draw c parallel to the closing line a F ; the total of the weights 1,100 pounds 
will be supported by abutment A, 500 pounds, and by abutment B, 600 pounds. 
In all the figures the weight of the beam itself is not taken into account, but, 
if considered, it is almost invariably of one section and therefore distributed, 
and its central load will be one half the total weight. 

The following table for the strength of yellow-pine beams is calculated for 
a safe central load, as determined by the graphic constructions or by taking one 
half the uniformly distributed load if this is given. 



TABLE OF THE SAFE CENTRAL LOAD OF YELLOW-PINE BEAMS, CALCULATED 



FROM THE FORMULA 120"^. 

I 



Span in 






DEPTH I^ 


INCHES OF YELLOW-PINE BEAMS, 


ONE INCH WIDE. 






feet. 


3 ins. 


4 ins. 


5 ins. i 6 ins. 

1 


Tins. Sins. 


9 ins. 


10 ins. 
3000- 


11 ins. 
3630- 


12 ins. 


13 ins. 


14 ins. 


15 ins. 


16 ins. 


4 


270- 


480- 


750- 


1080- 


1470- ;i920- 


2430- 


4320- 


j5070- 


5880- 


6750- 


7680- 


5 


216- 


384- 


600- 


864- 


1176- 1536- 


1944- 


2400- 


2904- 


3456- 


4056- 


4704- 


5400- 


6144- 


6 


180- 
154- 
135- 
120- 


320- 
274- 
240- 
213- 


500- 


720- 
616- 


980- 
840- 
735- 


1280- 

1097- 

960- 

853- 


1620- 
1389- 
1215- 

1080- 


2000- 
1714- 
1500- 
1333- 


2420- 
2074- 
1815- 
1613. 


2880' 
2469- 
2160- 
1920- 


3380- 
2897- 
2535- 
2253- 


3920- 
3360- 
2940- 
2613- 


4500- 
3857- 
3375- 
3000- 


5120- 


7 


430- 
375- 
333- 


4388- 


8 


540- 

480- 


3840- 


9 


653- 


3413- 


10 


108- 


192- 
175- 


300- 
273- 


432- 
392- 


588- 
535- 


768- 
700- 


972- 


1200- 
1092- 


1452. 
1320- 


1728- 
1571- 


2028- 
1844. 


2352- 
2140- 


2700- 
2457- 


3072- 


11 


882- 


2793- 


12 




160- 


250- 
230- 
215- 


360- 
332- 
308- 
288- 


490 
452' 
420- 
392- 


640- 
592- 
548- 
512- 


810- 
747- 
693- 
648- 


1000- 


1210- 
1117- 


1440- 
1328- 
1234- 


1690- 
1560- 
1448- 
1352- 


I960- 
1808- 
1680- 
1568- 


2250- 
2070- 
1928- 
1800- 


2560- 


13 


923- 
860- 
800- 


2363- 


14 


1037- 
968- 


2192- 


15 


1155- 


2048- 


16 








270- 


368' 


480- 


607- 


748- 


907- 


1080- 


1267- 


1470- 


1688- 


1920- 


17 








254- 


346- 


452- 


566- 


704- 


854- 


1016- 


1193- 


1384- 


1588- 


1808- 


18 










327- 


427' 


540- 


668- 


806- 


960- 


1126- 


1307- 


1500- 


1707- 


19 












404- 


512- 


632- 


764- 


909- 


1067- 


1238- 


1422- 


1616- 


20 












384- 


486- 


600- 


726- 


864- 


1014- 


1176- 


1350- 


1.536- 


21 














463- 


572- 


691- 


823- 


966- 


1120- 


1287- 


1463- 


22 














442- 


546- 


660- 


785- 


922- 


1070- 1 


1228- 


1395- 


23 
















522- 1 


631- 


752- 882- 


1023- 


1178- 


1329- 


24 
















500- 


605- 


720", 845- 


980- 


1125- 


1280- 


25 


















581- 


691-1 811- 


940- ( 


1080- , 


1230- 


26 
















1 


558- 


665-! 780- 


904- 1035- 


1182- 



240 MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 

The table gives the load which the beam can sustain, allowing a certain 
factor of safety, but the strength given is in excess of stiffness, and in perma- 
nent construction it is necessary to proportion the beams to bear its load with 
a certain limited deflection. Cross-lines on the tables represent those limits, 
but, as usually the weight of construction is much less than that of the change- 
able loads, and as the change of deflection is that to be guarded against, the 
weight of construction may be neglected, and it will only be necessary to con- 
sider the amount of movable loads above these lines. 

The table is deduced from Mr. Woodbury's experiments on yellow pine, 
of good quality and practical sizes. For spruce he takes loads of about one 
fifth less. 

The table is intended to be used as a unit of width by which the strength 
of timber of usual depths and spans can be estimated, by multiplying by such 
widths as are found in practice ; widths of less than two inches are not used. 
Mr. Woodbury established the limit of deflection in wooden beams at three 

432 w r 

quarters of an inch for 25-feet span, and his formula is E = , in which 

E, the modulus of elasticity per square inch, is for Southern pine 2,000,000, and 
for spruce 1,200,000 : W central load in pounds, I the span in feet, h the breadth, 
h the depth, and d the deflection of beam, all in inches. Using this formula, 
marks are drawn in each column of depth, above which the loads will be sup- 
ported stiffly, and below less than recommended ; the formula is only applicable 
to seasoned wood. Mr. Woodbury's results are confirmed by late experiments 
on the long-leaved pine by Prof. Johnson for the Forestry Division of the 
United States Department of Agriculture. 

He gives the shearing strength measured by the cross-section of the beam at 
about 600 pounds to the square inch, and the crushing strength across the grain 
at about 1,150 pounds. In the resting of the beam on abutments of masonry it 
will be difficult to exert a clean shearing stress, and the strength would be in 
excess of any likely to occur, but the stress would be a crushing one, and be met 
by the area in square inches resting upon the wall. 

In the above tables there is a factor of safety of six — that is, the rupture 
should not take place except at a load six times that given. This is to provide 
for some unknown weakness of the timber, or some sudden excess of load, de- 
preciation by age, etc., but this factor does not make up for want of inspection 
or knowledge of the material. It is well to load some of the timbers, as a test 
to the elastic limit, which can be done by placing two timbers at convenient dis- 
tances apart and loading with pig iron or barrels of sand. 

The early cast-iron beams used in framing have been almost entirely super- 
seded by wrought ones, as cheaper and more reliable. In the application of the 
former, the sections were adapted to the stresses, as shown in Figs. 476-478. 
Practical examples of cast-iron beams are given, as there may be conditions 
under which it may be necessary to make use of them. 

A beam subjected to a transverse stress, as shown in Fig. 462, one side is 
compressed, while the other side is extended ; and therefore, where extension 
terminates and compression begins, there is a lamina or surface, g 7i, which is 
neither extended nor compressed, called the neutral surface. As the strains 
are proportional to the distance from this surface, the material of which the 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



241 



beam is composed should be concentrated as much as possible at the outer sur- 
faces, as can readily be done in beams of cast and wrought iron. Mr. Hodgkin- 




FiG. 476. 



Fig. 477. 



Fig. 478. 



son found that the strength of cast-iron to resist compression is about six times 
that to resist extension ; the top web is therefore made only one sixth the area 
of the lower one. The depth of the beam is generally about one sixteenth of 
its length, the deeper of course the stronger ; the thickness of the stem or the 
upright part should be from ^ aii inch to 1-^ inch, according to the size of the 
beam. The rule for finding the ultimate strength of beams of the above sec- 
tion is : Multiply the sectional area of the bottom flange in square inches by 
the depth of the beam in inches, and divide the product by the distance be- 
tween the supports in feet, and 2-42 times the quotient will be the breaking 
weight in tons (2,000 pounds). The section thus determined is that of the 
greatest strain, and can be reduced toward the points of support, either by 
reducing the width of the flanges to a parabolic form (Fig. 479), or by reducing 
the thickness of the bottom flange ; the reduction of the girder in depth is not 
in general as economical or convenient. 

A 




izm 



mr 



^ 



Tza 



v^zv/?zm \ 



Fig. 479. 



For railway structures subject to an impulsive force, Mr. Joseph Cubitt, 
C. E., recommends that the section of the upper flange should be one third 
that of the lower. 




Fig. 480. 



17 



242 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



rig. 480 is side elevation, plan, and section of cast-iron girder, adopted by 
him for railway purposes, a pair of girders for each track, the rails being sup- 
ported on wooden cross-beams. 



DIMENSIONS FOR DIFFEEENT SPANS. 



Opening. 


Bearing on 
abutment. 


Height of girder 
at center. 


Top flange. 


Bottom flange 
at center. 


At end. 


Thickness of 
middle web. 


12 ft. 
30 ft. 
45 ft. 


l'-6" 
2'-6" 
2'-9" 


l'-3" 

3'- 

8-9" 


3" X li" 
5" X 2" 

r X 2i" 


l'-4" X If 
l'-6" X 2" 
2'- X 2i" 


l'-8" X H" 
I'-IO" X 2" 
2'- X 2i" 


2" 

2" 




Fig. 481. 



Eolled I-beams (Fig. 481) may be taken as the type in wrought-iron and 
steel sections. The depths of the beams, A, and the widths, B, of bottom and 

top flanges do not vary much with the different makers for the 

saDie class of beams, but the thickness of the stems varies more. 
The tables of the Strength of Wrought-iron and Steel Beams 
(pages 243, 244) have been made up by comparison of the 
'tables of different makers, the safeload is taken in units of 100 
pounds, and 00 are to be added to the tabulated figures to give 
the safe distributed load in pounds. 

It is assumed in these tables that proper provision is made 
for preventing the beam from deflecting sideways. They should 
be held in position at distances not exceeding twenty times the 
width of the flange ; this is usually effected by the brick arches 
between the beams, or the wooden joists resting on them. The beams will 
support the loads as given in the tables, but the deflection may be too much 
for the purposes to be served. A line is drawn in each column in the tables, 
at which the deflection is -^^ beyond that due to the weight of the beams, or 
one inch for every thirty feet of span, beyond which the deflection is apt to 
crack the plastering of ceilings. 

To find the sectional area of a beam, plate or rod from its weight, multiply 
weight per foot by 3 and divide by 10 ; and, conversely, to determine the weight 
multiply the sectional area by 10 and divide the product by 3. 

Thus, if a steel bar 12 feet long weigh 480 pounds, or 40 pounds per foot, 

its sectional area will be — ^^ — , or 12 square inches ; and a bar of 9 square 



inches section will weisrh 



10 
9 X 10 



= 30 pounds per foot. 



For naval constructions, deck-'beams (Fig. 482) are from 3" to 12" deep, with 
varied widths of flanges and thicknesses of stem ; lighter than the 
grades of heavy and light I-beams, but heavier can be rolled to order ; 
bulb angles with terminal bulbs similar to those of deck-beams, on 
long legs of from 5" to 10", and short legs of 2|" to d^" can be had 
of varied thicknesses. Properly proportioned, they are equal in 
strength to the I-beams. 
^_j Cou])led I-Beams. — When the load is beyond the strength of a 

Fig. 482. single I-bcam, two or more may be united, as shown in Fig. 483. 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 243 







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MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



245 



A cast-iron block, or separator, is inserted between the beams, and two bolts, 
through them and the block, add lateral strength. The bolt-holes, placed at 
some distance from the centre of the span, do not reduce the transverse strength. 
To strengthen an I-beam or box-girder composed of I-beams, rivet 
plates on the top and bottom flanges (Figs. 484 and 485), thus 
adding to the section by the area of the plate, less the rivet- 
holes. Box-girders, except of the larger sizes, are preferably 
composed of channel-beams (Fig. 486). 






Fig. 483. 



Fig. 484. 



Fig. 485. 



Fig. 486. 



The rivet spacing at the ends of a box-girder not over 3" at the middle 6".- 
Channel-beams can be furnished of depths the same as I-beams, from three 
to fifteen inches, of varied grades of light and heavy. 



COMPARATIVE 


STRENGTH 


AND 


STIFFNESS OF STEEL BOX GIRDERS. 






Fig. 492. 






Depth of Girder. 


Inches. 


10" 


12" 


15" 


20" 


Weight of [s per foot. 


Lbs. 


15 


24 


20 


30 


32 


51 


64 


80 


Size of Plates. 


Inches. 


12 xi 


14 xi 


16 xf 


18 xf 




10 


694- 


758- 


1004- 


1096- 


1836- 


2052- 


4030- 


4500- 




11 


631 




689- 


912- 


997- 


1669- 


1866- 


3664- 


4091- 




12 


578 




631- 


837- 


913- 


1530- 


1710- 


3359- 


3750- 




13 


534 


• 


583- 


772- 


843- 


1412- 


1579- 


3100- 


3462- 




14 


496 


• 


541- 


717- 


783- 


1311- 


1466- 


2879- 


3214- 




15 


463 




505- 


669- 


731- 


1224- 


1368- 


2687- 


3000- 




16 


434 




473- 


627- 


685- 


1147- 


1283- 


2519- 


2813- 




17 


408 




446- 


591- 


645- 


1080- 


1207- 


2371 • 


2647- 


rn 


18 


386 




421- 


558- 


609- 


1020- 


1140- 


2239- 


2500- 


1 


19 


365 




399- 


528- 


577- 


966- 


1080- 


2121- 


2368- 


§ 


20 


347 




379- 


502- 


548- 


918- 


1026- 


2015- 


2250- 


& 


21 


330 




361- 


478- 


522- 


874- 


977- 


1919- 


2143- 


S 


22 


815 




344- 


456- 


498- 


835- 


933- 


1832- 


2045- 




23 


302 




329- 


436- 


477- 


798- 


892- 


1752- 


1957- 


i g 

W H 
^ fe 


24 


289 




316- 


418- 


457- 


765- 


855- 


1679- 


1875- 


25 
26 


278 




303- 


402- 
386- 


438- 
422' 


734- 
706- 


821- 
789- 


1612- 
1550- 


1800- 


267 




291- 


1731- 




27 


257 




281- 


372- 


406- 


680- 


760- 


1493- 


1667- 


1 


28 


248 




271- 


359- 


391- 


656- 


733- 


1439- 


1607- 


29 


239 




261- 


346- 


378- 


633- 


708- 


1390- 


1552- 


< 


30 
31 


231 
224 




253- 

244- 


335- 


365- 


612- 
592- 


684- 
662- 


1343- 
1300- 


1500- 


U 


324- 


354- 


1452- 


S 


32 


217- 




237- 


314- 


343- 


574- 


641- 


1259- 


1406- 




33 


210 




230- 


304- 


333- 


556- 


622- 


1221- 


1364- 




34 


204 




223- 


295- 


322- 


540- 


604- 


1185- 


1324- 




35 
36 


198- 
193- 




216- 
210- 


287- 
279- 


313- 
304- 


525- 


586- 


1152- 
1120- 


1286- 




510- 


570- 


1250- 




37 


188- 


205- 


271- 


296- 


496- 


000- 


1089- 


1216- 




38 


183- 


199- 


264- 


288- 


483- 


540- 


1061- 


1184- 




39 


178- 


194- 


257- 


281- 


471- 


526- 


1033- 


1154- 




40 


173- 189- 


251- 


274- 


459- 


513- 


1008- 


1125- 



246 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



TABLE GIVING INCREASE OR DECREASE OF STRENGTH, IN PER CENT, 
ABOVE OR BELOW THAT GIVEN BY PRECEDING TABLE, FOR DIFFER- 
ENT THICKNESSES OF PLATES IN STEEL BOX GIRDERS. 



Thickness of Plate. 


f" 


i" 


i" 


i" 


i" 


1" 




12" 




10" 


[15# 


-19 





+ 20 


+ 41 






w 


12" 




10" 


[24^ 


-18 





+ 18 


+ 38 






"§ 


14" 


a 


12" 


[20* 







+ 19 


+ 40 






Ph 


14" 


M 


12" 


[30* 







+ 18 


+ 36 






"S 


16" 


o 


15" 


[32* 




-15 





+ 15 


+ 30 




•B 


16" 


o 


15" 


[51# 




-13 





+ 13 


+ 27 




i 


18" 
18" 


s 
s 


20" 
20" 


[64# 






-10 
-9 






+ 10 
+ 9 


+ 20 

+ 20 



It may be desirable, on account of position, to finish a box-girder as in Fig. 
487 ; in this case the dimensions must be such as to admit of a helper inside to 
hold the rivets. Fig. 488 shows a closed box-beam made of channel-bars and 
plates. The lower channel is first riveted, and the upper one afterward. This 








Fig. 487. 



Fig. 488. 



Fig. 489. 



Fig. 490. 



Fig. 491. 



Fig. 492. 





form gives a clean surface below, but the lower channel-bar can be reversed and 
riveted the same as the upper. 

Where the purpose can be served by I-beams, either single, or coupled, as in 
Fig. 483, or in numbers, they afford the best and cheapest construction. But, 
where the spans are large and loads heavy, it is often economical to obtain 
greater depth by means of plate-girders, as in Figs. 489, 490, 491, 492, or per- 
haps from requirements of position, as in Fig. 493, subject as above to the 

necessities of large inside dimen- 
sions. These girders are made up 
of plates of uniform thickness, 
and angle-irons riveted together. 

Angle-irons are made of varied 
dimensions, and are* classed as 
equal-legs (Fig. 494), unequal-legs 
(Fig. 495), and square-root angles 
when the thickness of the iron is uniform throughout, and consequently the 
interior angle a complete right angle without rounding. 

Angle irons are manufactured of equal legs, of f ", f ", f", 1", l-J", li", IJ", 
If", 2", 2i", 2i", 2f ", 3", 3 J", 4", 5", 6", of varied thicknesses, according to the 
size and necessities of construction, from -J" on the smaller sizes to -J" on the 
larger ones. 

Angles of unequal legs— 7" X 3i", 6^" X 4", 6" X 4", 6" X 3i", 5" X 4", 
5" X 3i", 5" X 3", 4i" X 3", 4" X 3^", 4" X 3", 3i" X 3", 31" X 2^", 3i"X 2", 
3" X 2J", 3" X 2", 2i" X 2", 2i" X If, 2" X If", If" X 1", with the same 
variety of thickness as the equal legs, up to 1 inch for the largest size. 



Fig. 493. 



Fig. 494. 



Fig. 495. 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



247 



y///?</^^^ 



L 







DIMENSIONS 


AND W 


EIGHTS 


OF Z BARS. 








SIZE IN INCHES. 


1 


Thickness 


SIZE IN INCHES. 




of metal 
in inches. 






Weight 


nf TTKifQl 








Weight 


Flange. 


Web. 


Flange. 


per foot. 


in inches. 


Flange. 


Web. 


Flange. 


per foot. 


f 


3i 


6 


3i 


15-6 


n 


3| 


H 


3| 


28-3 


■h 


3,% 


(HV 


3i\ 


18-3 


i 


S-k 


4 


3t^. 


8-2 


\ 


3f 


6i 


31 


21-0 


-h 


3i 


4iV 


3i 


10-3 


-h 


3i 


6 


3i 


22-7 


1 


3A 


4i 


3A 


12-4 


i 


3i% 


^-A 


3,% 


25-4 


tV 


3t^6- 


4 


3iV 


13-8 


ii 


3f 


H 


3f 


28-0 


i 


3i 


4-i\ 


3i 


15-8 


f 


3^ 


6 


3i 


29-3 


1% 


3x\ 


4i 


3A 


17-9 


If 


3A^ 


6tV 


3-A^ 


32-0 


f 


3tV 


4 


3tV 


18-9 


I 


3f 


6i 


3f 


34-6 


u 


3i 


4A 


3i 


20-9 


'h 


3i 


5 


3i 


11-6 


f 


3A 


H 


a 


22-9 


i 


3i^ 


5i\ 


3i\ 


13-9 


i 


2H 


3 


6-7 


^'6 


3f 


5i 


31 


16-4 


A 


2f 


3i^^ 


21 


8-4 


i 


3i 


5 


3i 


17-8 


f 


2H 


3 


2-H 


9-7 


-1% 


3A 


5iV 


3-1^ 


20-2 


1^ 


2f 


3i\ 


2f 


11-4 


i 


3f 


•^i 


3i 


22-6 


i 


2H 


3 


2ii 


12-5 


H 


3i 


5 


3i 


23-7 


1% 


2f 


3iV 


2f 


14-2 


f 


3A 


5A 


3t^. 


26-0 













T-irons (Fig. 496) may be used for top and bottom flanges in the manufac- 
ture of plate-girders by riveting a web on one side of the T, or on both sides, 

•. B : with a separator between of the thickness of the stem E ; but, as 

the areas of section of T-irons to be had are small, the flanges 
will be too slight in proportion to the webs at depths above that 
of rolled beams. Angle-irons are then to be preferred for flanges. 
The T-irons are well adapted in many positions as struts or 
braces, and can be bought of varied dimensions and weights, 
from widths, B, of from 2 to 5 inches, and equal or less depths, A, and thick- 
nesses from -^" to f ". 

Rivets for plate-girders are usually from |" to -J" diameter, and pitched or 
spaced not more than 6" nor less than 3" between centres. The number of 
rivets through flange and stem are the same, but alternating. Usuall}^ angle 
irons and plates can be had of the full length of girder, but, where joints are 
necessary, they should be butt, with a splicing-piece to make the strength as 
nearly as possible uniform. Stifleners are often necessary for the webs, which 
may be of band, angle, or T-iron, and one should always be placed at each end, 
where the shearing stress is the greatest. 

A common formula for determining the strength of a wrought-iron beam 



Fig. 496. 



or girder is W = 



8D(«+g)S 



in which W is the load in pounds, equally 



distributed on the beam, D the effective depth between the centres of gravity 
of the flanges, and L the clear span, both in the same unit, feet or inches ; a 
the area of the top or bottom flange in square inches ; a' the area of the stem. 
To construct a diagram from the formula, in which the relation of the fac- 



248 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



25 



tors may be shown. Let S be 10,000 for riveted girders of wrought iron 
(12,000 for steel), then W = -^ X C'^ + l) 80,000. On a sheet of cross-sec- 
tion paper, from a corner, 0, lay off on the line of ordinates, 5, 10, 15, 20, 

a' 
, representing the factor a -\- —. From the same 0, on the line of abscissas, 

h TO. tV' jV. yj^ to. ^V. tV. representing -. Suppose ^ = A. ^^^^ W = 

(a + |) 2,000. If 6? + |- be = 10, then W = 20,000. From the intersection 

of ordinate on line of -^q, and abscissa line of 10, draw a line to the point 0. 
This line will represent the safe distributed load W, and its intersections of the 



a-s--s: 



Z5 



20 



15 



L A 



li'/l''^ / . / '' '^ 


!??■ /Iq/ / / / / / -^^ .^ 


^ \^ /// ^ ^ 7 y 


^ / ^^ / <:^'^ ^ z / ,'' y 


M yw\ ^1 w v\ 14 y\ \\ V\ 


Till 2 Z s2 ZL ^^^ ^^ ^ ^ 


v-t- ^ y -> : ; w 7 ^ - ^^ - - ~ 


T t.W L^ ^ ^ . ^s^ 7 ^/ _ ^^ __ _ 


y.2 ^_^e 7 ^7-: ^Y y 7 ^-" -_ - ;? 


Z^S /r^ 1^7/7 7 / ^ ,^ 


7:^? / V V 5z ~ :'^ ^^ _sS^ ^^ -i 


yW fr^ nwA \\ y\ .m\ A\ \V\\ 


it /y Is z s ,^ v^ ■'So- ,^ ^ 


^^ ^ ^ /^^S'^ ^' oS^ ^ ^^ -.'' 


/ y y\ A Y y\ M ^^ \4 >i Wi 


////// \W y / 


X I jz ^ I ^ z y 7 ±7 ^y ± 


// / / / / / >1 \r \y >f J 


/,//.'// / /■ P>^/1 rvV,^" ^■' 


/ ' / ^ / / ,' / .C9^i ,^>> 


J / / / / / a^ *5? -^ 


-V- V-'^^ ^ y A y' - ^ - y^ ^^ ^4- ^^ 




J. . 7 1 7 J ^ / 7 y~^ ~2L ^ ■ " 


'^L" J. A 7- '^ / ^ : ± y : .-" : :: 


J- t ^ -, / 7 / / / Zit ^'^jl ^" t 


7^47 7 / I ^ / y _y ^^ J- ^, ^^- 






//// y y\ y i>i i>t wi > itvf L-ti"! 


// / / / / / y /' y y' .^' .n)^--' 


Ma(iA a <\ \\ A jf] i>r u WF^T 


.X Zy\.\^ ^ ^2 / ^'' ^^ ± ,5^ 


1/7 J y / 7 y'^ 7 ^^ ^- -^ ^^^^ ^-''- il 


,2/^'^z:7'..z ^^y y zy ^-" : .-" _ : - 


Z'^'^7/ 7 I / .^ y y-^ ^^"^ ZL - " 


All/ izz / /^ X. ^^. .^" :.-' : _ _ . 


Cv.LZ/^ ^ z_ ^- ^''_ ^''- - ^^'-- -- - _____ 


f//.'^// y y y' > ^' . .... --: 


A// 7 / / y y .y - .--' ^^- L s -'-"' 


j/'^//y ^ ±^ "-^ ■ "-"" " ~~ ^TK\^^--' - - 


alT.'/'/ / ^ y ' \.^ .-' ra-Oii'-" 


[//H^lrtLrr r 1 Hi L-nu L W^ TT 


%7 /^ 7 ^ ^ i''' -" ^^ ^^' - T 




P'^l^i^r J-f ji^'^ I44ttl L ^^ t^ 


^■^7-^-1 x'T ,,-- >--'''' -'-'l ! 





A^ 



-^0 

Fig. 497. 



"30 



^35 



"40 



ordinates and abscissas will represent the relative proportions of the two factors 
^P and a -{- — under this load. On the abscissa line 15, and ordinate ^-q, W = 

JU D 

30,000, on line 20, 40,000, and so on, and lines drawn from these intersections 
to will represent W. 

In the diagram lines below 5 and above 30 on line of ordinates are erased, 
as within these limits may be found most of the proportions required in 

practice. 

a' 

A2)plication of the Diagram. — What will be the area of section a -\- — oi 2i> 

girder, 40-foot span, depth 32", distributed load 90,000 pounds? 

D in the formula represents the distance between the centres of gravity of 

the flanges, which will be somewhat less than the depth of beam. Approxi- 

T) 480" 
mately assume it at 30", ^ = -^^rn- = yV. ^^^ ^^® intersection of the line 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



249 



of load, 90,000, with the ordinate ^, will be 18, on the line of a -\- — . A fair 



proportion of a to a' is 5 to 6, therefore 



oa 



= 18 or a' 



18. 



18;; 

30 



= 0'Q" = 



thickness of web, and a = ^ ot 18 = 15, or weight per foot of one flange = 

15 X 10 

== 50 pounds, which is slightly in excess of the weight of two angle- 

o 

irons 6 X 4 X f, compensated by thickness of web outside centres of gravity. 

This calculation is sufficiently near for all practical purposes, but D can be 
found more accurately by plotting the angle-irons, on thick card-board, cut- 
ting out, and then balancing for the centre of gravity. 

Comjyosite Beams. — Often, in constructions where the beams or girders are 
of wood, and on account of extent of spans and loads, the stress is beyond the 
strength and stiffness of beams of this material, of readily available dimen- 
sions, it is usual to supplement by some application of iron. A simple form, in 
which the iron is not exposed to view, is by bolting a plate orj^iYcAof wrought- 
iron between two beams, of the full length and depth of the beams, and of such 
thickness as may be necessar}^ In bolting them together, let the bolt-holes 
be so bored that the weight of the beam may primarily be on the wood ; the 
stress will then be better adjusted between the two materials when in service. 
It is usual to make the holes zigzag, in two lines about one quarter the depth 
of beam from each edge, the holes closer together nearer the ends. The safe- 
distributed load for the iron may be estimated from the formula : W. = 

= , h breadth, Ti depth, I length — all in inches. 

Fig. 498 represents a bracing truss of wTought-iron between two beams, 
which should be let into the wood. As it is held firmly laterally, the factor of 




Fig. 498. 



safety may be considered about one third of the crushing resistance of the ma- 
terial. The load on each inclined bar will be one half the load on the centre, 
multiplied by the length of the bar and divided by the rise. Instead of wrought- 
iron, cast-iron or wood is used. 



=0= 



Fig. 499. 



In Fig. 499 the beams are strengthened by a tension-rod, of which the 
strength may be determined by that of the material ; allowing the usual factor 
of safety, the load is obtained as in the example above. The deeper the block 
beneath the centre of the beam, the less the stress on the rods for the same 
load. In construction, the beam should not be cambered by the screwing up 



250 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



of the rod ; but, if the beams are crowning, the convex side should be placed 
upward, the nut turned by hand just to a bearing, and the tension put on by 
the settlement of the beams under the load. 




Fig. 500. 



Fig. 500 represents the trussing of a beam by two struts and a tension-rod. 
The stress on the tension-rod is the load on c, multiplied by the length a d^ 
divided by c d. 

The theory of trusses will be treated and illustrated under " Bridges " and 
" Eoofs," and the proportions of rivets and forms of plate-iron joints under 
" Boiler Construction." 

Bolts and nuts are of such universal application that their manufacture 
forms the centre of large industries. Much thought has been given to their 




Fig. 501. 



proportions and the forms of thread, but without producing complete uni- 
formity in the practice of different countries and makers. The old form of 
thread was the triangular pitch (Fig. 502), still used by some, especially when 
the threads are cut in a lathe. In this country the standard U. S. thread is 




Fig. 502, 



that recommended by the Franklin Institute in 1864 (Fig. 503). The angle is 
60°, with straight sides and fiat surface at top and bottom, equal to one eighth 
the pitchy or distance from centre to centre of threads. 

In England, the standard thread for bolts and nuts is the Whitworth (Fig. 
504) ; the angle is 55°, with top and bottom rounded. 



2.00 




Fig. 505. 



The square and rounded threads (Figs. 505 and 506) are only made to order 
and used in presses and the like as parts of machines. 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



251 



Figs. 507, 508, and 509 represent the proportions of the various parts of 
English nuts to the diameters of bolts, as 1, or unity. Fig. 508 is a flange-nut, 
in which a washer-like flange is forged with the nut. 




Fig. 506. 



Fig. 510 is a cap-nut, in which the thread does not go through the nut, to 
prevent leaking along the thread, and a soft copper washer is introduced to pre- 



vent leakage below the nut. 






Fig. 507. 



Fig. 508. 



Fig. 509. 



Figs. 511 and 512 are circular nuts, in one of which holes are drilled to 
insert a rod for turning, and in the other grooves for a spanner. 

Loch-nuts (Fig. 513) are intended to prevent the gradual unscrewing of 







Fig. 510. 



Fig. 511. 



Fig. 512. 



Fig. 513. 



nuts subjected to vibration, which is to a great extent prevented by the use of 
double nuts, the lock-nut being one half the thickness of the common nut. 
The usual practice is as shown, the lock-nut being outside ; the better way is 
inside. 

The following figures are from trade circulars ; the limits of sizes given are 
such as can usually be found in stock. 

Figs. 514, 515, and 516 are machine-bolts, from ^" to f" diameter, and 1" 
to 4" long, but not flanged, as in Fig. 514, unless expressly ordered ; the dot- 
ted line shows the radius of curvature of a finished head. The diagonal lines 
beneath the head (Figs. 515 and 516) represent square bolts tapering into round 
bolts, as shown by the curved lines. 



252 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



Figs. 517 and 518 are tap-bolts and set screws, from ^" to f" diameter, and 
from 1" to 3" long. 





Fig. 514. 



Fig. 519 is a carriage-bolt, from ^" to f" diameter, and from 1" to 16" long. 
Fig. 520 is a plough-bolt, from f " to -J-" diameter, and from 1'' to 4" long. 






■"r 

i 


\ 






I 


V^^' 

/-\^i 


ill '■ ) 








t 1.62 * 




] 


Pig. 515. 


i . 




Fig. 516. 



Fig. 521 is a stove-bolt, from ^" diameter and from f " to 3" long. 

Figs. 522 and 523 are machine-screws without nuts ; the holes in the metals 




T" 



if ^ 



Fig. 517. 




are tapped to receive them ; Fig. 522 is button-headed ; Fig. 523 a counter- 
sunk head — both slotted to admit of driving by a screw-driver. They are made 
of various-sized wire and lengths, and sold by the gross like the common wood- 



!■ 



P 



Li 



iH 



Fig. 519. 





J 


\ 


J f\l 


( ? Ill 


■4 


/; LLZi 


U 2.2S — ^ 


Fig. 520. 



screw (Fig. 524). The wood-screw is for connecting pieces of wood together, 
or metal to wood. They are of very great variety, usually with a gimlet-point, 






Fig. 521. 



^I^ 





Fig, 522. 



Fig. 523. 



g 

:|; 
'¥■ 

Fig. 524. 



^ 



Fig. 525. 



Fig. 526. 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



253 



so that they can be screwed into the wood, without any holes being previously 
made. When made of rods, with a square or hexagonal head (Figs. 525 and 
526) to admit of the use of a wrench, they are called lag-screws. It will be 
seen that wood-screws differ in their thread from bolts and machine-screws. 
The thread is a very sharp V, flatter on the upper surface, and the flat space 






Fig. 527. 



Fig. 528. 



Fig. 529. 



between the threads wide as the thread, making it of easier introduction into 
the wood, and retaining as much strength in the iron as in the wood. 

Fig. 527 is a stud-\iQ\i^ which is screwed firmly into one of the pieces of 
connected metal ; the other is bored so as to slip over the bolt, and the nut 
then brought down upon it. It is in common use for holding on the bonnets 
of steam-chests and water-chambers, the bolt remaining permanent. 

Fig. 528 is a liooh-'hoM ; it relieves the necessity of a bolt through the bot- 
tom-piece, and may be turned like a button, to loose or hold the bottom-plate. 

Fig. 529 is another kind of button-bolt ; the lower end can revolve on a stud 
or pin if the nut be raised enough to clear the cap or upper plate. By this 
arrangement there is no necessity of taking off the nut entirely ; the bolt lies 
in a slot in the cap, and the nut bears on three sides. 






Fig. 530. 



Fig. 531. 



Fig. 532. 



Figs. 530, 531, and 532 show expedients to prevent the bolt from turning 
when the nut is being screwed on or off. 

Fig. 533 is an anclior-hoit flattened and jagged, introduced into a hole in 
masonry, and firmly leaded or sulphured in; but later experiments with deep 
holes have established that it was not necessary to flatten and jag the bolts, and 
with holes If and If^ diameter and 3' 6" deep, and bolts V diameter when leaded 
or sulphured in, did not develop as uniform adhesion as when the spaces were 
filled in with Portland cement and allowed a set of two w^eks, when the bolts 
broke under the test. The resistance was 400 to 500 pounds per square inch of 
surface of bolt exposed. 

It is very common to split the bolt at the bottom (Fig. 534) and insert a 



254 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



wedge in the cleft and drive it against the bottom of the bolts, forcing open the 
cleft and holding the bolt in the hole. 

Fig. 535 is a bolt keyed into the stone, corresponding to a form of lewis for 
raising stones in which the key (Fig. 536) is wedged in, and when the stone is 



C>1 







Fig. 534. 



Fig. 535. 



Fig. 536. 



Fig. 537 is a double or chain 



set the wedge is struck and the lewis withdrawn, 
lewis. 

For small holes in brick or stone masonry drill a hole and insert a short 
piece of lead pipe and force in a wood-screw of a little larger diameter than the 
bore of the pipe, or drive a wooden pin into the hole, and screw into the wood. 

Take a clout-nail or picture-nail, turn up 
the point, cast a lead petticoat on it, and 
drive it into a loosely fitting hole ; by driv- 
ing, the point and the wedge form of the 
nail expands the lead and gives a firm hold. 
Similar forms of points to anchors of copper 
wire are convenient in holding stones to- 
gether or face stones of a building to the 
backing. 

Expansion-'boli^ (Fig. 538) from I" to 1" 
diameter are on sale and very convenient in 
connecting architectural iron-work to ma- 
'^'^^- ^^^- sonry, and have this convenience : that they 

can be removed when necessary; all that is required is a hole of uniform diam- 
eter and of suitable size and depth to insert the bolt with nut and jaw ; then 
by turning the head, the iron or composition nut is drawn outward, 
opening the wedge-shape jaws and causing them to bind strongly 
against the side. There is a small split-steel band around the jaws to 
keep them together before insertion in the hole and to free the jaws 
when they are to be removed. The bolts may have a head at the 
top, or a screw with a nut, or the lower nut may be formed as a head. 
Fig. 539 is a bolt with a fang -^wt or corner turned down and 
driven into the wood to prevent turning ; the screwing to be done at the 
head. 

It is often convenient to use bolts with two nuts, as in Fig. 540, or collar- 
bolts, which are readily made to order, and of any dimensions. 




Fig. 5S 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



255 



Fig. 541 is a ha7iger-ho\t ; the lag-screw part is screwed into the wooden 
beam, the hanger then put over the bolt, and the nut put on. 






Fig. 539. 



Fig. 540. 



Fig. 541 



Fig. 542. 



Figs. 542 and 543 represent forms of turn-huchles^ and the siuivel and pipe^ 
sometimes designated as siuivels. Turn-buckles are very useful in straining 
tierods, where neither end of the bolt can be got at. By turning the buckle, 
the rod can readily be made longer or shorter. In the pipe-swivel, right and 
left threads are cut on the bolts, so that each turn of the pipe shortens or 
lengthens the tie by double the pitch of the screw. The turn-buckle is also 
made in the same way, with two screws instead of a head at one end. 




Fig. 543. 



Screws, unless otherwise ordered, are made right-handed ; that is, turning 
the nut to screw up, the hand moves from left to right, the apparent motion of 
the sun. 

Oil the Strength of Bolts. — The strength of a bolt depends on its smallest 
section — that is, between the bottom of the threads. It is very common, there- 





Fig. 544. 



fore, to upset the screw-end, so that the screw may be cut entirely from this 
extra boss, or re-enforce. Bolt-ends (Fig. 544) are sold either with or with- 
out re-enforce, to be welded to bolts. It will be observed that the ends of the 
pipe-swivel bolts (Fig. 543) are thus upset. 

In the following table the sizes and dimensions of bolts and nuts are from 
the United States standard, and the strength, or safe-load of the bolts, is com- 
puted from the report of the committee on the test of wrought-iron and chain- 
cables to the United States Government in 1879. Nuts and heads as furnished 
are either hexagonal or square. Columns 4, 5,'and 6 apply equally to either. 

There is often an uncertainty in the determination of the load. The ef- 
fective load due to the forces acting on the machine may be estimated with 
tolerable accuracy. But that due to the forces used in tightening the nut is 
uncertain. If the bolt is screwed up so as to develop a reaction between the 
counected pieces, the additional load may be greater than the effective one. 



256 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



Washers (Fig. 545) — in common use to provide seatings for nuts which 
would otherwise rest on rough metallic surfaces, and also to adapt bolts to 



Diameter of 


Diameter at 


Thread per 


Short diam- 










screw in 


root of 


inch of 


eter of nut 


Thickness of 


Thickness of 


Safe-load of 


Safe-load of 


inches. 


thread. 


length. 


and head. 


nut. 


head. 


upset bolts. 


plain bolts. 


i 






A 


i 


A 






3 






1 3 


3 


13 






T^ 






^2" 


TIT 


if 






i 


•185 


20 


i 


i 


i 






1^ 


•240 


18 


if 


A 


if 






f 


•294 


16 


H 


f 


H 




1,700 


7 


•344 


14 


If 


A 


If 




1,900 


i 


•400 


13 


f 


i 


A 




2,200 


A 


•494 


12 


li 


A 


fi 




2,500 


f 


•5or 


11 


ItV 


f 


H 


- 


2,800 


H 






-If 


H 


If 




3,200 


f 


•620 


10 


li 


f 


f 


6,000 


3,600 


V 






iH 


if 


If 


7,000 


4,300 


I 


•731 


9 


ItV 


f 




8,000 


5,100 




•83T 


8 


If 


1 


fl 


10,000 


7,000 


n 


•940 


7 


141- 


If 


^M 


12,000 


9,000 


n 


1-065 


7 


2 


li 




15,000 


11,000 


If 


1-160 


6 


2fV 


If 


1/^ 


18,000 


13,500 


H 


1-284 


6 


2f 


li 


lA 


21,000 


16,000 


If 


1^389 


5i 


2A 


If 


lA 


24,000 


19,000 


If 


1^490 


5 


2f 


If 


li 


28,000 


22,300 


n 


1^615 


5 


2|| 


n 


lif 


82,000 


25,500 


2 


1^712 


4* 


Si 


2 


1—9 


86,000 


29,300 


2^ 






SA 


2i 


Ifi 


40,000 


83,000 


2i 


1-962 


4i 


Si 


2i 


If 


45,000 


37,000 


2f 






SH 


2f 


Iff 


50,000 


41,500 


n 


2-175 


4 


n 


2i 


HI 


55,000 


46,000 


2f 






4tV 


2f 


23V 






2f 


2-425 


4 


4i 


2f 


2i 






^ 






4tV 


21 


V. 






8 


2-629 


Si 


41 


3 


2A 






Si 


2-879 


H 


5 


Si 


2i 






3i 


3-100 


H 


5f 


Si 


m 






3 


3^317 


3 


5f 


Sf 


n 






4 


3-567 


3 


6i 


4 


StV 






4i 


3-798 


21 


6i 


4i 


Si 






4i 


4-028 


■2f 


6f 


4i 


StV 






4| 


4-255 


n 


7i 


4f 


Sf 






5 


4-480 


2i 


H 


5 


Sfl 






5i 


4-730 


2i 


8 


5i 


4 






5i 


5-058 


21 


8f 


5i 


^tV 






5i 


5-203 


2f 


8i 


5f 


4| 






6 


5-428 


2i 


9i 


6 


4A 







shorter spaces than their lengths — are sold for bolts up to 2" diameter. Cir- 
cular in form, their diameter is slightly in excess of that of the largest diam- 
eter of the nut, and the hole that of the bolt, and thickness from -j-^" to W 
according to the diameter of the bolt. 

Loch-nut Washers. — Nats subject to jars are apt to unscrew of themselves; 
to prevent which many expedients are adopted, as cupping the washer or turn- 
ing up one corner of a square washer against a face of the nut. The simplest is 
Shaw's Lock-nut, in which one side of a circular washer is cut through, one 
edge pressed up and the other down, to form a spring by which a pressure is 
brought on the thread when the nut is screwed home. In the Billing's lock- 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



257 



jiut by cupping a circular washer a similar effect is obtained through the elas- 
ticity of the cup. 

The square washer is used under both head and nut on surfaces of wood. 




Fig. 545. 



Fig. 546. 



and of dimensions suited to the stress. That they may neither sink into the 
wood nor bend or break, cast-iron is frequently used, and often, as shown in 
!Pig. 546, for roof-frames. 

Shafts and Axles. — Short shafts, revolving in bearings or boxes, or fastened 
with pulleys, drum, or wheels revolving on them, are called axles ; but long 
or heavy revolving bars are usually termed shafts. They may be independent ; 
that is, a single shaft, revolving in its bearings, or coupled, forming what is 
termed a line of shafting. The small shafts, as in clock-work and spinning- 
machinery, are termed pins and spindles. 

Shafts and axles are made of wood and metal, and of varied sections and 
form. 

Wooden shafts are polygonal, circular, or square section (Fig. 547). 







Fig. 547. 



Wrought metal, iron, or steel shafts, are almost invariably circular in sec- 
tion, but sometimes square. 

Cast-iron is used in great variety of section and form for shafts (Fig. 548) ; 
without uniformity longitudinally, but adapted to their position and load. 




Fig. 548. 

Formerly, either wood or cast-iron was invariably used for water-wheel 
shafts ; but a change of motors, from the breast, over-shot and under-shot 
wheels to reactors or turbines, has involved an entire change of construction, 
and now only wrought-iron is used. AYooden shafts are often used in ma- 
chines subject to wet and shocks, or from the greater convenience in obtaining 
the material, and from this last necessity the journals and boxes are sometimes 
of wood; but for wooden shafts it is the usual practice to insert cast-iron jour- 
nals with boxes or bearings of the same material. 
18 



258 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 




Fig. 549. 




Fig. 550. 



Fig. 549 is a side view of a wooden shaft with 
one end in section, and Fig. 550 an end view of 
the shaft. On the journal B is cast four wings, 
c c, and a small spindle, i. The ends of the shaft 
are bored for the spindle and grooved to receive 
the wings ; the casting is then drawn into place, 
hooped with hot ferules, aa^ and after this hard 
wood wedges are driven on each side of the wings 
and iron spikes are sometimes driven into the 
end of the wood ; most millwrights omit the spin- 
dle Z'. 

Figs. 551, 552, and 553 represent different 
views of a cast-iron shaft of a water-wheel. Fig. 
551 is an elevation of the shaft, with one half in 
section to show the form of the core ; Fig. 552, an 
end elevation ; Fig. 553, a section on the line c c 
across the centre. The body is cylindrical and 
hollow, and cast with four feathers, c c, disposed 
at right angles to each other, and near the extrem- 
ities of these feathers four projections, for the at- 
tachment of the bosses of the water-wheel or pul- 
ley. These projections are made with facets, so 
as to form the corners of a circumscribing square 
(Fig. 552), and are planed to receive the keys 
by which they are fixed to the naves which are 
grooved to receive them. The shaft is cast in 
one entire piece, the journals turned, and the 
feathers of an external parabolic outline to stiffen 
the shaft. 

Shafts like the examples given are for pur- 
poses where their loads are nearly constant and 
for moderate speeds, and cast-iron gives satisfac- 
tory results. 

The usual length of such journals is from one 
to one half times the diameters, and the safe load 
500 pounds to the square inch, taking the area 
as d^^ the square of the diameter, the diameter 
and length of journal being considered equal. 

To determine the size of a shaft, considered as 
a beam merely, but with a shifting load — as by 
the revolution of the shaft — each longitudinal line 
of surface has to undergo successively tension and 
compression. The safe load of wrought-iron is 
estimated at 6,000 pounds per square inch, and 
the formula on which the graphic diagram (Fig. 
554) is constructed \^ d = -06 y^l^ d being di- 
ameter, I = length between bearings, both in 
inches, w the load in pounds ; the load is not only 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



259 




Fig. 552. 



the weight of shaft and pulleys or gears, but also the 
stress in transmitting the power. 

, Use of Diagram. — Suppose w = 50,000 pounds, 
and Z = 6 feet = 72", then w I = 3,600,000, the or- 
dinate of 3-6 cuts the curve 
on the abscissa 9*2, which 
is the required diameter of 
the shaft in inches. 

Fly - wheel and crank 
shafts are of forged iron or 
steel, often forged in steps 
(Fig. 555) with the largest 
boss beneath the wheel hub, 
and sufficiently raised above 
the next to admit of the 
planing of the key seats. 

The transverse stress upon the shaft, due to the 
transmission of power, is equal to the H. P. divided 
by the velocity of surface, 
whether of belt or of gear, 
by which it is transmitted, 
and the same acts by torsion 
through the leverage of the 
radius of the pulley or gear. 
This stress is seldom calcu- 
lated, as it is sufficiently met 
by the tables and diagrams 
for the determination of 
the diameters of shafts. 

Keys are pieces of met- 
al, usually steel, employed to secure the hubs of pul- 
leys, gears, and couplings to shafts. They may be 
sunk keys (Fig. 556), flat keys (Fig. 557), and 
hoUoio keys (Fig. 558). The shaded circle repre- 
sents the shaft. The breadth of the key (Fig. 559) 
is uniform, but the thickness is tapered about 
one eighth of an inch per foot. The shoulder h 
is for the purpose of drawing out the key. Sunk 
keys are not necessarily taper. Some prefer them 
of uniform section, and to force the hub on over 
the key. 

It is good practise in fitting keys that they shall 
always bind tight sideways, but not necessar-ily 
touch either at the bottom of the ke3^-seat or the 
top of the slot cut in the hub. Such keys depend 
upon a forcing fit of the wheel upon the shaft so 
tight as to require screw-pressure to put the wheel 
in place upon the shaft. 




Fig. 553. 



tSv 



Tj 




Fig. 551, 



260 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



PROPORTIONS OF SUNK KEYS. 



DIAMETER OF SHAFT, 
IN INCHES. 


1 

•25 
•10 
•15 


2 


3 


4 


5 
If 

•61 
•20 
•41 


6 


7 

•80 
•25 
•55 


8 


9 


10 


11 


12 


Breadth of key 

Thickness of key 

Depth sunk in shaft. . 
Depth sunk in wheel . 


•125 

•215 


1 

•43 

•15 

•28 


•52 

•175 

•345 


If 

•71 
•225 

•485 


2i 
•89 
•275 
•615 


2f 
•98 
•30 

•68 


2f 
1-07 
•325 
•745 


lie 

•35 

•81 


3i 
1^25 
•375 

•875 



14" 



13 



12 



10 





1 

::: 

1 
1 

i 


^4+- 
++- 

yff' 


T 

It 

i 

1 


::: i: 

::: x: 

::±:::^ 


: x:: 


4^ 

i 


f-- 

:: 

-- 

\\ 


1 


4f^ 

* 

+ -+ + - 

#4 


iMniM 

1 I ; il i 1 r 

,1111! 

m 




i 


1 


i 


r 

"4- 


==F 
E+ 

1; 


- 1 M M 1 M ' -^ 
:g::::::-::T 

mm 


P 












X u 


4--U4-- MM 








4±±- 






1 

1 




e; 


1 


m 


■■ 


1 


::: 




1 




I 






1 


1 


t::±tp 
:::±:: 


H 


g 


1 


1 





4 5 6 7 8 9 

Product of Load and Span m Millions. 

Fig. 554. 



10 



11 



12,000,000 



Car- Axles. — Fig. 560 is the form and dimensions of axle adopted as stand- 
ard by the American Master Car-Builders' Association for wrought-iron and 
steel. 



, I 



Fig. 555. 



Shafting. — Thus far, independent shafts or axles have been treated of, and 
the dimensions have been established mostly by the load acting transversely; 





Fig. 5.)U. 



Fig. 557. 



Fig. 558. 



Fig. 559. 



but, in transferring power to machines, lines of shafting are necessary, almost 
invariably of wrought-iron or steel bars, which are subject not only to trans- 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



261 



verse but also torsional stress. When there are no pulleys or gears on the 
shafts between the bearings, and the couplings are close to the bearings, there 
is still an amount of deflection due to the weight of the shaft. James B. 
Francis, C. E., puts the maximum distances between bearings for shafts of 
wrought-iron or steel, under these conditions, as follows : 



Diameter 
of shaft. 


Distance between 
bearings. 


Diameter 
of shaft. 


Distance between 
bearings. 


Diameter 
of shaft. 


Distance between 
bearings. 


1" 


12 ft. 


5" 


21 ft. 


9" 


26 ft. 


2 


15 


6 


22 


10 


27 


3 


18 


7 


24 


11 


28 


4 


20 


8 


25 


12. 


28 



The diagram (Fig. 561) is one established by J. T. Hen- 
thorn, M. E., to determine the size of wrought-iron shaft- 
ing, to transmit a fixed amount of horse-power. 

Use of Table. — To find the size of a shaft making 150 
revolutions, and transmitting 350 horse-power. 

The intersection of the ordinate of 350 with the abscissa 
of 150 is between the diagonals 5 and 5J, and the diameter 
of the shaft may be taken safely at b\". 

Mr. Francis has constructed a table from his own experi- 
ments, of which the following is a synopsis : 

" The following table gives the power which can be 
safely carried by shafts making 100 revolutions per minute. 
The power which can be carried by the same shafts at 
any other velocity may be found by the following simple 
rule : 

" Multiply the j^oicer given in tlie table by the number 
of revohitions made by the shaft per minute; divide the 
product by 100; the quotient ivill be the power 'which can 
be safely carried.'''' 

The diagram and table given are applicable to shafts 
which are called second movers, subject to no sudden 
shock. For first movers, Mr. Francis takes but one half 
the horse-power given in the table for any diameter of 
shafts. Of late, cold-rolled shafts can be procured in the 
market, which are much stiffer than turned shafts, but not 
equal to that given for steel in the table. 

It is usual to make the shafts of second and third movers 
throughout manufactories and shops of uniform diameter, 
without reduction at the journals, the end-slip being pre- 
vented by collars keyed or fastened by set-screws. The 
usual length between bearings is from 7 to lO feet; but 
that they may run smooth, and not spring intermediately, 
it is desirable that they should never be less than 2 inches 
diameter, and that the pulleys or gears through which the 
power is transmitted to the next mover or to the machine 
should be as near as possible to the bearing. 



Fig. 5G0. 



tu 

I ICO 

I *^ 



\ii^^- 



0) 01 



^V 



.-^- 






.'?^.^ 



.-^^. 



.3fc 



.±h 



262 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



Horse-power which can be safely transmitted by shafts making 100 revolutions per minute, in which the 
transverse strain, if any, need not be considered ; if of 



Diameter 
in inches. 


Wrought- 
iron. 


Steel. 


Diameter 
in inches. 


Wrought- 
iron. 


Steel. 


! Diameter 
in inches. 

! 


Wrought- 
iron. 


Steel. 


1- 


2-0 


3 2 


4-5 


182- 


291- 


7-5 


843- 


1350- 


1-5 


6-7 


10-7 


5- 


250- 


400- 


8- 


1024- 


1638- 


2- 


16-0 


25-6 


5-5 


332- 


532- 


8-5 


1228- 


1965- 


2-5 


31-2 


50- 


6- 


432- 


691- 


9- 


1458- 


2332- 


3- 


54-0 


86-4 


6-5 


549- 


878- 


9-5 


1714- 


2743- 


3-5 


85-7 


137- 


7- 


686- 


1097- 


10- 


2000- 


3200- 


4- 


128- 


204- 
















Horse-power. 
Fig. 561. 

Fig. 562 represents a line of shafting. A is an npright shaft; a a, bevel- 
gears ; 1 1, bearings for the shafts ; c, coupling or connection of the several 
pieces of shafting. These shafts are of wronght-iron or steel, of nniform sec- 
tion. As the power is distributed froni this line of shafting, the torsional 
strain diminishes with the distance from the bevel-gears or first movers, and 
the diameter of each piece of shafting may be reduced consecutively, if neces- 
sary ; but uniformity Avill generally be found to be of more importance than a 
small saving of material. The drawing given is of a scale large enough to 
order shafting by, but the dimensions should be written in. 

In laying out lines of shafting, the position of the bearings is usually fixed, 
and the lengths of shafts must be determined thereby, with as few couplings as 
possible. When there is no necking or reduction of the shafts, which is usually 
the case, the orders given for shafting will be so many lengths and of such 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



263 



diameters, and so many couplings and hangers. When there is to be a neck- 
ing, the sketch for the order may be very simple, showing length and diameter 
of shaft, and position, length, and diameter of bearing. 

The couplings and pulleys are to be placed as near the bearings as possible. 
It frequently happens, therefore, that the coupling and pulley are needed at 




Fig. 562. 

the same point ; to remedy this, as the position of the pulley depends on the 
machine which it is required to drive, it frequently can not be moved without 
considerable inconvenience or loss of room ; the shaft will have, therefore, to 
be lengthened or shortened, to change position of coupling ; or, if the coup- 
lings are plate couplings, they may be made wdth faces for belts. 



H/IE 




Fig. 563. 



# 


\ 

1 


3! 






-e> 

-' 1 


i 

1 


Ljr ' 

"n ^ 



Fig. 564. 



When a horizontal shaft is supported from beneath, its bearing is usually 
called SLpiUotv- or plumber -block ^ or standard ; if suspended, the supports are 
called hangers. 

Figs. 563 and 564 are the elevation and plan of a pillow-block. It consists 
of a base plate. A, the body of the block B, and the box C. The plate is bolted 



264 



MACHINE DESIGI:^ AND MECHANICAL CONSTRUCTIONS. 

F ' G^m Fi 




































c 




i 

1 ; 1 






- 




1 : 1 




E 


L 


s 




h 




E 


V 


.......W 


V 






^ t ^ 




)' 




[ 


3 


"""■"I" 'X 




" 'P\ — \ 


f^ i \ 



Fig. 567. 



Fig. 566. 



B 



securely to its base, the surface on which the block B rests being horizontal. 
A and B are connected by bolts passing through oblong holes to adjust the 
position in either direction laterally. The box or bush C is of composition, in 
two parts or halves, extending through the block, and forming a collar by 
which it is retained in its place. The cap of the block is retained by the screws 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



265 



Fig. 568. 



000 ; in the figure there are two screws on one side and one on the other; 
often four are used, two on each side, but most frequently but one on each 
side". 

The standard is for the support of horizontal shafts at a considerable dis- 
tance above the foundation-plate. Fig. 565 is a front elevation ; Fig. 566, a 
plan ; and Fig. 567, an end elevation of a standard. Like the pillow-block, the 
plate A is fastened to the foundation itself, and the upper surface is placed per- 
fectly level in both directions. On these bearing surfaces, a a «, the body of the 
standard rests, and can be adjusted in position horizontally, and then clamped 
by screws to the foundation-plate, or keyed at the ends. 

Elevations and plan are usually drawn in such positions to each other that 
lines of construction can be continued from one to the other, which not only 
simplifies the drawings, but makes them more readily intelligible. Letters and 
dotted lines in these figures illustrate this sufficiently. 

The sides of the elevations are represented as broken ; this is often done 
in drawing, when the sides are uniform, and economy of space on the paper is 
required. 

Hangers. — Figs. 568, 569, and 570 are the plan side and front elevation of 
a side hanger especially adapted to a position in which the strain is in one di- 
rection and against the upright 
part. ' 

Figs. 571, 572, and 573 are side 
elevation, plan, and section on 
line A B of a centre hanger of an 
old pattern, but simple, adapted to 
any strain, and if adjusted to a 
position where the shaft is not 
likely to be moved, the form is 
strong and economical. 

Fig. 574 is of a later pattern, 
in which the shaft can be readily 
adjusted or removed. 

Hangers are bolted to the floor- 
timbers, or to strips placed to 
sustain them, the centres of the 
boxes being placed accurately in 
line, both horizontally and later- 
ally. 

Figs. 575-578 represent differ- 
ent views of what may be called a 
yohe-lianger. A is the plate which 
is fastened to the beam, E is the 

yoke, and B the stem of the yoke, cut with a thread so as to admit of a vertical 
adjustment ; the box D of the shaft C is supported by two pointed set-screws 
passing through the jaws of the yoke ; this affords a very flexible bearing, and 
a chance for lateral adjustment. 

The last hangers are of the design of William Sellers & Co., who have made 
improvements in the designs for bearings, pillow-blocks, hangers, shafting, and 



. — . ^ r ^ 


p)^i— t R 


^^h-McD 


V y /^ ^ ^ ^ 




Fig. 569. 



Fig. 570. 



266 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



couplings, which are in use in their own shops and have been extensively copied 
by others. Some of the distinctive forms are further illustrated. 




Fig. 572. 



Figs. 579 and 580 are the front and side elevations of a pillow-block, one 
half of each being in section. The length of the box is about four diameters 




Fig. 574. 



of the shaft. The centre bearings are spherical and fit in corresponding recesses 
in the block and cap, permitting the bearing to adjust itself to the journal of 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



26^ 



the shaft. Lubrication is ordinarily through the centre of the cap ; but the 
upper box has two cups containing a mixture of oil and tallow which is usually 




Fig. 575. 



Fig. 576. 





Fig. 577. 



Fig. 578. 



solid but melts when the bearing heats. The maximum pressure allowed is 
50 pounds per square inch, the diameter multiplied by the length of bearing 
or4D. 




Fig. 579. 



Fig. 580. 



Another feature of the Sellers bearings is the spherical-shaped drip-pan to 
catch the waste oil. By the distribution of the oil the metal of the shaft will 



268 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



not touch that of the box. Any metal can be used for the box ; cast-iron is the 
cheapest and best if the surface is kept oiled, but the poorest if allowed to run 

dry. The oil cup at the centre of the cap for a 
shaft 2^" in diameter making 120 revolutions per 





Fig. 582. 



minute has a capacity of 2*2 fluid ounces, which- is sufficient for six months' 
run. The above revolutions per minute are Messrs. Sellers & Oo.'s practice 
for machine shops, for wood-working machinery 250, for that of cotton and 
woollen mills 300 to 400 per minute. 




Fig. 583. 




Fig. 581 is a ball-and-socket hanger the construction of which is similar to 
the pillow-block. The centre spherical bearings are adjusted vertically by the 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



269 



screws d and e, the interior of whicli are made in hexagonal form and into 
which a key is fitted for the operation of the screw. 

Fig. 582 is a view of a side hanger adapted to a counter-shaft ; the square 
slot a is for the shipping bar. 

Fig. 583 represents the elevation of a bracket, or the support of a shaft 
bolted to an upright ; the box is movable, and is adjusted laterally by the set- 
screws. Fig. 584 is a front elevation of the back-plate cast on the post ; it will 
be seen that the holes are oblong, to admit of the vertical adjustment of the 
bracket. The Sellers pillow-block (Figs. 579 and 580) maybe used for the same 
purpose. 

For Upriglit Shafts. — Footstej)^ or Step, for an Upright Shaft. — Fig. 585 
represents a half elevation and section of the step. It consists of a foundation 
or bed-plate, A, a box, B, and a cup or socket, C. The plate A is firmly fast- 




,^/U^ 



Fig. 585. 



ened to the base on which it rests ; in the case of heavy shafts, often to a base 
of granite. The box B is placed on A, the bearing surface being accurately 
levelled, and fitted either by planing or chipping and filing ; the bearing sur- 
faces b are commonly called chipping-pieces, which are the bearing surfaces of 
the bottom of B. A and B are held together by two screws ; the holes for these 
are cut oblong in the one plate at right angles to those of the other ; this ad- 
mits of the movement of the box in two direc- 
tions to adjust nicely the lateral position of the 
shaft, after which, by means of the screws, the 
two plates are clamped firmly to each other. 0, 
the cup or bushing, which should be made of 
brass, slips into a socket in B. Frequently circu- 
lar plates of steel (Figs. 586 and 587) are dropped 
into the bottom of this cup for the step of the 
shaft. The cup C, in case of its sticking to the 
shaft, will revolve with the shaft in the box B ; if 
plates are used, these also admit of movement in 
the cup. 

Fig. 588 represents the elevation of a bearing for an upright shaft, in which 
the shaft is held laterally by a box and bracket above the step. The step B is 
made larger than the shaft, so as to reduce the amount of wear incident to a 
heavy shaft. The end of the shaft and the cup containing oil are shown in 





Fig. 586. 



Fig. 587. 



270 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



dotted line. The bed-plate A rests on pillars, between which is placed a pil- 
low-block or bearing for horizontal shaft. 




Fig. 588. 

Figs. 589 and 590 represent the elevation and vertical section of the suspen- 
sion bearing used by Mr. Boyden for the support -of the shaft of his turbine- 
wheels. It having been found difficult to supply oil to the step of such wheels, 
it was thought preferable by him to suspend the entire weight of wheel and 
shaft, where it could be easily attended to. The shaft (see section) is cut into 
necks, which rest on corresponding projections cast in the box t ; the spaces in 
the box are made somewhat larger than the necks of the shaft, to admit of Bab- 
bitting, as it is termed, the box ; that is, the shaft being placed in its position 





Fig. 589, 



Fig. 590. 



in the box, Babbitt, or some other soft metal melted, is poured in round the 
shaft, and in this way accurate bearing surfaces are obtained ; projections or 
holes are made in the box to hold the metal in its position. The box is sus- 
pended by lugs ^, on gimbals c, similar to those used for mariners' compasses, 
which give a flexible bearing, so that the necks may not be strained by a slight 
sway of the shaft. The screws e e support the gimbals, consequently the shaft 
and wheel ; by these screws the wheel can be raised or lowered, so as to adjust 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



271 



its position accurately ; beneath the box will be seen a movable collar, to adjust 
the lateral position of shafts. 

No weight rests on the foot of the shaft, but a cast-iron plate is firmly bolted 
to the floor of the wheel pit, with side flanges, and set screws by which iron or 
wooden cushions can be adjusted to preserve the shaft in its central position. 

The great care in design and mechanical construction of his wheels and their 
details enabled Mr. Boyden to obtain large percentages of effect, and led to the 
general introduction of turbines. In form and construction they have been 
much simplified, and with economy. Some makers still retain a form of upper 
hangers and bottom guides, but wooden steps (Fig. 591) are now almost uni- 
versally adopted. They are made either conical or a portion of a sphere, of 
various woods, usually lignum-vitae, but oak and poplar are preferred by some. 




y//////////77Z<. 



q / Z 3 4 - yS 6 7 8 9 //>3. 

Fig. 592. 





Fig. 591. 



Fig. 594. 



The load is from 50 to 75 pounds per square inch. The fibres of the wood are 
placed vertically, and afford an excellent bearing surface. Water is sometimes 
introduced into the centre of the wood, or into a box around it, from the upper 
level of w^ater. When cast-iron or steel is used for the step, it is usual to incase 
the box and supply oil by leading a pipe, sufficiently high above the surface of 
the water, to force the oil down. 

For long, upright shafts, it is very usual to suspend the upper portion by a 
suspension-box, and to run the lower on a step, connecting the two portions 
by a loose sleeve or expansion coupling, ^to prevent the unequal meshing of the 
bevel-wheels, incident to an alteration of the length of shaft by variations of 
temperature. The suspension is frequently made by a single collar at the top 
of the shaft. 



272 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 




Fig. 595. 



Fig. 596. 



Fig. 592 is a one half outside end view, and one half transverse. Fig. 593 
is a section on the centre line of axle, and Fig. 594 sectional plan of box on 
centre line of axle with a plan of journal and journal bearing of the standard 
journal box adopted by the Master Car-Builders' Association, 1874. 

Thrust Bearings for Screto Propeller Shafts.— The thrust along the shaft 
of a steamship propelled by a screw is taken ,up by collar bearings, and through 

them transmitted to the 
ship. Small shafts up to 
8" in diameter have gen- 
erally one thrust collar, 
but sometimes compara- 
tively small shafts have 
several thrust collars. In 
the latter case the bearing 
may have a brass bush in 
halves containing grooves 
to receive the collars on 
the shaft. The general 
practice is to fit between 
the collars cast-iron or 
cast-steel horseshoe - shaped pieces, clamped between two nuts, which are 
threaded on a screwed steel bar, supported at its ends by solid bearings cast 
on the block, as shown in Figs. 595 and 596. In this design each horseshoe 
piece may be adjusted separately by the nuts on each side, or they may be all 
moved together by means of the nuts at the ends of the bars. 

A useful diagram (Fig. 597), with accompanying explanation, by George E. 
Bate, Assoc. M. Inst. 0. E., is presented in the Practical Engineer for N"ov. 2, 
1894. " In its construction the effective horse power, or the power actually 
employed in propelling the ship, has been assumed to be equal to two thirds 
the indicated H. P. of the engines, so that 

" I. H. P. = the indicated H. P. of the engines. 

" E. H. P. = effective H. P. = I. H. P. x f . 

" K = speed of the vessel in knots. 

" T = total thrust, or load on thrust block in pounds. 

" P = pressure on thrust collars, pounds per square inch. 

" S = surface of thrust collar, square inches per I. H. P. ; then 

— -^ = K X 101 -3 = speed in feet per minute and work done per 

60 

minute in foot-pounds. 

" = T X K X 101-3, so that T X K X 101-3 = E. H. P. X 33,000 ; therefore 

_ E. H. P. X 33,000 

^ ~ K X 101-3 

" Again, if E. H. P. = f I. H. P., we may write 

21 H. P. X 33,000 I. H. P. X 22,000 I. H. P. x 217 . 



3 K X 101-3 K X 101-3 K 

therefore S, the surface of thrust collars in square inches per 

217 
K X P- 



I. H. P. 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



273 



" The diagram gives the value of S with P, varying from 30 to 80 pounds 
per square inch. In ordinary practice this pressure is 50 to 60 pounds per 
square inch in naval, and 40 to 50 pounds per square inch in mercantile 
steamers, although, in cases where white metal is fitted, it is found that these 
loads may be safely increased by 25 per cent. 

" As an example, suppose the case of a thrust block for a vessel having en- 
gines of 3,000 I. H. P., driving her at a speed of 18 knots, to determine the 
necessary surface of thrust collars that the pressure on them may not exceed 
60 pounds per square inch. At the point marked 18 knots on the scale for 
speed of vessel follow the ordinate up till it cuts the line marked 60 on the 
scale of pressures on the thrust collars to the left of the diagram, at which 
point of intersection follow to the right, and read off the corresponding surface 
of collars per I. H. P.— i. e., 0-201 square inches; then 0-201 x 3,000 = 603 
square inches, the total thrust surface required for E. H. P. = 3,000 x f = 
2,000 X 33,000 



2,000, and 



T, the load on the block equal to 36,180 pounds; 



18 X 101-3 
then, if pressure per square inch between surfaces is not to exceed 60 pounds, 

-^-— = 603, as per diagram." 



we have total surface of block = 



X 

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SPEED OF VESSEL, KNOTS. 

Fig. 597. 



25 30 



Couplings are the connections of shafts, and are- varied in their construction 
and proportions, often distinctive of the mechanic making them. 

The Face Coupling (Fig. 598), the one in general use for the connecting of 

wrought-iron shafts, consists of two plates or disks with long, strong hubs, 

through the centre of which holes are accurately bored to fit the shaft ; one 

half is drawn on to the shaft and tightly keyed ; the plates are faced square 

19 



274 



MACHIXE DESIGN AND MECHANICAL CONSTRUCTIONS. 



with the shaft, and the two faces are brought together by bolts. The nuraber 
and size of the bolts depend upon the size of the shaft ; never less than 4 for 
shafts less than 3 inches diameter, and more as the diameter increases ; the 
size of the bolts varies from f to 1^ inch in diameter. The figure shows a 
usual proportion of parts for shafts of from 2 to 5 inches diameter ; for larger 
than these, the proportion of the diameter of the disk to that of the shaft is 
too large. 

Fig. 599 is a rigid sleeve coupling for a cast-iron shaft ; it consists of a 
solid hub or ring of cast-iron hooped with wrought-iron ; the shafts are made 

with bosses, the coupling is slipped 
on to one of the shafts, the ends 
of the two are then brought to- 




■^ 




Fig. 599. 

gether ; and the coupling slipped back over the joint, and firmly keyed. This 
is an extremely rigid connection. Some makers use keys without taper, and 
force the couplings on the shafts. 

Fig. 600 is a screw coupling for the connecting of the lighter kinds of 
shafts. It will be observed that this coupling admits of rotation but in one 

direction — the one tending to bring 
^^HL^^^%i__^ /^^^^\ ^^^ ends of the shafts toward each 

other; the reverse motion tends to 
^^^^^^>:^>:>;;^s^Ix\'^^\n^:j^^^ \ ^^^^^/ / uuscrcw, throw them apart, and un- 
couple them. 

Figs. 601 and 602 is a double-cone 
vice coupling ; B is the outer shell or 
sleeve, C C the two cones, and D the bolts. The sleeve is cylindrical outside, 
but bored with a double taper inside, smallest at the centre. The cones are 
bored to fit the shaft, and turned outside to fit the interior cones of the sleeve. 




Fig. 600. 




Fig. 601. 



Fig. 602. 



There are three bolt grooves in the cones and sleeves, and one is cut through to 
give elasticity to the cones. The sleeves and cones are adjusted over the joint 
of the shafts, leaving it an easy fit, some f inch between the ends of the cones. 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



275 



If the bolts be introduced and screwed np, the cones are brought nearer to each 
other and tlie shafts are securely clamped together. 

Fig. 603 is a clamp coupling for a square shaft. 

In many cases it occurs that rigid couplings, such as have been given, are ob- 
jectionable ; they necessarily imply that, to run with the least strain possible, 



-• 




fv^ 














1 










I 




\ 


"^ 


\> 


1 





Fig. 603. 



Fig. 604. 



the bearings should be in accurate line ; a7iy displacement involves the spring- 
ing of the shaft, heating of the journals, and loss by friction. Wherever, from 
any cause, the alignment can not be very nearly accurate, some coupling that 
admits of lateral movement 
should be adopted. The 
simplest of these is the box 
or sleeve coupling (Fig. 
604), sliding over the end 
of two square shafts, keyed 
to neither, sometimes held 
in place by a pin passing 
through the coupling into one of the shafts. For round shafts, the loose 
sleeve Coupling is a pipe or hub, generally 4 to 6 times the diameter of the 
shaft in length, sliding on keys fixed on either shaft. 




Fig. 605. 




Fig. 606. 



Fig. 605 is a horned coupling. The two parts of the coupling are counter- 
parts, each firmly keyed to its respective shaft, but not fastened to each other ; 



2Y6 MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 




Fig. 607. 



the horns of the one slip into the spaces of the other, and, if accurately fitted, 
it affords an excellent coupling, and is not perfectly rigid. 

It often happens that some portion of a shaft or machine is required to be 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



277 



stopped while the rest of the machinery continues in motion. It is evident 
that, if one half of a horned coupling be permitted to slide lengthwise on the 
key — the key being fixed in the shaft, forming in this case what is more 
usually called a feather — when the horns of one half are out of the spaces of 
the other, communication of motion will cease between the shafts. 

Fig. 606 represents a coupling of this sort for a large shaft, from the Cor- 
liss Steam-Engine Company. The horns are 8 in number on each part, and 
are thrown readily in or out of action by the handle h turning nut in the loose 
part of the clutch on the screw cut on the shafts. 

Fig. 607 is another form of disengaging a large pulley from a main shaft, 
from the Corliss Steam-Engine Company. The pulley is fastened to a cast- 
iron pipe or sleeve p through which the main shaft s passes. The two are 
attached by means of the coupling c, one half 
of which is attached to the shaft and the other 
to the sleeve. When bolted together, the pul- 
ley and main shaft move together ; but if the 
bolts be removed, then the pulley becomes sta- 
tionary even if the shaft is running. Shaft 
and sleeve have independent bearings. A 
section of the coupling c on a larger scale 
shows the strong taper of the bolts without 
head. 

It is difficult to maintain shafts in exact 
line, and slight disarrangements are met by 
the elasticity of the shafts but, as a further 
precaution, flexible couplings are used, of which 
Fig. 608, called Oldham's Coupling, makes a 
stronp- connection and admits of considerable 
variation in the lines of the coupled shafts. 
It consists of two heads fastened to their several shafts, across the face of these 
heads two grooves are cut, and between these faces an intermediate plate is in- 
serted with two tongues at right angles to each other, slide-fitted to the grooves 
in the heads, thus coupling the two shafts. 

In Fig. 609 the coupling admits of more motion. The grooves are in the in- 
termediate plate, and one of the tongues is fitted in its head with a T or dove- 
tail groove held in position by a set screw or pin, by the removal of which the 
tongue can be withdrawn and the shaft uncoupled. 




t 





[T 








1 


1 




' — 


_[ 







3 



Fig. 608. 




Fig. 610. 



Hooke's Joint or Universal Coupling is used to connect two shafts whose 
axes intersect, and it has the advantage that the angle between the shafts may 



278 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 




Fig. 611. 



be varied while they are in motion. Fig. 610 shows the entire coupling partly 
in section ; the shafts to be coupled are forked at their ends ; these forked ends 
carry between them a cross the arms of which are at right angles to each other. 

The arms of the cross are jointed to 
the forks so that they may turn freely 
about their axes. The angular veloci- 
ties of the shafts will be unequal ex- 
cept at every quarter revolution, but 
by using a double Hooke's joint, as 
shown in Fig. 611, the two shafts will have the same angular velocities, if 
they make equal angles with the intermediate shaft and are in the same plane 
with it. 

It is often necessary to engage shafts, when one is in motion, or disengage 
when both are in motion. One of the oldest forms of clutch for this purpose 
is the slide or clutch couplings, when the motion is required but in one direc- 
tion (Fig. 612). A represents the half of the coupling that is keyed to the 
shaft, B the sliding half, c the handle or lever which communicates the sliding 
movement ; the upper end of the lever terminates in a fork, inclosing the hub 
of the coupling, and fastened by two bolts or pins to a collar round the neck 
of the hub ; to support B the end of its shaft extends a slight distance into the 
coupling A. Shafts can not be engaged with this form of coupling while the 

driving shaft is in rapid 
motion without shock. To 
obviate this, other forms of 
coupling are requisite ; one 
of these is represented (Fig. 
613). On the shaft B is 
fixed a drum or pulley, 




Fig. 612. 



Fig. 613. 



which is embraced by a friction 
this band consists of two straps 
ends projecting on either side ; 
is the common form of hayonet 
affords a guide to the prongs or 
ping these prongs forward, they 
friction band ; the shaft A being 



band as tightly as may be found necessary ; 
of iron, clamped together by bolts, leaving 
the portion of the coupling on the shaft A 
clutch ; the part c c is fixed to the shaft, and 
bayonets h &, as they slide in and out. Slip- 
are thrown into gear with the ears of the 
in motion, the band slips round on its pulley 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



279 



till the friction becomes equal to the resistance, and the pulley gradually attains 
the motion of the clutch. 

But of all slide couplings, to engage and disengage with the least shock and 
at any speed, th.Q friction-cone coupling (Fig. 614) is by far the best. It con- 
sists of an exierior and interior cone, a, Z? ; a is 
fastened to the shaft A, while h slides in the usual 
way on the feather of the shaft B ; pressing h 
forward, its exterior surface is brought in contact 





J 



Fig. 614. 



Fig. 615. 



with the interior conical surface of a ; this should be done gradually ; the 
surfaces of the two cones slip on each other till the friction overcomes the 
resistance, and motion is transmitted comparatively gradually and without 
danger to the machinery. The longer the taper of the cones, the more difficult 
the disengagement ; but the more blunt the cones, the more difficult to keep 
the surfaces in contact. An angle of 8° with the line of shaft is a very good 
one for surfaces of cones of cast-iron on cast-iron. When thrown into gear, 
the handle of the lever or sMpper (Fig. 615) is slipped into a notch, that it 
may not be thrown out by accident. 

The objection to this coupling is 
that it will work out of gear unless the 
shipper - handle is held firmly in its 
position, and producing considerable 
friction against the collar. To ob- 
viate this the shipper is made to act 
on a toggle-joint fastened to the shaft, 
and, once thrown, the pressure is self- 
continued and preserved without any 
action of the shipper, and without fric- 
tion. 

Fig. 616 represents a double-friction clutch, of the Weston-Capen patent. 
The clutch G is slid over the toggle, and the friction cone is forced into the 
pulley and engaged therewith. In the figure, D' is thus engaged with A', while 
D and A are not in contact. 




Fig. 616. 



280 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



When from any cause, as in rolling mills, the gearing is subject to sudden 
shocks, which might be injurious unless some means were adopted to modify 
the blow, friction couplings may be introduced of which Fig. 617 is an illus- 




FiG. 617. 

tration, in which the frictional resistance is sufficient to transmit the required 
power, but under sudden shocks yields and slips. It consists of two hubs, both 
keyed to their shafts; one of the hubs has a wood-lined groove into which the 
plate of the other is inserted and friction is produced between the two, by the 
bolts, which bring together the parts of the groove ; loosening the bolts removes 
the frictional contact and disengages the clutch. 

Fig. 618 is a longitudinal section and Fig. 619 a transverse section of the 
Weston clutch. The five iron disks A engage with solid keys on the long boss 
of the spur wheel E, within which the driving shaft C turns freely when no 
coupling pressure is applied to the disks. The drum D containing the six in- 
termediate wood disks B slides on feathers on the shaft 0, and the groove G- on 
the outer end of the drum receives the forked end of a lever by which the coup- 
ling pressure is applied, compressing the disks against the fixed collar F on the 
shaft, and thereby coupling the spur wheel E to the shaft 0. 





Fig. 618. 



Fig. 619. 



In Fig. 620 is shown the cylinder-friction clutch of Koechlin. In this case 
the clutch movement takes place readily. The part A is a hollow cylinder in 
which three internal clamp pieces are fitted, each being provided with a bronze 
shoe. These are thrown in and out of action by means of a sliding collar B' 
which operates right- and left hand-screws by means of the lever h. The clamps- 
slide in radial grooves. The nuts for the right- and left-hand screws can be 
closely adjusted and clamped by set screws, so that a radial movement of less 
than ^" is sufficient to throw the clutch in or out of action. 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



281 



Figs. 621 and 622 are sections and elevation of a friction clutch in which 
the piece A is in the form of a ring of unequal thickness and divided at its thin- 




FiG. 620. 



nest part. From the thickest part of the ring A a strong arm proceeds to a 
central boss which is keyed to the shaft. This ring, arm, and boss are all cast 
in one piece. An outer ring or shell B is bored or turned to fit easily over the 




^^^^ 



Fig. 621. 



Fig. 622. 



ring A. On the back of the piece B is a boss which serves to carry a wheel or 
pulley. To use the arrangement as a shaft coupling, the boss on the back of 
B is keyed to one shaft, the boss of A being keyed to the other. 

To take the place of fast and loose pulleys, as shown in the figures, the piece 
B rides loose on the shaft, except when it is bou-nd to the ring A. The pieces 
A and B are bound together by the expansion of the former caused by the rota- 
tion of right- and left-handed screws working in two nuts which fit into sockets 
in the ring A, one on each side of the line of division. By pushing the sliding 
boss C along the shaft, movement of rotation is communicated to the screw 
througli the link D and lever E. The lever E is secured to the middle portion 



282 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



of the screw by a grooved key, whicli is held by a set screw. At the back of 
this key there is a clearance space sufficient to allow of the key being with- 
drawn clear of the grooves, so that the lever may be turned on the screw into 
another position and take up the wear of the screw threads. 

Bovet's magnetic conpling (Fig. 623) consists of a block or head keyed to 
the power shaft, on the face of which is a groove containing the iron-wire core, 
connected with the brushes which bear on the rings. 




Fig. 623. 



Fig. 624. 



The shaft to be clutched is provided with a block F, capable of sliding along 
and approaching D until it is in contact. It follows, therefore, that when the 
wire B is traversed by a current, F is attracted against C D and participates in 
the motion of A. Adhesion is obtained without any external reaction. 

Fig. 624 is a spring hub used on a large rope-driving wheel to take up the 
shock of starting. The wheel W runs loose on the driving shaft S and is pro- 
vided with lugs a, a, «, which project into the spring hub H keyed to the driv- 
ing shaft S. Three heavy springs interposed between the lugs and the hub al- 
low a circumferential movement of four feet on a six-foot-diameter wheel. 

Pulleys are used for the transmission of motion from one shaft to another 
by the means of belts ; by them every change of velocity may be effected. The 
speeds of two shafts will be to each other in the inverse ratio of the diameter 
of their pulleys. Thus, if the driving shaft make 100 revolutions per minute, 
and the driving pulley be 18 inches in diameter, while the driven pulley is 12 
inches, then, 

12 : 18 :: 100 : 150; 

that is, the driven shaft will make 150 revolutions per minute without allow- 
ance for slip. Where there is a succession of shafts and pulleys, to find the 
velocity of the last driven shaft : Multiply together all the diameters of the 
driving pulleys by the speed of the first shaft, and divide the product by the 
product of the. diameters of all the driven pulleys. 



MACHINE DESIGN AND MECHANICAL CONSTJiUCTIONS. 



283 



Pulleys are made of cast-iron and of every diameter, from 2 inches up to 
20 feet. The number of arms vary according to the diameter ; for less than 
8 inches diameter the plate pulley is preferable (Fig. 025) ; that is, the rim is 
attached to thc/hub by a plate ; for pulleys of larger diameters, those with arms 
are used, never less than four in number. The arms are made usually straight 
(Fig. G26), sometimes curved (Fig. 627). 






Fig. 625. 



Fig. 626. 



Fig. 627. 



Fig. 628 represents a portion of the elevation of a pulley sufficient to show 
the proportion of the several parts, and Fig. 629 a section of the same. The 
parts may be compared proportionately with the diameter of shaft ; thus the 





Fig. 



thickness of the hub is about -^ the diameter of the shaft ; this proportion is 
also used for the hubs of couplings ; the width of the arms from f to full diam- 
eter ; the thickness half the Avidth ; the thickness of the rim from I- to -J- the 
diameter ; the length of hub the same as the width of face. 

Fig. 630 is a large pulley of the Southwark Foundry pattern. The hub is 
cast with four divisions, to admit of contraction in cooling, and the rim is in 
halves, to admit of the pulley being put on the shaft without removing it from 
its bearings, a very common practice with large pulleys. Wrought-iron rim- 
pulleys consist of a spider — that is, the hub and arms — of cast-iron, and a 
wrought-iron plate-rim is bolted to flanges on the extremities of the arms. 

Fig. 631 represents a faced coupling pulley, an expedient sometimes adopted 
when a joint occurs where a pulley is also required ; the two are then combined ; 



284 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



the pulley is cast in halves — two plate pulleys, with plates at the side instead of 
central, faced and bolted together. 




Wooden pulleys called drums are used for pulleys of very wide face. Fig. 
632 represents one form of construction in elevation and longitudinal section. 

It consists of two cast-iron pulleys A A, with nar- 
row rims ; they are keyed on to the shaft at the 




^J 



Fig. 631. 



"~ | — 1^ required distance from each other, and plank or 
lagging is bolted on the rims to form the face of 
the drum ; the heads of the bolts are sunk beneath 
the surface of the lagging, and the face is turned. 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



285 



Fig. 633 represents a wooden plate pulley, consisting of sectors of inch 
boards firmly glued and nailed together, the joints of the boards being always 
broken. The face is formed in a similar way by nailing and gluing arcs of 
board one to another to the required width of face ; these last should be of 




Fig. 632. 



clear stuff. The whole is retained on the shaft by an iron hub, cast with a 
plate on one side, and another separate plate sliding on to the hub ; the hub is 
placed in the centre of the pulley, the two plates are brought in contact with 
the sides of the pulley, and bolted through ; and the pulley turned. A similar 
arrangement of hub is used for the hanging of grindstones. 

Fig. 634 is an elevation of Chase's pulley similar in its rim to that of Fig. 
633, but an iron spider supplies the place of the wooden plate. They are built 






Fig. 633. 



Fig. 634. 



up with solid rims or split, as in the figure. They are made of the usual pulley 
dimensions up to 15 feet in diameter, and any desirable width of face, and able 
to transmit any amount of H. P. at any speed safe for a belt. 

Fig. 635 is a perspective of a pulley with a wrought-iron rim. It is shown 



286 



Machine design and mechanical constructions. 



with two spiders, but it can be made with a single one or with any number, ac- 
cording to the width of belt required. They are also made in halves, adapted 
to any position, and safe under all practical requirements. 

A counter-shaft is one distinct from the main shaft, but connected with it 
by a belt for the purpose of driving a machine. On the counter-shaft there is 

an arrangement of fixed and loose 
pulleys by which motion can be 
communicated to it or cut off. 

In Fig. 636, B is the belt from 
the main shaft which is being 
shifted on or off the fast pulley F 
on the counter by the fingers // 
on the shipper bar. The belt is 
shifted to a full position on either 
the pulleys F or L. When the belt 
is on the fixed pulley F, the motion 
of the main shaft is communicated 
to the counter ; when on the loose 
pulley L, the counter-shaft remains 
still and the pulley revolves upon 
it. It-sometimes happens that the 
friction of the loose pulley upon 
the counter induces its revolution ; 
to prevent which an arrangement is made, as shown in section (Fig. 637), by 
which the loose pulley moves on a fixed sleeve. 

The shipper handle, not shown, is held positively by notches, or by some 
arrangement attached to the shipper bar. The faces of the pulleys should be 
flat or but slightly rounded. The fixed sleeve should be kept oiled. 




Fig. 035. 



F L 




Fig. 636. 



Fig. 637. 



At the other end of the shaft cone pulleys are shown which correspond to 
similar cones on the machine but reversed so that the speed of the machine 
can be changed by shifting the belt from one set of cones to the other when 
the machine is stopped. 

Cone pulleys may be made continuous (Fig. 638), thus becoming conoids 
upon which the belt can be shifted to any line by an adjusting guide. 

It is often necessary to reverse the motion of a machine. This is readily 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



287 



done by a system of fast and loose pulleys, as shown in the plan and elevation 
(Figs. 639 and 6-iO), in which A is a drum or wide-faced pulley on the driving- 
shaft, B a fast pulley on the driven shaft, and 
and D loose pulleys on the same. The move- 
ment is indicated by the direction of the arrows. 
The driving-shaft revolves always in the same 
direction, but on the driven shaft the loose pul- 
ley of the straight belt is drawn from the bottom, 
and partakes of the same motion as the driving- 
pulley ; while by the cross-belt the draft is at the 
top of its pulley, and the motion reversed. If 
the straight or open belt be shipped on to the 
fast pulley B, the motion given to the shaft is 
like that of the driving-shaft ; if the cross-belt be 
shipped on to the fast pulley, the motion of the 
shaft is reversed. In the elevation, the lower side 
of the open belt is straight, while there is a sag 
in the upper ; the first is the tight or leading 
belt, through which the power is transmitted, Fig. 538. 

while the npper side is the loose or slack belt. 

When the belt is shifted, while in motion, to a new position on a drum or 
pulley, or from fast to loose pulley, or vice versa, the lateral pressure must be 
applied on the advancing side of the belt, on the side on which the belt is ap- 




FiG. 640. 



proaching the pulley, and not on the side on which it is running off. It is only 
necessary that a belt, to maintain its position, should have its advancing side 
in the plane of rotation of that section of the pulley on which it is required to 
remain, without regard to the retiring side. On this account, the shipper yoke 
or pins must be on opposite sides of the shipper bar. 

When the main shaft is connected directly with a machine, and it has to be 
thrown out, the belt is often slipped from the pulley (Fig. 641), and hangs 
loosely from the shaft, by which the belt is worn and often becomes entangled 



288 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



with the shaft or with couplings. It is better to have a hook suspended from 
the ceiling to catch the belt when thrown off ; or, still better, iron suspended 
bows (Fig. 641), from which it is easier to slip the belt on the pulley again. 




Fig. 641. 

Motion may be transmitted by belts to shafts at right angles to each other. 

Figs. 642 and 643 is a plan and elevation in which A is the driving-shaft 
and pulley and B the driven one, at right angles to each other. The arrows 
show the advancing sides of the belts and their position with regard to the face 
of the pulleys. 




Fig. 643. 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



289 



In the case of inclined axis (Fig. 644) the leading line falls in the middle 
plane of each pulley, but the following side of the belt does not, hence such 
systems can only be run in one direction. The leaving points in the figures 





Fig. 644. 



Fia. 645. 



are at a and h. The arrangement gives an open belt when the angles between 
the planes of the pulleys = 0°, and at cross belt = 180°. In the intermediate 
positions a partial crossing at the belt is pro- 
duced, the angle = 90° ; the belt is quarter 
twist (Fig. 645) ; if = 45°, it is quarter crossed. 
The maximum leading-off angle is 25°, which 
occurs when the distance between the axis is 
equal to twice the diameter of the largest pul- 
ley. 

Guide pulleys are very useful in belt trans- 
mission for shafts at varied angles, and the 
proper direction is obtained when each guide 
pulley is placed at the point of departure of 
its plane with that of the next following pul- 
ley. 

Fig. 646 is an arrangement adopted in 
portable grist-mills for driving the vertical 
shafts, rt, J, of mill-stones, from pulleys on a 
horizontal shaft. Here it is thought necessary 
to use guide-pulleys. 

Figs. 647 and 648 are the elevation and 
20 




Fig. 646. 



290 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



plan of another arrangement of pulleys and guide-pulleys \ ah is the intersec- 
tion of the middle plane of the principal pulleys. Select any two points a and 
b on this line, and draw tangents ac, b d^ to the principal pulleys. Then c ac 



y 





Fig. 617. 



Fig. 648. 



and eb d are suitable directions for the belt. The guide-pulleys must be placed 
with their middle planes coinciding with the planes cacajidebd. The belt 
will run in either direction. 

In Figs. 649 and 650 are parallel axes with two guide-pulleys. In the first 
the guide-pulleys are placed in planes tangent to both operating pulleys, and 
hence driving may occur in either direction. Usually, however, it is required 
to provide for motion in but one direction, in which case the second form is 
used as being simpler. The pulley B may be used as one of the guide-pulleys, 
in which case it may be placed loose upon the same shaft as A, and C or D be 
made drivers or driven. 

r^ It is necessary to stretch the belt over the pulleys to prevent its slip while 
conveying power. But if the belt is very heavy, and runs nearly horizontally, 






Fig. 649. 



Fig. 650. 



its weight will supply a portion of the adhesion which diminishes with the in- 
clination of the belt till it becomes vertical, when the friction of the stretch is 
the only factor of the adhesion of the belt to the lower pulley ; and, as the belt 
lengthens by use, the value of this friction becomes nothing. This position of 
pulleys should not obtain if it can be avoided ; but if not, the friction-stress 
should be by means of an idler or binder (Fig. 651) on the loose belt ; distinc- 
tively the idler rests in a loose frame against the belt, acting by gravity, while 
the binder is forced against the belt by mechanical appliances. By the relief 
of the binder the belt becomes slack, the friction of the belt on the pulleys be- 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



291 



comes nothing, and motion stops on the driven pulley ; but that of the belt may 
continue by its friction on the driver, from which it can be raised by a rope 
attachment or by a more positive contrivance. This is not found necessary 
when the arrangement is used for the engaging or disengaging of machines, 
but the driver pulley is provided with flanges so that the 
belt can not slip off. Idlers or binders are of necessity 
when the two pulleys are near to each other, as in steam 
hoist engines, either to increase the bearing surface on the 
pulleys or make up for the slight weight of a short belt. 

Belts run the best when their length and position are 
such as to give the frictional stress without much stretching 
on the pulleys, and without binders, and for this purpose 
the tight side of the belt — that is, the one approaching 
the driver pulley — should be at its under side. 

In determining the necessary length of a belt for any 
position, the simplest way is to measure it, if the construc- 
tion is complete ; if not, to make a drawing of the pulleys 
in position to a scale, and measure on the drawing. 

The width of the belt should always be a little less 
than the face of the pulley ; both are to be determined by 
the power to be transmitted and the velocity of movement. 

Allowance should be made in calculation of speed of a 
driven pulley for the slip of the belt, which is always some- 
thing, but should not fall behind more than one per cent 
that of the driver ; the friction, with too tight a belt is too 
much, and the slip, with a too slack one. Too small dimen- 
sion of pulley or too little of arc of contact increases slip. 
lar harm to have a belt unnecessarily wide, but it does to have it too narrow. 
If the diameter of the pulleys be increased, the speed of the belt is also in- 
creased, and for transmitting the same power, its width decreased. 

By experiments of H. B. Gale at the Washington University, St. Louis, the 
practical limits of speed of belt may be taken at from 3,000 to 7,000 feet per 
minute. The flesh side of leather possesses much greater tension than the 
grain or hair side, and on this account, and in the practice of most mill- 
wrights, the grain side is put in contact with the pulley, and in double belts 
the flesh side is placed centrally. 

D X TT X R .. ^ V 




Fig. 651. 



It does no particu- 



John T. Henthorn's formula for double belts is 



H. P. or 



450 450 

per inch in width, in which D is the diameter of pulley in feet, R the revolu- 
tions per minute. This is expressed graphically in Fig. 652. 

Use of Diagram. — To find the horse power that can be transmitted by a 
24" belt on a 20-foot pulley making 100 revolutions per minute : The abscissa 
line 100 intersects the diagonal 20 on the ordinate line 14 ; 14 x 24 = 336 = 
horse power transmissible. 

To find the belt necessary to transmit 100 horse power through a 10-foot 
pulley and 120 revolutions per minute of shaft: The abscissa 120 cuts the 

diagonal 10 on the ordinate line 8J ; -^^ = 12" width of belt. If the pulley 



292 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



were 12-foot instead of 10, it will be seen by the diagram that the intersection 

of diagonal would be at 10, and the width of belt — - = 10". 

This rule referred to single belts capable of transmitting one half the power 
of the double belt, would require a velocity of 900 feet per minute for a belt of 

Diameter of Pulleys, shown by Diagonals. 




» 10 u 
Horse-Power per Incli of Width. 
Fig. 652. 

1" in width to transmit 1 horse power, and if the belt were triple, and running 
with the same velocity, it would transmit 3 horse power, which is a rule in 
common use. 

The above rules are applicable to India rubber and canvas belts, which are 
largely used. They are made of plies of closely woven duck, stitched and cross- 
stitched together, with or without rubber between the plies and on the outer 
surfaces ; the rubber belts are the only ones that can be run in wet places. 
The plain duck belts depend largely on the close stitching of the plies, and can 
be used as cross belts, or in any place where leather belts can be used. 

There is a great difference among mechanics as to the amount of power 
that may be transmitted by a belt with economy, but the rules as given by 
Henthorne above are within limits of pra-ctice. The Amoskeag Manufacturing 
Co., Manchester, N. H., run two double belts each 40" wide, and one 24" wide, 
on a 30' fly-wheel pulley, of 110" face, making 61 revolutions per minute with 
1,950 indicated H. P. on the steam engine and transmitted through the belts, 
say 1,800 H. P., gives 17-3 H. P. for each inch in width of belt, and Henthorne 
12*8. The belts were considered heavily loaded but not overtaxed. 

Samuel Webber, in the "American Machinist," February, 1894, reports the 
case of a belt 30" wide, f " thick, running for six years at a velocity of 3,900 feet 
per minute on a pulley of 5 feet diameter and transmitting 556 H. P., w^hich 
gives a velocity of 210 feet per minute per inch width per H. P. By Mr. Fred. 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 298 

W. Taylor's rule it would be used to transmit only 123 H. P., who as Mem. A. S. 
C. E., in Vol. XV. of its "Transactions," has given conclusions from his prac- 
tical use of belts in the running of a machine shop day and night for nine 
years, a very long life if estimated in day's work of ten hours eacli, with ample ■ 
opportunity for repairs, and for narrow belts transmitting power to machinery. 
He finds by testing the tension of belts by a spring balance between two clamps 
attached to the ends of the belt whiie stretching, the most economical average 
total load for double belting to be 200 to 225 pounds per square inch of sec- 
tion, that a total load of 111 pounds per inch width corresponds to a pulling 
power of 65 pounds, of 54 pounds to 26 pounds, and that the maximum speed 
for economy should be from 4,000 to 4,500 feet per minute. 

" Belts are more durable and work more satisfactorily when made narrow 
and thick than wide and thin. Minimum diameter of pulley for a double belt 
12", for a triple 20", for a quadruple 30". Tlie ends of a belt should be fastened 
together by splicing and cementing instead of lacing, wiring, or using hooks or 
clamps of any kind." 

Leather belts may be purchased from stock from 1" to 48" in width, round 
belts from ^'' to f " in diameter. 

Rubber 3-ply is equal to single leather. The following are stock sizes : 2-ply 
from 1" to 28" width ; 6-ply up to 60" ; 7- and 8-ply to order. 

Full rolls contain 400 to 450 feet, and endless belts are made to order. Solid 
cotton belts, 2-ply 1" to 6" wide ; 4-ply 1" to 22". 

The use of endless ropes instead of belts is of very old application, by single 
lines of rope with outdoor exposure, and large pulleys at considerable distances 
apart. In Fig. 653 an arrangement is shown for the transfer of a reciprocat- 




FiG. 653. 

ing power ; one end of the rope is attached to and wound on one barrel while 
the other end is wound in an opposite direction on another barrel, so that as 
the ropes are unwound from one barrel they are taken up by the other, the 
length of the reciprocating movement being the length of transfer from one 
barrel to the other. 

This arrangement is sometimes applied to hoists, and with chains instead of 
ropes to the old type of planers. 

Of late the use of ropes for the transmission of power has increased very 
rapidly both in this country and in England, on account of their economy in 
first cost and maintenance, in transmitting large amounts of power to consider- 
able distances with simplicity in changes of direction and distribution of power, 
smooth running, and absence of slip. 

There are two forms of arrangement, in one of which a single spliced endless 
rope by its tension gives the necessary adhesion (Fig. 654), and as the rope grows 
slack by use, taking it up by a fresh splice ; in the other the slack is taken u]i 
by a tension carriage. In both forms increase of power is met by multiple 
grooves or pulleys and in the number of loops of rope. 



294 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



Fig. 655 shows the tension carriage as applied to the driving cable on the 
Brooklyn Bridge. A is the pulley connected with the steam engine, on which 




Fig. 654. 



there are four grooves and lines of rope for adhesion ; one line passes over the 
large standing 10-foot sheave B, thence round the tension pulley on a weighted 
car moving in inclined rails, thence over the sheave D to the line of bridge, over 




Fir. 655. 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



295 



the bridge beyond track, and returning tlie otlier to the pulley A. The cable 
in diameter and general arrangement is similar to that for cable roads, and is 
only given as an illustration of an extreme size of tension car. For transmis- 
sion of power to machinery the diameter of rope does not exceed 2 inches, and 
the tension car is usually a light grooved pulley, sliding on vertical or horizon- 




FiG. 656. 



tal tracks, with weights attached and moving vertically to give the requisite 
adhesion. 

With most makers the pulleys are single multiple grooves, but the Link Belt 
Engineering Co. make light pulleys, with a single groove to 
each, which can be bolted together to make a multiple grooved 
sheave of the requisite number of ring sections. 

" The diameter of the pulleys has an important effect on the 
wear of the rope. The larger the sheaves, the less the fibres of 
the rope slide on each other, and consequently there is less in- 
ternal wear of the rope. The pulleys should not be less than 
forty times the diameter of the rope for economical wear, and 
as much larger as it is possible to make them. This rule applies 
also to the idle and tension pulleys as well as to the main driv- 
ing-pulley." 

Fig. 656 is a view of a horizontal tension carriage ; Fig. 657, 
a half turn with vertical tension ; Fig. 658, a portion of the line 
of shaft of the factory of the same company. 

The usual material for rope gearing of mills is either hemp, 
manilla, or cotton. The ropes are untarred hawser laid — that 
is, formed with three strands twisted together right-handed ; a 
strand is made by twisting yarns together left-handed. 

The " Stevedore " rope of the Link Belt Engineering Co. is a 
4-strand rope, manufactured from long-fibre manilla laid in tallow mixed with 
plumbago (to reduce the friction in the bending of the strands passing around 



Fig. 



296 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



the sheaves), which renders it nearly waterproof, therefore suitable for out-of- 
door work. 

Fig. 659 represents a section of the grooves of a pulley as designed by E. 
J). Leavitt, M. E. 




Fig. 658. 



For the strength of a rope, the assumption of Mr. C. W. Hunt is that " a 
rope one inch in diameter should have a working strain of 200 pounds at all 
speeds. This is about one twentieth of the strength of the splice. This large 




Fig. 659. 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



297 



42 
40 
38 
36 
34 
32 




ROPE 


DRIVING. 


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:J4 


Horse power of manilla 
rope at various speeds. 












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40 50 60 70 ! 

VELOCITY OF DRIVING ROPE 

Fig. 660. 



:0 90 100 110 120 

IN FEET PER SECOND. 



margin is to enable the rope to perform a great amount of useful work 
it is so weakened by wear that it is necessary to be renewed. There are 
strains which can not be computed 
owing to the irregularities of the 
power and the work. The diagram 
(Fig. 660) takes into consideration 
the effects of the centrifugal force 
so that the strain on the rope is con- 
stant on the driving side in trans- 
mitting the tabular horse power, no 
matter what the speed may be. It 
shows also the power a rope trans- 
mits at various speeds, illustrating 
the rapidity with which the horse 
power decreases when the speed gets 
beyond about eighty feet per sec- 
ond." 

It is desirable in all cases of rope 
transmission to so arrange the drive 
that the slack side of the rope shall 
be on the upper part of the pulley, 
thus increasing the arc of contact, as 
the two sides will then approach 
ei,ich other when in motion. 

In order that the desired tensions 
shall be attained in the two parts 
of a rope, the deflection or sag must 
be of predetermined values. 

Fig. 661 is another diagram of 



before 
many 







""" 


-i/^r-ir- rM->i\»iM/-> 






- 










r~ 


144 
141 
138 


The curves show the sag of the 
ropes when transmitting the normal 
amount of power, it is the same at 
all speeds for the driving part, but 
variable for the slack part. The sag 
for the slack part is computed for 
speedsof 40, 60 and 80 ft. per sec. 






























1 


IX) 










i 


129 
126 
123 

120 
117 
114 
111 
108 
105 
102 
09 
96 
93 
90 
87 
84 








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20 40 60 80 100 120 140 

DISTANCE BETWEEN PULLIES IN FEET. 

Fig. 661. 



298 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



Mr. Hunt's showing the sag of the rope. The rope is supposed to have the 
strain constant at all speeds on the driving side and in direct proportion to the 
area of cross section, hence the catenary of the driving side is not affected by 
the speed or by the diameter of the rope. 

The deflection between the pulleys on the slack side varies with each change 
of load or change of speed. 

Having determined the sag of the rope from the diagram, lay oS the pulleys 
as in Fig. 662, draw a horizontal line A B, and from the centre of this line and 
normal to it the line E equal to the sag of the rope, and construct a parabola 




by dividing the line D into, say, five equal parts and the line A D into the same 
number of equal parts; the intersections of the lines Cl, C3, C3, etc., by the per- 
pendiculars at 1', 2', 3', etc., give the points of the curve. 

The determination of the sag of ropes whose "points of contact with their 
pulleys are not level may be determined by calculation ; but as it can only be 
for one condition of speed and load, it will be sufficient to determine it practi- 
cally by taking a cord equal to the whole distance between the points of con- 
tact, and that of the sag as given by the Hunt diagram, when the sag is central. 
Fix one end of the cord and raise the other to the level of the position it is to 
occupy in running, and the amount of sag and its position will be defined by 
the cord. If it is necessary to represent it by drawing, construct two parabolas. 

Wire-rope power transmission is applicable for distances of from 50 to 400 
feet, and withstands weather exposure. It is of much less diameter than hemp 
rope to transmit the same power and has more endurance. For endurance the 
diameters of wheel and rope and sag must be proportioned to each other. The 
table below is from the circular of the Trenton Iron Works Co., gives the pro- 
portionate diameters of wheels and ropes, and the H. P. transmission at 100 
revolutions : 



Diameter 


Diameter 




Diameter 


Diameter 




Diameter 


Diameter 




of wheel, 


of rope, 


H. P. 


of wheel. 


of rope, 


H. p. 


of wheel, 


of rope. 


H. p. 


in feet. 


in inches. 




in feet. 


in inches. 




in feet. 


in inches. 




3 


f 


7 


7 


9 


86 


9 


f 


82 


4 


i 


9 


6 


f 


88 


10 


f 


91 


5 


# 


11 


7 


f 


44 


8 


i 


99 


5 


i\ 


16 


8 


f 


51 


9 


i 


112 


5 


i 


20 


7 


-\k 


54 


10 


i 


124 


6 


i 


24 


8 


J 1 
1 fi 


61 


8 


1 


130 


5 


-^ 


26 


9 


•u- 


69 


9 


1 


146 


G 


1% 


81 


8 


1 


73 


10 


1 


162 



In applying this table for a given amount of horse power, preference should 
be given to the larger wheels as most serviceable. 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



299 



If more H. P. is to be transmitted it may be obtained by increasing the revo- 
lution in a direct proportion np to the limit of 80 feet per second, but not by 
the increase of tension of rope as shown by sag, which may be taken for a span 
of 100 feet at -7 feet, and for other spans directly as their squares — that is, for 
200 feet it would be '7 X 4 = 2*8 feet. The sag as given is that measured from 
a horizontal line through the point at which the rope leaves the wheel. If the 
two wheels are not on the same level the sag must be measured from the level 
of the point of contact with the lower wheel, and the span to be used in deter- 





FiG. 663. 



Fig. 664. 



mining the sag below this level is the distance along the horizontal line from 
the wheel to the point at which it again intersects the rope. This point may 
be ascertained by hanging a wire in place on the wheels before splicing the rope. 

If the difference of level is very great, run the rope over intermediate carry- 
ing sheaves so placed as to give a level stretch of rope of which the sag can be 
taken from the rule of sag. 

Intermediate supporting pulleys should be avoided as far as practicable, as 
each one increases the wear on the rope. When they can not be dispensed with 
they should not be less than one half to two thirds the diameter of the main 
wheels. 

The sag of the rope when doing full work will be one half that when at rest. 
The driving-sheaves should always be lined with some elastic material, as rubber, 
leather, or wood. Figs. 663 and 664 give the section of grooves as made at dif- 
ferent works. 




Power-transmission hy Chains. — Fig. 665 is a sectional perspective of a pul- 
ley in which there is a groove for the vertical links of the chains and a face for 



300 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



the horizontal ones, which serve merely as guides for hoisting in cranes or saw- 
mills and the like. By the introduction of ribs on the face (Fig. 666) adapted 
to the length of the link or pitch 
of the chain the motion is deter- 
minate and is used to transmit 
power. 

Fig. 667 is a sprocket wheel for 




Fig. 665. 




( 
( 


' I: 




Fig. 667. 



punched links with teeth between each link, especially adajoted to position 
where the stress is great and the movement slow, for which they can readily be 
proportioned. 

The same class of wheel and chains are made light and used as in bicycles, 
and driven at considerable speeds with little friction. 




Fig. 668. 



Fig. 669. 



Fig. 670. 



The link belting is made with malleable iron links and detachable, so that 
the belt can be readily lengthened or shortened. The sprocket wheels are 
machine finished to pitch. 

Figs. 66S, 669, and 670 are drawings of links of different forms. They are 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



301 




^^^ 



made of all dimensions to suit the purposes and stresses required. At the 

usual speeds of leather belts, link belting is noisy and wears rapidly, but at 

moderate speeds — for conveyors of 

grain, clay, and the like — they are 

admirably adapted, and in such 

positions and conditions of speed 

can be used to transmit power. 

Leather link belting consists 
of links made of leather con- 
nected by iron or steel pins. A 
belt of this design can be made of 
any width, works freely on a pul- 
ley of small diameter, and can be 
driven at very high speed, which, 
combined with its great strength, 
make this form of belt very suita- 
ble^ for driving dynamos. When 
the link belt runs between guides, 
or on flanged pulleys, the rivet 
heads are faced on the outside 
links with leather after the belt is 
riveted up. 

When a link belt of considerable width works on a curved pulley, either 
there is contact at the centre only, or the pins are bent where the band is in 
contact with the pulley. The belt in this case is in two or more longitudinal 
strips, hinged together, as shown in Fig. 671. 




(2^ 



Fig. 671. 



GEARING. 

The term gearing, in a general sense, is applied to all arrangements for the 
transmission of power; but, in a particular sense, to toothed gearing, which 
may in general be divided into three classes — spur, bevel, and screw. In the 
former the axis of the driving and driven wheels are parallel to each other; in 
the bevel they may be situated at any angle ; if of equal size and at right angles, 
they are called mitre gears. In screw gearing a toothed wheel is driven by a 
screw with their axes usually at right angles to each other. Spur wheels are 
termed external or internal, according to the disposition of their teeth with re- 
gard to the rim of the wheel. 

Hack gear and pinion are employed to convert a rotary into a rectilinear 
motion, or vice versa. In this arrangement the pinion is a spur wheel, acting 
on teeth placed along a straight bar (Fig. 680). 

Bevel gearing consists of toothed wheels formed to work together in differ- 
ent planes, their teeth being disposed at an angle to the plane of their faces. 

Trundle pins or wheels (Fig. 672) are constructed with cylindrical pieces 
called staves or pins, instead of teeth. A pinion with double plates is called a 
lantern ; the wheel, a face or crown wheel ; this construction is very useful 
when iron gears can not be easily obtained or repaired. 

Fundamental principle. — In order that two circles A and B (Fig. 673) may 
be made to revolve bv the contact of the surfaces of the curves m m and n n of 



302 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



their teeth precisely as they would by the friction of their circumferences, it is 
necessary and sufficient that a line drawn from the point of contact t of the 
teeth to the point of contact c of the circumferences (pitch-circles) should, in 





\ l!/ / 

\ ; I / /' 

\ i i / / 

A 

Fig. 672. 

every position of the point ^, be perpendicular or normal to the surfaces of con- 
tact at that point to both the curves m m and n n/a particular property of that 
curve known as the cycloid. 

When one wheel conducts the other, it is called the driver or leader, and the 
other the driven or follower. The angular velocities of the pitch circles is the 
same, but the number of revolutions of the wheels is inversely as their diam- 
eters taken at the pitch circles. If the driver is 24" diameter, making 120 
revolutions per minute, and the driver is required to make 200 revolutions per 
minute, then the diameter of the driven gear would be 

120 X 24 4^' 

200 --^^10- 

Fig. 674 gives the designation of the various parts of a spur wheel by which 
names they will hereafter be called. 




Fig. 074. 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 

There is considerable variation in the proportion of teeth, as — 
Thickness of teeth, from -45 to -48 pitch. 
Space between teeth, from -55 to *52 pitch. 



303 




Height of teeth outside pitch circle, from -2 to -3 pitch. 

Depth of teeth inside pitch circle, from -3 to '4 pitch. 

The above is for cast teeth, used without finishing ; the teeth are made 
narrower than the space, and the height less than the depth on account of the 
irregularities of a rough casting. The teeth and space, when machine cut, may 
be made the same or very nearly so. 

The cycloid (Fig. 675) is a curve described by any point on the circumfer- 
ence of a circle on a straight line as a base which is the pitch line of the rack 
in its application to the formation of teeth of a rack and pinion. 

Divide the circumference of the generating or rolling circle A into a num- 



7^ 

r" 


3'" 
6" 7" 


\ 1 

V \ \ 

X 1 


/ / 
/ V 


\ 


6' ~W^ 



Vo. 



Fig. 676. 



304: 



MACHIXE DESIGN AND MECHANICAL CONSTRUCTIONS. 



ber of equal parts, say 12 ; draw chords from each of these points to ; divide 
the base line into an equal number of parts of the same length as the arcs of 
the generating circle numbered 0, 1', 2', etc., and from each of these points 
erect a perpendicular intersecting the centre of the circle A B at 1", 2", etc. ; 
from each of these points describe arcs with a radii equal to the generating 
circle. From the points 1', 2', 3', 4', etc., on the base line, and with radii equal 
successively to the chords 1, 02, 3, 4, etc., describe arcs cutting the pre- 
ceding, the intersections will be points of the required curve. 

The epicycloid (Fig. 676) is a cycloid formed on the circumference of a 
circle as base, which, in its application to the teeth of wheels, is the pitch circle 
of external gearing. 

The path of the centre of the generating circle is concentric with the base 
circle. Divide the generating circle from and the arc of the base circle into 
the same number of equal parts. Kadial lines from C, passing through 1', 2', 
etc., and intersecting A B, give the points from which the arcs of the generat- 
ing circle are described; from the points 1', 2', 3', etc., on the base circle, and 
with radii equal successively to the chords 1, 2, 3, etc., describe arcs cut- 
ting the preceding ; the intersections are points in the required curve. 

The hypocycloid (Fig. 677) is a cycloid with a base of the interior circum- 
ference of a circle corresponding to the pitch circle of internal gearing. 




Fig. 



Proceed as in the previous example and divide the generating circle and 
base line into equal parts, describe the path of the centre of the generating 
circle A B concentric with the base circle, and from each division of the base 
line draw radial lines from C, intersecting the line A B at 1", 2", etc. ; from 
these centres describe arcs of a radius equal to the generating circle ; from the 
points 1', 2', 3', etc., on the base circle, and with radii equal successively to the 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



305 



chords 1, 2, 3, etc., describe arcs cutting the preceding ; the intersections 
are points of the required curve. 

INVOLUTE. 

The involute (Fig. 678) is the curve described by the end of a string being 
unwound from the circumference of a circle. 




Divide the circumference of the given circle into any number of equal parts, 
as 0, 1, 2, etc. At each of these points draw tangents to the given circle ; on 
the first of these lay off the distance 1-1', equal to the arc 0-1 ; on the second 
lay off 2-2', equal to twice the arc 0-1 or the arc 0-2 ; establish in a similar 
way the points 3', 4', 5', as far as may be necessary, which are points in the 
required curve. 

The involute curve may be described mechanically in several ways. Thus, 
let A (Fig. 679) be the centre of a wheel for which the form of involute teeth 
is to be found. Let m ?^ a be a 
thread lapped round its circum- ^ 
ference, having a loop-hole at its 
extremity, a ; in this fix a pin, 
with which describe the curve or 
involute ab . . . . h,hy unwinding 
the thread gradually from the 
circumference, and this curve will 
be the proper form for the teeth 
of a wheel of the given diameter. 

In all the problems in which 
curves have been determined by 
the position of points, the more 
numerous the points the more accurately can the curve be drawn. 

Spur Wheel and Rack (Fig. 680). — The pitch-circle of the spur wheel is 
drawn and the proper curve for the flank and face of the teeth obtained by 
21 




Fig. 679. 



306 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



rolling a generating circle on the inside and outside of the pitch-circle; thus 
the point A' on the generating circle gives for the flank of the teeth the hypo- 
cycloid A' B', and for the face the epicycloid A' 0'. 




Fig. 680. 



The curve for the teeth of the rack is obtained by rolling the same generat- 
ing circle on the upper and lower side of the rack pitch-line, giving two cy- 
cloids, A and A B, for the face and flank of the teeth. The diagram showing 
the construction of above curves is, to avoid confusion, separate from the draw- 
ing of the spur wheel and rack. 

The diameter of the generating circle is to a certain extent arbitrary. In this, 
and the following examples it is taken at a little less than the radius of the 
smallest spur wheel ; if taken at exactly the radius, the flanks of the teeth of 
this wheel will be radial lines, which is not usually as satisfactory as where the 
flanks are of hypocycloidal form, as the teeth, being narrower at the root, have 
a tendency to break at this point. 

When a number of wheels are intended to gear together, the same size of 
generating circle and the same pitch and dimensions of the teeth must be main-^ 
tained. The generating circle should never be larger than the radius of the 
smallest wheel of the set. 

Where a drawing of a whole wheel is to be made, the circumference can be 
divided by radial lines into the same number of parts as there are teeth. The 
curve of one tooth having been found, a templet can be made and applied 
successively; or find an arc of a circle corresponding as closely as possible 
to the cycloidal curve, and apply this at the proper divisions ; the latter way 
is the more common. 

Spur Wheels. — Fig. 681 shows two wheels gearing together, one of ten and 
the other of thirty teeth. The diameter of the generating circle is less than 
the radius of the pitch-circle of the smaller wheel ; when the generating circle 
rolls on the exterior and interior of both pitch-circles, it will in the former 
case generate the faces of the teeth as shown at A and A' C, and in the latter 



machin:e design and mechanical constructions. 



307 



case their flanks A B and A' B'. In other respects the construction is similar 
to the former example. 

The simplest illustration of the action of epicycloidal teeth is when they are 
employed to drive a trundle, as represented in Fig. 672. Let it be assumed that 




Fig. 681. 

the staves of the trundle have no sensible thickness ; that the distance of their 
centres apart, that is theiv pitch, and also their distance from the centre of the 
trundle, that is their pitch-circle, are known. The pitch-circles of the trundle 
and wheel being then drawn from their respective centres B and A, set off the 
pitches upon these circumferences, corresponding to the number of teeth in the 
wheel and number of staves in the trundle ; let five pins, a be, etc., be fixed into 
the pitch-circle of the trundle to represent the staves, and let a series of epicy- 
cloidal arcs be traced with a describing circle, equal in diameter to the radius 
of the pitch-circle of the trundle, and meeting in the points klmn, etc., alter- 
nately from right and left. If motion be given to the wheel in the direction 
of the arrow, then the curved face m r will press against the pin h, and move 
it in the same direction ; but as the motion continues, the pin will slide up- 
ward till it reaches m, when the tooth and pin will quit contact. Before this 
happens, the next pin a^ will have come into contact with the face al oi the next 
tooth, which, repeating the same action, will bring the succeeding pair into con- 
tact ; and so on continually. 

To allow of the required thickness of staves, it is sufficient to diminish the 



308 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



size of the teeth of the wheel by a quantity equal to the radius of the staves 
(sometimes increased by a certain fraction of the pitch for clearance) by draw- 
ing within the primary epicycloids, at the required distance, another series of 
curves parallel to these. In practice, a portion must be cut from the points of 
the teeth, and also a space must be cut out within the pitch-circle of the driver, 
to allow the staves to pass; but no particular form is requisite; the condition to 
be attended to is simply to allow of sufficient space for the staves to pass with- 
out contact. 

Internal Gearing (Fig. 682). — Draw the spur wheel as in the previous exam- 
ples ; the face of the teeth of the internally geared wheel will be the hypocycloid 




Fig. 682. 

A 0, formed by the generating circle rolling on the interior of the pitch-circle, 
and the flanks the epicycloid A B, formed by the generating circle rolling on the 
exterior of the pitch-circle. 

INVOLUTE TEETH. 

Fig. 683 is a pair of spur wheels showing the mode of drawing involute teeth. 
The addendum, pitch, and root-circles of both wheels are first drawn, then the 
base-circles of the two wheels, which must bear the same proportion to each other 
as the pitch-circles. To arrive at this proportion a semicircle is constructed on 
the line A C B with a diameter equal to the radius A of the pinion ; a per- 
pendicular erected where the larger addendum-circle intersects the line A B 
intersects the semicircle at E ; a line is then drawn from A to E and a normal to 
it at E of indefinite length ; then from B a parallel to A E intersecting the nor- 
mal at E' ; circles concentric to the pitch-circles drawn through E and E' give 
the base-circles. 

All teeth on the line E E' will be in contact at the same time, called, there- 
fore, the line of contact. The involute curves of the teeth of both wheels are 
drawn from their respective base-circles, which correspond to the given circle of 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



309 



Fig. 678. Both involutes in Fig. 683 start from the point of contact E, hence 
one curve is described forward, the other backward. 

Thus on the normal E' E there are eight parts, and from the commencement 
of the next normal seven parts are marked off, the next six, and so on until 
finally the involute reaches the base-circle. The part of the tooth within the 
base-circle may be a radius to it and tangent to the involute, and small fillets 
should be drawn connecting their roots to the root-circle. 




Fia. 683. 



A pinion gearing into a rack is shown in Fig. 684. The faces of the teeth of 
the rack can be taken at an angle of 23° with the perpendicular ; this angle 
gives the longest line of contact, which may be considered the jDitch-line of the 
rack, and, the pitch-circle of the pinion being indicated, the base-circle for the 
construction of the involute curves is obtained by drawing a line through the 
point C where the two pitch-lines come together at an angle of 23° with 
the horizontal and where a normal from this line intersects the centre C of the 
pinion a line is drawn, and through its junction E of the line of contact a 
base-circle is described ; at this point E the involute is drawn as in the pre- 
vious example. As in cycloidal teeth, the exact curve may be laid down for one 
tooth, and an arc corresponding as closely as possible to the involute used to 
describe the remainder. 

All involute wheels whose teeth have the same pitch and obliquity to the 
line of contact work well together, but no wheel should have less than twelve 
teeth to work well. 

Involute wheels can not be made with very long teeth, because the obliquity 
of the line of contact will be too great. 

The diameters of spur wheels are in proportion to the number of their revo- 



310 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



lutions per minute, but the relative sizes of a pair of bevel wheels is determined 
by a division of the angle included between the two axes inversely as the ratio 




Fig. 684. 



of their angular velocities. Let B and (Fig. 685) be the position of the two 
given axes, and let them be prolonged till they meet in a point A. Further, let 
it be required that makes seveyi revolutions while B makes four. From any 
points D and E in the lines A B, A 0, and perpendicular to them, draw D d 
and E e of lengths (from a scale of equal parts) inversely as the number of rev- 
olutions which the axes are severally required to make in the same unit of time. 
Thus, the angular velocity of axis B being 4, and that of the axis C being 7, 
the line D d must be drawn = 7, and the line E e = 4. Then through d and e 
parallel with the axes A B and A draw d c and e c till they meet in c. A 
straight line drawn from A through c will then make the required division 

of the angle BAG, and define the 
1 line of contact of the two cones, 

by means of which the two rolling 
frusta may be projected at any 
convenient distance from A. 

If the relative perimeters, di- 
ameters, or radii, of the pair have 
been determined, then the lines D 
d and E e are to each other direct- 
ly as these quantities. B F and 
C F are radii of the pitch-circle. 

The case in which the axes are 

neither parallel nor intersecting 

admits of solution by means of a 

pair of bevels upon an intermediate axis, so situated as to meet the others in 

any convenient points. 

When the contiguity of the shafts is such as to permit of their being con- 
nected by a single pair, skewed bevels (Fig. 702) are sometimes employed. 




Fig. 685. 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



311 



When the axes are at right angles to each other, and do not intersect, the 
wheel and screw may be employed to connect them. The velocity of motion is 
in this arrangement immediately deduced from that of the screw, its number 
of threads, and the number of teeth in its gearing-wheel. Thus, if it be re- 
quired to transmit the motion of one shaft to another, contiguous and at right 
angles to it — the angular motions being as 20 to 1 — then, if the screw be a 
single-threaded one, the wheel must have 20 teeth ; but if double-threaded, the 
number of teeth will be increased to 40, for 2 teeth will be passed at every revo- 
lution. If the screw have few threads compared with the number of teeth of 
the wheel, it must always assume the position of driver on account of the ob- 
liquity of the thread to the axis ; and in this respect its action is analogous to 
that of a travelling rack, moving endwise one tooth, while the screw makes one 
revolution on its axis. 

If the pitch-circle be divided into as many equal parts as there are teeth to 
be given to the wheel, the length of one of these parts is termed the pitch of 
the teeth. 

The pitch depends on the power to be transmitted or the stress on each tooth. 
The diagram (Fig. 686) is by John T. Henthorn, M. E., in which pitch and 




1,000 2,000 



3,000 



4,000 5,000 

Stress in Pounds. 

Fig. 686. 



6,000 



7,000 



9,000 



face, represented by multiples of the pitch, are proportioned to the stress in 
pounds. 

If the pitch be known, the number of teeth in a wheel can be determined 
approximately by dividing the circumference of- the wheel by the pitch, but 
there must be no remainder in the quotient — there can be no fraction of a pitch 
— either the pitch or diameter of wheel must be changed to produce this re- 
sult ; generally the latter, as gears are usually made of determinate inches and 
fractions, as given in the table, by which also calculation for diameters aud 
number of teeth is much simplified. 



312 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



PITCH IN 

INCHES 

AND 

PARTS OP 

AN INCH. 


p 

D = — X N. 


N = -p- X D. 


RtXLB.— To find the 
diameter in inches, 
multiply the number 
of teeth by the tabu- 
lar number answer- 
ing to the given 
pitch. 


KiTLE.— To find the 
number of teeth, 
multiply the given 
diameter in inches 
by the tabular num- 
ber answering to the 
given pitch. 


Values of 
P. 


P 

Values of — 

IT 


Values of^ 


6 


1-9095 


•5236 


5 


1-5915 


•6283 


H 


1-4270 


•6981 


4 


1-2732 


•7854 


H 


1-1141 


•8976 


3 


•9547 


1^0472 


2f 


•8754 


1-1333 


2i 


•7958 


1-2566 


2i 


•7135 


1-3963 


2 


•6366 


1-5708 


n 


•5937 


1^6755 


If 


•5570 


1^7952 


If 


•5141 


1-9264 


H 


•4774 


2-0944 


H 


•4377 


2-2848 


n 


-3979 


2-5132 


H 


-3568 


2-7926 




•S18S 


3-1416 


i 


•2785 


3 • 5904 


f 


•2387 


4^1888 


1 


•1989 


5^0266 


- i 


•1592 


6-2832 


t 


•1194 


8-3776 


i 


•0796 


12-5664 



20 
40 



Example 1. — Given a wheel of 88 
teeth, 2^-inch pitch, to find the di- 
ameter of the pitch-circle. Here the 
tabular number in the second col- 
umn answering to the given pitch is 
•7958, which multiplied by 88 gives 
70-03 for the diameter required. 

2. Given a wheel 33 inches diam- 
eter, If-inch pitch, to find the num- 
ber of teeth. The corresponding 
factor is 1^7952, which, multiplied 
by 33, gives 59*242 for the number 
of teeth— that is, 59^ teeth nearly. 
Now 59 would here be the nearest 
whole number, but as a wheel of 60 
teeth may be preferred for conven- 
ience of calculation of speeds, we 
may adopt that number, and find 
the diameter corresponding. The 
factor in the second column answer- 
ing to If. pitch is ^557, and this mul- 
tiplied by 60 gives 33-4 inches as the 
diameter which the wheel ought to 
have. 

Another mode of sizing wheels in 
relation to their pitches, diameters, 
and number of teeth, is adopted, in 
some machine shops, by dividing the 
diameter of the pitch-circle into as 
many equal parts as there are teeth 
to be given to the wheel. To illus- 
trate this by an arithmetical exam- 
ple, let it be assumed that a wheel of 
20 inches diameter is required to have 
40 teeth ; then the diametral pitch, 



— = h inch 

7n ^ 



that is, the diameter being divided into equal parts corresponding in number 
to the number of teeth in the circumference of the wheel, the length of each 
of these parts is ^ an inch, consequently w' = 2 ; and according to the phrase- 
ology of the workshop, the wheel is said to be one of tivo pitch. 

A decided advantage is obtained by the use of the diametral-pitch sys- 
tem, since circular pitch 



X 3-1416 . _ circ. pitch X No. of teeth 
No. of teeth ' '^^^'^' " 3^l4l6 ' 



which always brings out the diameter as a number with an inconvenient frac- 
tion if the pitch is in even inches or simple fractions of an inch. By the di- 
ametral-pitch system the diameter may be in even inches or convenient frac- 
tions, and the number of teeth is usually an even multiple of the number of 
inches in the diameter. 



MACHIXE DESIGN AND MECHANICAL CONSTRUCTIONS. 
RELATION OP DIAMETRAL TO CIRCULAR PITCH. 



313 



Diametral 


Circular 


Diametral 


Circular 


Circular 


Diametral 


Circular 


Diametral 


pitch. 


pitch. 


pitch. 


pitch. 


pitch. 


pitch. 


pitch. 


pitch. 




In. 




In. 




In. 




In. 


1 


3-143 


11 


0-286 


3 


1-047 


H 


3-351 


H 


2-094 


12 


0-262 


2i 


1-257 


i 


3-590 


2 


1-571 


14 


0-224 


2 


1-571 


if 


3-867 


^ 


1-396 


16 


0-196 


n 


1-676 


f 


4-189 


2i 


1-257 


18 


175 


If 


1-795 


H 


4-570 


2f 


1-142 


20 


0-157 


If 


1-933 


f 


5-027 


3 


1-047 


22 


0-143 


H 


2-094 


A 


5-585 


3i 


0-898 


24 


0-131 


w. 


2-185 


i 


6-283 


4 


0-785 


26 


0-121 


If 


2-285 


^6 


7-181 


5 


0-628 


28 


0-112 


1-1% 


2-394 


f 


8-378 


6 


0-524 


30 


0-105 


n 


2-513 


A 


10-053 


7 


0-449 


32 


0-098 


lA 


2-646 


i 


12-566 


8 


0-393 


36 


0-087 


If 


2-793 


it 


16-755 


9 


0-349 


40 


079 


iiV 


2-957 


i 


25-133 


10 


0-314 


48 


0-065 


1 


3-142 


A 


50-266 



To find the outside diameter of spur-gear blanks, add two parts of the pitch to 
the pitch diameter. Thus for an 8-pitch gear of 40 teeth the outside diameter 
of blank is ^, equal to 5^ inches ; for a 12-pitch gear of 36 teeth the outside 
diameter of blank is -f f , equal to 3^ inches ; for a 16-pitch gear of 46 teeth the 
outside diameter of blank is ff, equal to 3 inches. 

To obtain the distance between the centres of two gears, add the number of 
teeth together and divide half the sum by the diametral pitch. Thus if two 
gears have 40 and 30 teeth respectively and are 5 pitch, add 40 and 30, making 
70, divide by 2, and then divide this quotient 35 by the diametral pitch 5, and 
the result, 7 inches, is the distance between centres. 

It is a common practice of shops to take as the diameter of the rolling circle 
the radius of the smallest pinion which will ever be used for gears of this pitch, 
and constructing the epicycloids for different diameters of this pitch, and allow- 
ing arcs of circles corresponding very closely to these epicycloids. On this 
principle Robert Adcock, C. E., constructed a table of radii for these arcs, for 
rolling circles of pinions of 8, 10, and 12 teeth. We give the last only as best 
suited to the usual conditions of practice : 





TABLE OF RADII 


OF 


ARCS OF CIRCLES FOR 


GEAR TEETH. 




<s 


6 


SMALLEST PINION, ! 


-g 


o 


SMALLEST PINION, 


.£3 


6 


SMALLEST PINION, 


'^r 


TWELVE TEETH. ' 


O) 


«« ^ 


TWELVK TEETH. 


<S 


«- ^ 


TWELVE TEETH. 


4) 


= •3 




S 


3 J 




o 








^ 


Eadiiofthe Radii of the 


Eadii of the 


Eadiiofthe 


Eadii of the 


Eadii 


of the 




-b.^ 


faces of flanks of | 


n 


'S:S 


faces of 


flanks of ' 


o 


'f..^ 


faces of 


flanks of 


^ 


-^ 


teeth. teelh. i 


^ 


M^ 


teeth. 


teeth. 1 


42 


6^69 


teeth. 


teeth. 


12 


1-93 


1-88 0-75 




27 


4^31 


4-23 


0-84 


4-63 


1^41 


6^60 


0-89 


6^91 


1^20 


13 


2-09 


2-04 0-76 7-45 


7-14 


28 


-46 


•39 


•85 


•37 


•38 


43 


•85 


•76 


•89 


7-06 


•20 


14 


2-25 


-19 


•77 4-86 


4^27 


29 


•62 


•55 


•85 


•92 


•36 


44 


vol 


92 


•89 


•22 


•19 


15 


2-40 


-35 


•7^ 3-92 


3^04l 


30 


•78 


•70 


•86 


5^07 


•34 


45 


•17 


7^07 


•89 


•38 


•18 


16 2-56 


•50 


-78 -62 


3-53| 


31 


-94 


•86 


•86 


•21 


•32 


46 


•33 


•23 


•90 


•53 


•18 


17 


2-72 


-66 


•79 -58 


2^22' 


32 


5-10 


5 02 


•86 


•37 


•30 


47 


•49 


•39 


•90 


•09 


-17 


18 


2-88 


•82 


•80 -59 


2-02 


33 


•26 


•18 


•86 


•52 


'•29 


48 


•64 


•55 


•90 


•84 


•16 


19 


3-04 


-97 


•81 


•63 


1-87 


34 


•42 


•34 


•87 


•67 


•28 


49 


•80 


•71 


•90 


8^00 


•16 


20 


3-20 


3-13 


-81 


-73 


1-76 


! 35 


•58 


•49 


•87 


•82 


•26 


50 


•96 


•86 


•90 


•96 


•16 


21 


3-35 


-29 


•82 


•83 


1-Q8 


36 


•74 


•65 


•87 


•97 


•25 


51 


8-12 


8^02 


•91 


•31 


•16 


22 


3-51 


•44 


•82 


•95 


1^61 


37 


•90 


•81 


•88 


613 


•24 


52 


•28 


•18 


•91 


•47 


-If 


23 


3-67 


•60 


•83 


4^07 


1^56 


38 


6-05 


•97 


•88 


•29 


•23 


53 


•44 


•34 


•91 


•63 


•It 


24 


3-83 


•76 


•83 


•21 


1^51 


39 


•21 


6-13 


•88 


•44 


•23 


54 


•60 


•50 


•91 


•79 




25 


3-99 


•91 


•84 


•34 


1.47 


40 


•37 


•28 


•88 


•60 


•22 


55 


•76 


•66 


•91 


•95 


•14 


26 


4-15 


4-07 


•84 


•48 


1-44 


41 


•53 


•44 


•89 


•75 


•21 


56 


•92 


•81 


•91 


9^10 





314 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



5 


1 


SMALLEST PINION, 1 


^ OJ 1 SMALLEST PINION, 1 


■3 


.2 1 


SMALLEST PINION, 


% 




TWELVE TEETH. | 


% 


«- 2 


TWELVE TEETH 


. 


■s 


^2 


TWELVE TEETH. 


^ 








B 


"=•5 






-2 


="•3 




'z 


il 


Eadii of the 


Eadii of the 


"S 


si 


Eadii of the Eadii of the 


'o 


hI 


Eadii of the Eadii of the 


o 


■-SB 


faces of 


flanks of 


o 


1-^ 


faces of 


flank 


sof 




'-53 1 


faces of 


flanks of 


jI 


jS'S 


teeth. 


teeth. 


^ 


M^ 


teeth. 


teeth. 


^ 


w'^ 


teeth. 


teeth. 


51 


9-08 


8-97 


0-91 


9^26 


1-13 


120 


19-10 


18-99 




19^10 




183 


2913 


2900 


•97 


29-27J 




58 


•23 


9-13 


•91 


•42 


•13! 


121 


•26 


19-15 




•42 


1-06 


184 


•28! 


•16 


1 


•43 


1-03 


69 


•37 


•29 


•92 


•57 


•13| 


122 


•42 


-30 


•95 


•57 




185! 


•44 


•32 




•59 




60 


•55 


•45 


•92 


•73 


•13 


123 


-58 


-46 




•73 


•06 


186 


•60 


•48 


-97 


•74 


1-03 


61 


•71 


•61 


•92 


•89 


•12 


124 


•74 


-62 




•89 




187 


•76 


•64 




•90 




62 


•87 


-77 


•92 


10-05 


•12 


125 


•90 


•78 


•95 


20-05 


•06 


188 


•92' 


•80 




30-06 




63 


10-03 


-92 


-92 


•20 


•12 


126 


20^05 


•94 




•21 




189 


30^08 


-96 


•98 


•22 


1-03 


64 


•19 


10-08 


•92 


•36 


•12 


127 


-21 


20-10 




-37 


•05 


190 


•24 


30-12 




•38 




65 


•35 


•24 


•92 


•52 


•12 


128 


•37 


•26 


•96 


-53 




191 


•40 


•28 


•98 


•54 


1-02 


66 


•61 


•40 


•92 


•68 


•11 


129 


-53 


•42 




•69 


•05 


192 


•55 


•43 




•70 




67 


•67 


•66 


•92 


•84 


•11 


130 


•68 


•58 




•84 




193 


•71 


•59 




•86 




6S 


•83 


•72 


•92 


•99 


•11 


131 


-84 


•74 


•96 


21-00 


•05 


194 


•87 


•75 


•98 


31-02 


1-02 


69 


•98 


•88 


•93 


1115 


•11 


132 


21-00 


-89 




•16 




195 


31-03 


•91 




•18 




10 


11-14 


11^04 


•93 


•31 


•11 


133 


-17 


21^05 




-32 


•05 


196 


•19 


31-07 




•33 


1-02 


71 


•30 


11-20 


•93 


•47 


MO 


134 


•33 


•21 


•96 


•48 




197 


•35 


•23 


•98 


•49 




72 


•46 


-35 


-93 


-63 


•lo' 


135 


•49 


•37 




•64 


•05 


198 


•51 


•39 




•65 


1-02 


73 


•62 


•51 


•93 


•79 


-10, 


!l36 


•65 


•53 


•96 


•80 




199 


•67 


•55 




•81 




74 


•78 


•67 


•93 


•95 


-10 


il37 


•81 


•69 




•96 


•05 


200 


•83 


-71 


•98 


•97 




75 


•94 


•83 


•93 


12-10 


•10 


138 


•96 


•85 




22^11 




1201 


•99 


•87 




32-13 




76 


12-10 


11-99 


•93 


•26 


■09 


139 


22-12 


22-01 


•96 


•27 


•05 


202 


32-15 


32-02 




•29 




77 


•26 


12-15 




•42 


•09 


140 


-28 


•17 




•43 


•05 


1203 


•30 


-18 




•45 




78 


•42 


•30 


•93 


•58 


•09 


141 


-44 


•33 




•59 




i204 


•46 


-34 




•61 




79 


•58 


•47 




•74 


•09 


142 


-60 


•48 


•96 


•75 


•05 


205 


•62 


•50 




-77 




80 


•73 


-63 


•93 


•90 


•09 


|143 


•76 


•64 




•91 




206 


•78 


•66 




•92 




81 


•89 


-79 




13-06 


-09 


!l44 


•92 


•80 




23^07 


^05 


207 


•94 


•82 




33-08 




82 


13-05 


•94 


•93 


•22 


•09 


[145 


23-08 


•96 


•96 


•23 




208 


33-10 


•98 




•24 




83 


•21 


13-10 




•38 


•09 


|l46 


•24 


23^12 




•38 


1^04 


209 


•26 


33-14 




-40 




84 


•37 


-26 


•94 


•53 


•08 


1147 


•40 


•28 




•54 




1210 


•42 


•30 




•56 




85 


•53 


•42 


•94 


•69 


•08 


!l48 


•56 


•44 




•70 


•04 


1211 


•58 


•46 




•72 




86 


•69 


•58 




•85 


•08 


149 


•72 


•60 -96 


•86 




212 


•74 


•61 




•88 




87 


•85 


•74 


•94 


14^01 


•08 


150 


•87 


•76 


24-02 


•04 


1213 


-90 


•77 




34-04 




88 


14^01 


•90 


•94 


•17 


•08 


151 


24-03 


•92 


•18 




214 


34-06 


-93 




-20 




89 


•17 


14-06 




•33 


•08 


152 


•19 


24-07 -96 


•34 




215 


•21 


34^09 




-36 




90 


•33 


-22 


•94 


■49 


•08 


153 


•35 


•23 


•50 


•04 


1216 


•37 


•25 




•51 




91 


•49 


•38 


•94 


•65 


-08 


154 


•51 


•39 


•65 




|217 


-53 


•41 




•67 




92 


•64 


•53 




•81 


•08 


155 


•67 


•55 ^96 


•81 


•04 


218 


-69 


•57 




•83 




93 


•80 


•69 


•94 


•97 


•08 


156 


•83 


•71 


•98 




219 


•85 


•73 




•99 




94 


•96 


•85 


•94 


15-12 


•07 


157 


•99 


-87 


25-13 


•04 


220 


35-01 


•89 




85^15 




95 


15-14 


15-01 




•30 


•07 


158 


25-15 


25-03 -97 


•29 




221 


-17 


35-05 




•31 




96 


•28 


-17 


•94 


•44 


•07 


159 


•31 


•19 


•45 


•04 


222 


-33 


•20 




•47 




21 


•44 


•33 




-60 


•07 


160 


•47 


•35 


•61 




[223 


-49 


•36 




•63 




98 


•60 


•49 


•94 


-76 


•07 


161 


•62 


•51 


-97 


•77 




224 


•65 


•52 




•79 




99 


•76 


•65 




•92 


•07 


162 


-78 


•66 




•93 


•04 


225 


•80 


•68 




-95 




100 


•92 


•81 


•95 


16-08 


•07 


163 


-94 


•82 




2609 




1226 


•96 


•84 




36-10 




101 


16-08 


•97 




-24 


•07 


164 


26-10 


•98 


•97 


•25 


-04 


,227 


3612 


36-00 




•26 




102 


•24 


16-13 




-40 




jl65 


•26 


26-14 




-42 




1228 


•28 


•16 




•42 




103 


-39 


•28 


•95 


-56 


•07 


166 


•42 


-30 




•56 


•04 


229 


•44 


•32 




•58 




104 


-55 


•44 




•72 




167 


•58 


•46 




•72 




230 


•59 


•48 




•74 




105 


•71 


•60 




•87 


•07 


168 


-74 


-62 


•97 


•88 


•03 


231 


• -75 


•64 




•90 




106 


•87 


•76 


•95 


17-03 




169 


•90 


•78 




27-04 




232 


•91 


•79 




37-06 




107 


17-03 


•92 




•19 


•06 


170 


27-06 


•94 




•22 


-03 


233 


37-08 


•95 




•22 




108 


-19 


17-08 




•35 




171 


•22 


27-10 


■91 


•36 




234 


-24 


37-11 




•58 




109 


•35 


•24 


•95 


-51 


•06 


172 


•38 


•25 




•52 


•03 


235 


•40 


•27 




•54 




110 


•51 


•40 




•67 




173 


•53 


•41 




•68 




236 


•56 


-43 




•69 




111 


•67 


•56 




-83 


•06 


174 


-69 


•57 


•97 


•84 




237 


•72 


-59 




•85 




112 


•83 


•71 


•95 


-99 




175 


-85 


•73 




TOO 


•03 


238 


•87 


-75 




38-01 




113 


•99 


•87 




18-15 


•06 


176 


28-01 


•89 




28-16 




239 


38-03 


•91 




-17 




114 


18^15 


18-03 


-95 


•30 




177 


-17 


28-05 


•97 


•31 


•03 


240 


•19 


38-07 




•33 




115 


•30 


•19 




•46 


-06 


178 


•33 


•21 




•47 




241 


•35 


-23 




•69 




116 


•46 


-35 




•26 




179 


•48 


•37 




•63 




242 


-51 


•38 




•65 




117 


•62 


•51 


•95 


•62 


-06 


180 


•64 


•53 


•97 


•79 


•03 


243 


-67 


•54 




39-01 




118 


•78 


•67 




•78 




181 


•80 


•69 




•95 




244 


-83 


-70 




•17 




119 


-94 


-83 


•95 


•94 


1-06 


182 


•97 


•84 




29-11 


1-03 


I245 


-99 


•86 




•33 





MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



315 



? 


6 


SMALLEST PINION, 


.d 


«• 


SMALLEST PINION, 


^ 


6 


SMALLEST PINION, 


"^'i 


TWEL-VE TEETH. 




o| 


TWELVE TEETH. 


1 


-1 


TWELVE TEETH, 


s-s 


Kadiiofthe 


Eadii of the 


o 


eg 


Kadiiofthe 


Eadii of the 


? 


ll 


Radii of the 


Radii of the 


v 


^•^ 


faces of 


flanks of 




^ " 


faces of 


flanks of 




i-^ 


faces of 


flanks of 


o 


^^ 


teeth. 


teeth. 


il 


«'^; ^^^^•^• 


teeth. 


i 


(§ ^ 


teeth. 


teeth. 


246 


39-15 


39 02 




39^28 




265 


42-1742-04 




42-31 


j 


284 


45^19 


45^06 




45-33 




247 


•31 


•18 




44 




266 


•331 -20 




•46 




285 


-35 


.22 




-49 




248 


•47 


•34 




•60 




267 


•49 -36 




•62 




286 


-51 


•38 




-64 




249 


•64 


-50 




•76 




268 


•64 ^52 




-78 




287 


-67 


•54 




•80 




250 


•78 


-86 




•92 




269 


•80 


•68 




•94 




288 


•83 


•70 




•96 




251 


•94 


-82 




40-08 




270 


-97, ^84 




43-10 




289 


-99 


•86 




4612 




252 


40-10 


•97 




•24 




271 


43-13 


1-00 




-26 




290 


46-15 


46^02 




-28 




253 


•26 


40-13 




•40 




272 


-28 


43-15 




•42 




291 


•30 


•17 




•44 




254 


•42 


•30 




-56 




273 


•44 


•31 




•58 




292 


-46 


-33 




•60 




255 


•59 


•45 




•72 




274 


•60 


•47 




•74 




293 


•62 


•49 




•76 




256 


•74 


•61 




•87 




275 


•76 


-63 




•90 




294 


•78 


•65 




•82 




257 


•90 


•77 




41-03 




276 


•92 


•79 




44-05 




295 


-94 


-81 




•98 




258 


41-06 


-93 




•20 




277 


44-08 


•96 




•2] 




296 


47-10 


•97 




47-13 




259 


•22 


4109 




•36 




278 


-24 


4411 




•37 




297 


•25 


47^13 




•29 




260 


•38 


•25 




•51 




279 


•40 


-27 




•53 




|298 


•42 


•29 




•45 




261 


-53 


•41 




•67 




280 


•55 


•43 




•69 




299 


•58 


-45 




•61 




262 


-69 


•56 




•83 




281 


•71 


•69 




•85 




300 


•74 


•61 




-77 




263 


•85 


•72 




•99 




282 


•87 


•74 




45-01 




Rack 




•129 


l-00;0-129 


1-00 


264 


42-01 


•89 




42^15 




283 


45^03 


-90 




•17 










1 





Eule. — Seek in the first column of the table for the number of teeth it is 
proposed that the wheel shall contain. In a line with such number of teeth 
take from columns 2, 3, 4, 5, and 6 the numbers that are in them ; and in 
every case multiply such numbers by the pitch. The products will be the 
number of inches and parts of inches to which the compasses must be opened 
to describe the circles and parts of circles that are required. 

Example. — Suppose that a wheel (Fig. 687) is to be made to contain thirty 
teeth, and that the pitch of the teeth is to be 2^ inches, proceed as follows : 




Seek in column 1 for 30, the number of proposed teeth, and take from col- 
umn 2 the numbers 4o-78, which multiplied by 2|- inches, the product will be 
11^957". Open the compasses, therefore, to this radius and describe a circle, 
which will be the " pitch-circle." On an arc of this circle lay off 2^5 X '48 = 
1-2" for the thickness of a tooth, and 2-5 x -52 = 1^3" for the space. Having 



316 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



determined the number of teeth and pitch, next, in column 3, and in the same 
line with 30 teeth, will be found the numbers 4*70, which multiply by 2^ 
inches — the product will be 11*75. With the compasses opened to this dis- 
tance, and from the same centre as the last, describe another circle, which will 
be the paths of centres for the curves of the faces of the teeth. From column 
4 similarly take the numbers 0'86 and multiply by 2J inches. The product is 
2*15, to which distance the compasses must be opened to describe the faces of 
the teeth. 






Fig. 688. 



Again, in column 5, multiply 5*07 X 2-5 = 12'675", and from the centre, 
with this radius, describe another circle for the paths of centres of flanks of the 
teeth, from column 6, 1*34 x 2*5 = 3*35, the radius of the flanks of the teeth. 

For the height of a tooth a common proportion is -^^ of pitch outside of 
pitch-circle, and -^-^ of pitch within, which leaves -^ pitch for clearance at the 
bottom, where usually small arcs are described to connect the teeth with the 
wheel. 

Having described a few teeth of any gear to its full size, the rest may be laid 
off from a templet, or cutters made by which the teeth may be accurately 
formed. In the illustration the teeth and spaces are proportioned to a common 
form (see page 303). 

It is not uncommon to make one of the set of gears with wooden teeth, 
mortices being cast in the periphery of the wheel for the insertion of these 
teeth — hence called mortise or core ; the elasticity of the wood diminishes the 
effect of shocks, and they run with less noise. 

The usual proportions and construction of mortise wheels are shown in Fig. 
688, a section across and with the rim of the wheel. The figures represent the 
proportions to pitch as unity ; b is from 2 to 3 ^. The teeth are held in posi- 
tion by wooden dovetailed keys. 

Fig. 689 is a section across the rim of mortised bevel-gear ; the figures are 



Fig. 689. 




^ 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 317 

as before in ratios to p. In this illustration the teeth are held in by pins, com- 
mon also to spur-mortise-gears. 

It is unusual in drawings to complete gears with teeth according to the ex- 
amples given ; it is sufficient for the purposes of pattern-making that the pitch- 
circle, pitch and form of one tooth be given. For 
lines of shafting, spur-gears may be represented, like 
plain pulleys, tangent to each other, of the diameters 
of the pitch-circle, with the pitch and number of 
teeth written in : bevel-gears, as in Fig. 690. In fin- ^ 
ished drawings, detail is necessary. The following 
simple forms of describing spur-and bevel-gears will 
in general answer the purpose, but if more accuracy 
is required use Adcock's tables. [T 

Projections of a Spur Wheel. — To draw side ele- F,e q^o. 

vation (Fig. 691), an edge view (Fig. 692), and a ver- 
tical section (Fig. 693) of a spur wheel with 54 teeth and a pitch of two inches : 

Determine the radius of the pitch-circle from the table, page 312 
(•6366 X 54 = 34-376 = D. R = 17-19) ; draw the central line A C B and the 
perpendicular D E ; on as a centre, with a radius 17-19, describe the pitch- 
circle, and divide it into 54 equal parts. To effect this division, without defa- 
cing by repeated trials that part of the paper on which the teeth are to be repre- 
sented, describe from the same centre c, with any convenient radius, a circle 
abed; with the same radius divide its circumference into six equal parts, and 
subdivide each sixth into nine equal parts, and draw radii to the centre c; these 
radii will cut the pitch-circle at the required number of points. Divide the 
pitch (2 inches) into 10 equal parts ; mark off beyond the pitch-circle a dis- 
tance equal to 3 of these parts, and within it a distance equal to 4 parts, and 
from the centre C describe circles passing through these points ; these circles 
are projections of the cylinders bounding the points of the teeth and the roots 
of the spaces respectively. 

In forming the outlines of the teeth, the radii, which, by their intersections 
with the pitch-circle, divide into the required number of parts, may be taken 
as the centre lines of each tooth. The thickness of the tooth, measured on the 
pitch-circle, is -46 pitch x 2" = -92, and the width of the space is equal to 
•54: p X 2" = 1-08. These distances being set off, take in the compasses the 
length of the pitch, and from the centre g describe a circular arc h i ; and from 
the centre 7, with the same radius, describe another arc h h touching the 
former ; these arcs, being terminated at the circles bounding the points of the 
teeth and the bottoms of the spaces respectively, form the curve of one side of 
a tooth. The other side is formed in a similar manner, by drawing from the 
centre / the arc m ?z, and from the centre p the arc m 0, and so on for all the 
rest of the teeth. 

The teeth having been completed, proceed to the delineation of the rim, 
arms, and eye of the wheel. The thickness of the rim is usually made equal to 
that of the teeth, say one half of the pitch, which distance is accordingly set off 
on a radius within the circle of the bottoms of the spaces, and a circle is de- 
cribed from the centre C through the point q thus obtained. Within the rim, 
a strengthening feather q r, in depth about three fourths of the thickness of the 



318 MACHINE DESIGN AND MECHANICAL CONSTRIJCTIONS. 




'''^ Fig. 692. 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 319 

rim, is generally formed, as shown in the plate. Describe the eye^ or central 
aperture for the reception of the shaft, to the specified diameter, as also the 
circle representing the thickness of metal round the eye, usually equal to the 
pitch of the teeth. 

To draw the arms, from the centre C, with the radius C u equal to the 
pitch, describe a circle ; draw all the radii, as L, which are to form the centre 
lines of the arms, and set off the distance L v^ equal to one third pitch, on each 
side of these radii at the inner circumference of the rim; and through all the 
points thus obtained draw tangents to the circle passing through u. The con- 
tiguous arms are rounded off into each other by arcs of circles (Fig. 691). 
Draw the central web of the arm by lines parallel to their radii, making the 
thickness about f inch for wheel of about this size. 

Having completed the elevation for the edge view and vertical section, 
draw the perpendiculars F G and H I (Figs. 692 and 693) as central lines in 
the representations ; set off on each side of these lines half the breadth of the 
teeth, and draw parallels; project the teeth of Fig. 691 upon Fig. 692, by 
drawing through all the visible angular points straight lines parallel to A B, 
and terminated at either extremity by the verticals representing the outlines of 
the breadth of the wheel ; project in like manner the circles of the hub ; lay 
off half length on each side of F G, and draw parallels to it. The section (Fig. 
693) is made on the line D E of the elevation ; project, as in Fig. 692, those 
portions which will be visible in this section, and shade those parts which are 
in section. The arms are made tapering in width, and somewhat less than the 
face of the wheel (Fig. 694) ; a cross-section of one of them is made by a plane 
passing through X X' and Y Y'. The points y, 2;, in Fig. 691, and correspond- 
ing lines in Fig. 693, represent the edges of key-seat. 

Oblique Projectio7i of a Spur Wheel. — In drawing an object in an oblique 
position with respect to the vertical plane of projection, lay down in the first 
place the elevation and plan as if it were parallel to that plane (Figs. 695 and 
696). Then transfer the plan to Fig. 698, giving it the same inclination with 
the ground line which the wheel ought to have in relation to the vertical plane ; 
and assuming that the horizontal line A B represents the axis of the wheel, 
both in the parallel and oblique positions, the centre of its front face in the 
latter position will be determined by the intersection of a perpendicular raised 
from the point C (Fig. 697) with that axis. Take any point, as a in Fig. 695, 
and the projection of that point on Fig. 696 must be in the line a «, parallel to 
A B ; this point being projected at a' (Fig. 698), must be in the perpendicular 
a' a ; therefore the intersection of these two lines is the point required. Thus 
all the remaining points ^, c, fZ, etc., may be obtained by the intersections of the 
perpendiculars raised from the points Z>', c', d\ etc. (Fig. 698), respectively, with 
the horizontals drawn through the corresponding points in Fig. 695. Since the 
points e and/, in the further face of the wheel, have their projections in a and 
b (Fig. 695), their oblique projections will be situated in the lines a a and b J, 
but they are also at e and/; consequently the lines e a and fb are the oblique 
projections of the edges a' e' and b' f. 

All the circles which, in the rectangular elevation (Fig. 695), have been em- 
ployed in the construction of this wheel are projected in the oblique view into 
ellipses ; thus, since the plane F' G', in which these circles are situated, is verti- 



320 MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 




MACHINE DESIGN AND MECHANICAL CONSTHUCTIONS. 321 

cal, the major axes of all the ellipses in question are perpendicular to the line 
A B, and equal to the diameters of the circles of which they are respectively the 
projections ; and the minor axes, representing the horizontal diameters, will all 
coincide with the line A B. 

To obtain the ellipse into which the pitch -circle is projected, set off upon 
the vertical D E (Fig. 697) above and below C the radii of the pitch-circle for 
the major axis, and project i' j' (Fig. 698) to the horizontal axis at i and/ (Fig. 
697) for the minor axis. 

The intersection of the horizontal lines g g, h 7i, etc., with the projection of 
the pitch-circle gives the thickness of the teeth at the pitch-line ; in the same 
manner the circles bounding the extremities and roots of the teeth may be de- 
termined. If strict accuracy is required, a greater number of points is neces- 
sary for the construction of the curvature of the teeth, and two additional cir- 
cles, m n and o p^ may be drawn on Fig. 695 and projected to Fig. 697, and the 
points of their intersection with the curves of the teeth projected to correspond- 
ing points as indicated by the same letters. 

Projections of a Bevel Wheel. — Fig. 699 is an edge view, Fig. 700 a face view, 
and Fig. 701 a vertical transverse section. For the determination of the divi- 
sion of the angle of inclination of the axes of a pair of bevel wheels, see Fig. 
685 ; for their size and proportion, the rules given for spur wheels ; thus, con- 
sider the base of the cone A B (Figs. 700 and 701) as the diameter of the pitch- 
circle of a spur wheel, and proportion the pitch, form, and breadth of teeth, ac- 
cording to the stress to which they are to be subjected. 

Having determined and laid down, according to the required conditions, the 
axis S of the primitive cone, the diameter A B of its base, the angle A S 
which the side of the cone makes with the axis, and the straight lines A o, D o\ 
perpendicular to A S, and representing the sides of two cones, between which 
the breadth of the wheel (or length of the teeth) is comprised, the first opera- 
tion is to divide the primitive circle, described with the radius A C, into a num- 
ber of equal parts corresponding to the number of teeth or pitch of the wheel. 
Then upon the section (Fig. 701) draw with the radius o A or o B, moving par- 
allel to itself, outside the figure, a small portion of a circle, upon which con- 
struct the outlines of a tooth M, and of the rim of the wheel, with the same 
proportions and after the same manner in reference to spur wheels ; set off from 
A and B the points a^ cl, and /, denoting respectively the distances from the 
pitch-line to the points and roots of the teeth, and to the inside of the rim, and 
join these points to the vertex S of the primitive cone, terminating the lines of 
junction at the lines D o', E o' ; the figure abed will represent the lateral form 
of a tooth, and the figure c dfe a section of the rim of the wheel, by the aid of 
which the face view (Fig. 700) is constructed. 

The points a, Z>, c, d, and e, having been projected upon the vertical diame- 
ter A' B', describe from the centre C a series of circles passing through the 
points thus obtained, and draw any radius, as C'Jj, passing through the centre 
of a tooth. On either side of the point L set off the distances L ^, L Z, making 
the thickness of the tooth M at the point, and indicate, in like manner, upon 
the circles passing through the points B' and d', its thickness at the pitch-line 
and root ; then draw radii through the points i, I, k, g, m, etc., terminating 
them respectively at the circles forming the projections of the corresponding 
22 



322 MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 




MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



323 



parts at the inner extremity of the teeth ; these radial lines will represent the 
rectilinear edges of all the teeth. The curvilinear outlines may be delineated 
by arcs of circles, tangents to the radii g C and i C, and passing through the 
points obtained by the intersections of the radii and the various concentric cir- 
cles. The radii of these circular arcs may in general, as in the case of spur 
wheels, be taken equal to the pitch, and their centres upon the interior and ex- 
terior pitch-circles ; thus the points g and i, n and o, for example, are the centres 
for the arcs passing through the corresponding points in the next adjacent teeth, 
and vice versa. 

The drawing of the teeth in the edge view (Fig. 699), and of such portions 
of them as are visible in the section (Fig. 701), are explained by inspection of 
the lines of projection. In the construction observe that every point in the 
principal figure from which they are derived is situated upon the projection of 
the circle drawn from the ce.atre C, and passing through that point. Thus the 
points g and i, for example, situated upon the exterior pitch-circle, will be de- 
termined in Fig. 699 by the intersection of their lines of projection with the 
base A B of the primitive cone ; and the points k and I will be upon the straight 
line passing through 
a a (Fig. 701), and so 
on. Further, as the 
lateral edges of all the 
teeth in Fig. 699 are 
radii of circles drawn 
from the centre C, so 
in Fig. 700 they are 
represented by lines 
drawn through the va- 
rious points found as 
above for the outer ex- 
tremities of the teeth, 
and converging toward 
the common apex S ; while the cen- 
tre lines of the exterior and interior 
extremities themselves all tend to 
the points o and o' respectively. 

SJceiu- Bevels. — When the axes of 
wheels are inclined to each other, 
and yet do not meet in direction, 
and it is proposed to connect them 
by a single pair of bevels, the teeth 
must be inclined to the base of the 
frusta to allow them to come into 
contact. Set o^ ae (Fig. 702) equal 
to the shortest distance between the 
axes (called the eccentricity)^ and 
divide it in c, so that a c is to e c as 

the mean radius of the frustum to the mean radius of that with which it is to 
work ; draw c m d perpendicular to a e. The line c m d gives the direction of 




324 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



the teeth ; and, if from the centre a^ with radius « c, a circle be described, the 
direction of any tooth of the wheel will be a tangent to it, as at c. Draw the 
line d e perpendicular to cm d^ and with a radius d e equal to c e describe a 
circle ; the direction of the teeth of the second wheel will be tangents to this 
last, as at d. 

System composed of a Pinion driving a Rack (Fig. 703). — The pitch-line 
M N of the rack and the pitch-circle A B D of the pinion being laid down 
touching one another, divide the latter into twice the number of equal parts 
that it is to have teeth, and set off the common distance of these parts upon 
the line M N, as many times as may be required ; this marks the thickness of 




Fig. 703. 

the teeth and width of the spaces in the rack. Perpendiculars drawn through 
all these points to the solid part of the rack will represent the flanks of the teeth 
upon which those of the pinion are to be developed in succession. The curva- 
ture of these latter should be an involute A c of the circle A B D. The teeth 
might be cut olf at the point of contact d upon the line M N, for at this posi- 
tion the tooth A begins its action upon that of the rack E ; but it is better to 
allow a little more length ; in other words, to describe the circle bounding the 
points of the teeth with a radius somewhat greater than d. 

For the form of the spaces in the rack, set off from M N, as at the point e, 
a distance slightly greater than the difference Ka oi the radius of the pitch- 
circle, and that of the circle limiting the points of the teeth, and through this 
point draw a straight line F G parallel to M IST. From this line the flanks of 
all the teeth of the rack spring, and their points are terminated by a portion 
of a cycloid A &, which, however, may in most instances be replaced by an arc of 
a circle. As the depth of the spaces in the pinion depends upon the height 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



325 



of this curved portion of the teeth ; their outline is formed by a circle drawn 
from the centre C, with a radius a little less than the distance from this point 
to the straight line bounding the upper surface of the teeth of the rack. 

System composed of a Rack driving a Pinion. — In this case the construc- 
tion is identical with that of the preceding example, except that the form 
proper to be given to the teeth of the rack is a cycloid generated by a point A 
in the circumference of the circle AEG rolling on the line M N. The curva- 
ture of the teeth is an involute as before. 

System composed of an Internal Spur Wheel driving a Pinion (Fig. 704). — 
The form of the teeth of the driving-wheel is in this instance determined by 
the epicycloid described by a point in the circle A E 0, rolling on the concave 




Fig. 704. 



circumference of the primitive circle MAN. The points of the teeth are to 
be cut off by a circle drawn from the centre of the internal wheel, and passing 
through the point E, indicated by the contact of the curve with the flank of 
the driven tooth. 

The wheel being supposed to be the driver, the curved portion of the teeth 
of the pinion may be very small. This curvature is a part of an epicycloid 
generated by a point in the circle MAN rolling upon BAD. 

System composed of an Internal Wheel driven dy a Pinion. — Fig. 705 
involves a different mode of treatment from that employed in the preceding 
cases. The epicycloidal curve A a, generated by a point in the circle having 
the diameter A 0, the radius of the circle MAN, and which rolls upon the 
circle BAD, can not be developed upon the flank A J, the line described by 
the same point in the same circle in rolling upon the concave circumference 



326 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



MAN; and for the reason that that curve is situated without the circle 
BAD, while the flank, on the contrary, is within it. In order that the pinion 




Fig. 705. 

may drive the wheel uniformly according to the required conditions, form the 
teeth so that they shall act always upon one single point in those of the wheel. 
By taking for the curvature of the teeth of the pinion the epicycloid A dy de- 
scribed by the point A in the circle MAN rolling over the circle B A D, as in 
the preceding examples, the tooth E of the pinion begins its action upon the 
tooth F of the wheel at the point of contact of their respective primitive cir- 
cles, and it is unnecessary to be continued beyond the point c, because the suc- 
ceeding tooth H will then have been brought into action upon G ; consequently 
the teeth of the wheel might be bounded by a circle passing through the point 
c. One of the practical advantages which this species of gearing has over 
wheels working externally is that the surfaces of contact of the wheel and 
pinion admit of being more easily increased ; and, by making the teeth some- 
what longer than simple necessity demands, the strain may be distributed over 
two or more teeth at the same time. The flanks of the teeth of the wheel are 
formed by radii drawn to the centre 0, and their points are rounded off to en- 
able them to enter freely into the spaces of the pinion. 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



327 



DRAWIKG OF SCREWS. 






Projections of a Triangular -threaded Screw and Nut (Fig. 706). — Draw the 
ground line A B, and the centre lines C c' of the figures, from as a centre, 
with a radius equal to that of the exterior cylinders, describe the semicircle 




t-B 



« 3 6 ; and with the radius of the interior cylinder the semicircle Ice. Draw 
the perpendiculars a a" and 6 6", J) h" and e e\ to represent the vertical projec- 
tions of the exterior and interior cylinders ; divide the semicircle a 3 6 into any 



328 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



number of equal parts, say 6, and through each part draw radii to divide the 
interior. On the line a' a!' set off the length of the pitch as many times as re- 
quired ; and through the points of division draw lines parallel to the ground 
line A B. Divide the pitch into twice the number of equal parts that the 
semicircles have been divided into, and following instructions laid down (page 
140), construct the helix a! 3' 6 both in the screw and nut. 

Having obtained the point &', by the intersection of the horizontal line pass- 
ing through the middle division of a' a with the perpendicular h V\ describe the 
helix V c' e', which will represent the bottom of the groove. The apparent out- 
lines of the screw and its nut will then be completed by drawing the lines h' a\ 
a' h\ etc., to the curves of the helices ; these are not, strictly speaking, straight 
lines, but their deviation from the straight line is, in most instances, so small 
as to be imperceptible. 

When a long series of threads have to be delineated, they should be drawn 
mechanically, by means of a templet constructed in the following manner : Take 
a small slip of thin wood or pasteboard, and draw upon it the helix a! 3' 6 to the 
same scale as the drawing, and cut the slip carefully and accurately to this line. 
Applying this templet upon Fig. 706, so that the points a^ and 6 on the plate 
shall coincide with a! and 6 on the drawing, the curve a! Z' ^ can be drawn 
mechanically, and so on for the remaining curves of the outer helix. The same 
templet may be employed to draw the corresponding curves in the screw-nut 
by simply inverting it ; but for the interior helix a separate one must be cut, 
its outlines being laid off in the same manner. 

Projections of a Square-threaded Screw and JVut (Fig. 707). — The depth 
of the thread is equal to its thickness, and this latter to the depth of the 
groove. The construction is similar to the preceding ; the same letters and 
figures mark relative parts. The parts of the curve concealed from view are 
shown in dotted lines. 




Fig. 708. 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



329 



System composed of a Wheel and Tangent^ or Endless Screiv. — In laying out 
the work, the pitch of the teeth is to be determined by the required stress, as 
for spur wheels, and the number of the teeth in the wheel by the number of 
turns of the screw for each revolution of the wheel. With these determined, 
take (Fig. 708) to be the centre of the wheel, E F the axis of the screw, C A the 
radius of the pitch-circle of the wheel, and G A that of the pitch-cylinder of 
the screw ; the line M N drawn through A, parallel to E F, will be the gen- 
eratrix of that cylinder, which will serve the purpose of determining the form 
of the teeth. The section is made through the axis, and is the case of a rack 
driving a pinion ; consequently the curve of the teeth, or rather thready of the 
screw should be simply a cycloid generated by a point in the circle A E C, de- 
scribed upon A C as a diameter, and rolling upon the straight line M N. The 
outlines of the teeth are helical surfaces described about the cylinder forming 
the screw, with the pitch A h equal to the distance, measured upon the primi- 
tive scale, between the corresponding points of two contiguous teeth. These 
curves are expressed by dotted lines. The teeth of the wheel are set at angle 
to the plane of its face, and with surfaces corresponding to the inclination and 




Fig. 709. 



Fig. 710. 



helical form of the thread of the screw. Usually the points of the teeth and 
bottoms of the spaces are formed of a concave outline, adapted to the convexity 



330 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 




of the screw, in order to pre- 
sent as much bearing surface 
as possible to its action. In 
this kind of gearing it is al- 
most invariably the screw that 
imparts the motion. 

A screw is designated as 
right or left hand, according as 
the forward motion is imparted 
by turning the screw to the 
right or left. 

In the proportions adopted 
by the Yale & Towne Manu- 
facturing Co. for worm gear- 
ing, the wheel under the weight 
will revolve the screw slowly. 
This angle (slightly less than 
the angle of quiescence, see 
Morin's table, page 199) of the 
teeth is found to be the best 




Fig. 711. 



Fig. 712. 



adapted for economy of power. In the wheel the teeth in section are those of 
a spur wheel, cut with a chasing cutter, and in the screw turned in a lathe. 

Figs. 709 and 710 are two views, worm and wheel, with such lines of con- 
struction dotted as will explain the manner of drawing. 




Fig. 711 is the Albro worm and worm wheel as used on the cruisers of the 
United States Government for ship steering and for heavy windlass work. 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



331 



Frictional Gearing. — When motion is not continuous for a long time, but 
frequently stopped and started or reversed, frictional gearing is very often 
used. The starting is with as little shock as with belting, as by the usual ap- 
pliances this pressure may be applied gradually and is fully as positive. The 
simplest form of frictional gearing is that in which the surfaces in contact cor- 
respond to that of the pitch-circles (Fig. 712). 

Fig. 713 is a plan of a bevel frictional gear. One half is shown in section. 
The surface of the large or driven gear is of cast-iron, that of the pinion of 
paper, in washers compressed by a hydraulic press and firmly held together by 
bolts. The bevel in section is in contact with the large wheel-surface, the other 
is disengaged. A slight motion to the right will throw the one in contact out, 
and not throw in the other, and motion ceases in the large driven wheel ; a still 
further motion throws in the left pinion, and the motion of the driven wheel is 
reversed. 

The mode in which this is done is shown in the elevation (Fig. 714). The 
shipper consists of a bell-crank, controlled by a 
screw. The screw works in a stand, on the top of 
which is a hand wheel ; the hand wheel can be 
moved in either direction, and any desirable pres- 
sure can be brought upon the frictional surfaces 
by means of the screw. It is not unusual, instead 
of two pinions to have one pinion, with a little 
clearance on each side, revolving between two 
wheels, a slight lateral motion, in either direction, 
bringing it in 
contact with one 
or the other of 
the wheels. Some 
provision, by a 



> 





C 



loose coupling or otherwise, must be made to admit of this lateral movement 
in the pinion shaft. Straight pulleys, or what would correspond to spur-gears 
without teeth, are constructed, as in the example given, and are thrown in or 
out of gear by a lateral motion of the pinion. 

In proportioning the face of the pulleys it has been found safe to consider 
it the same as belts, given in the table (page 292). The pressure can be ap- 
plied according to the requirements of driving, and there is no falling off in 
the friction. The frictional surfaces are not always paper ; wood, leather, and 
prepared rubber are frequently used. 



332 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



Wedge Gearing, or Robertson Grooved- Surface Frictional Gearing. — Fig. 
715 is the cross-section of the rims of two wheels of this gearing. The angle 

recommended by Eobertson is 50° (usually not 
over 30° in our practice), and the pitch to vary 
somewhat with the velocity and power to be 
transmitted. For the adhesion, it is safe to 
make the horizontal face equal to that of a belt 
under the same circumstances of transfer of 
power. 

Fig. 716 shows the application of wedge 
gearing to a hoist drum d. The power is ap- 
plied through the shaft s ; one end of the drum 
shaft rests in a swivel box, the other in an eccentric box. Motion is given 
through the eccentric handle by which the drum gear can be engaged with that 





1 


///,''/' 


r -1 








^ t 
i.... 








fIS 




1 




i 

1 


Fia. 


na. 






Fig. 716. 

of the pinion of the driving shaft ; the drum is revolved and the load raised. 
In lowering, the drum is thrown out by the eccentric, and the brake h applied, 
which is controlled by a system of levers brought within reach of the man at 
the eccentric lever. 

When applied to the driving of a rotary fire pump, the friction pinion on 
the pump shaft is thrown into gear with the friction wheel of the main shaft 
by a sliding frame of iron with a screw and hand wheel. With this apparatus 
the pump can be started without shock or jar and without reducing the speed 
of the main shaft. 

For large, straight pulleys, wooden rims from 6" to 8'^ deep, and built up in 
segments from V to %" thick, so placed that the direction of the fibres shall 
follow the circumference of the wheel as nearly as possible. The segments are 
firmly clamped together and secured by glue joints, nails, and bolts, and the 
rim is bolted to the arms of the pulley with additional outside and deeper rings 
secured to the rim. The whole is then turned and finished. This pulley may 
be used with a belt as a friction gear. 

Figs. 717 and 718 are sections of wooden bevel friction gears, showing the 
way in which they are formed by wooden disks planed and fitted, glued, nailed, 
and bolted, and then turned to the proper angle and face. 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



333 



For the transmission of small powers, the combination of one conical wheel 
and one narrow disk wheel with rounded edges, both of iron, is sometimes used 




Fig. 717. 



Fig. 718. 





Fig. 719. 



Fir;. 



(Fig. 719). The pressure is applied to the disk wheel, and is so arranged that 
it can be shifted along its axis for a variable speed motion. The surfaces in 

contact are limited, the diameters, therefore, should 
be as large as possible, with high velocity. 

Another variable speed 
gear is made by using, instead 
of a cone, a crown plate on 
which the disk rests which 
can be moved inward or out- 
ward from the centre of the 
driving j)late. 

Rope for running rigging 
for derricks and general hoist- 
ing work is made of hemp or manilla, but rope of iron or steel wire, mostly 
with hemp centres, is preferred for many positions. 

The shells of the common and lighter blocks are made of solid wood, mor- 
tised for the reception of the sheaves, and rope-strapped (Fig. 720). Larger 
and better blocks are made of separate pieces of wood, riveted or bolted to- 
gether top and bottom, and iron-strapped (Fig. 721) ; the sheaves (Fig. 722) are 

usually of lignum-vitae, metal-bushed ; 

S the pin is fastened to the shell, and 

v|p the sheaves revolve on the pin. To 

~ f fz — ^.—^ diminish friction under heavy weights, 



friction rolls are introduced (Fig. 723). 






Fig. 721. 



Fig. 722. 



To strengthen the pin, blocks are inside-strapped (Fig. 724), or with 
wrought-iron straps or malleable-iron shells (Fig. 725) and cast-iron sheaves, 
entirely without woodwork. Most blocks (Figs. 724 and 725) have beckets 
attached. 

In the Appendix will be found a table of the strength and weight of hemp, 
steel-, and iron-wire rope and chain ; but as a simple rule of their working 
strength, multiply the square of the girth or circumference of a hemp rope by 



334 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



100, of an iron-wire rope by 600, of steel- wire rope by 1,000, and the square of 
the diameter of the rods of which a chain is made by 12,000. 






Fig. 723. 



Fig. 724. 



Fig. 725. 



The following table of sizes are from the Boston and Lockport Block Com- 
pany : 



DIMENSIONS. 



Size sheave. 


For dia. rope. 


Size shell. 


2ix fxf 


i 


4 inches. 


3 X fxf 


f 


5 




3^x1 xi 


f 


6 




4^x1 xi- 


i 


7 




4fxlixf 


1 


8 




S^xlixl 


1 


9 




6ixlix| 


li 


10 




7i X 11 X f 


n 


11 





DIMENSIONS. 



Size sheave. 



8 xlfxf 

9 xl^xf 
9ixHxf 

10 xlfxl 

11 x2ixl 

12 x2fxl 

14 x2fxli 

15 x3fxli 

16 x3fxlj 



For dia. rope. 



If 

2 
3 



Size shell. 



12 inches 

13 

14 

15 

16 

18 

20 

22 

24 



Gin-Mocks (Fig. 726) are made with wrought- and malleable-iron frames 
and wrought swivel-hook. 

Winding-drums or barrels must have their "diameters pro- 
portioned to the diameters of the rope or chain to be used (see 
table of sheaves above), and their length to the length of rope 
or chain to be taken in, and when the coils or turns of the rope 
are numerous, provision must often be made for keeping the 
rope or chain so that one coil may not ride on another. This 
is done by spiral grooves in the barrel, or shifting the barrel or 
the rope-guide automatically. 

Fig. 726. Fig. 1806 shows the way in which a chain cable is taken in 




MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



335 



with but few coils on the barrel. The coils are sufficient for the friction of 
taking up the cable ; the tight cable is wound on the larger part of the barrel, 
and as the coils are unwound on the slack side the tight coil slips down to a 
smaller diameter ; the weight of the chain on the slack side, as it drops into 
the locker, is sufficient to preserve the friction ; but with a rope and a few 
turns on the barrels the force of a man is sufficient, and he can readily slack 
and hold the load in position or lower without changing the direction of mo- 
tion or the speed of the barrel. 




Fig. 729. 



Fig. 728. 



Fig. 727. 



Chain-wheels with pockets are especially applicable to the purpose of hoist- 
ing, requiring a width only slightly greater than that of the chain, and a diam- 
eter sufficient to give the proper engagement with it. 

Yale & Towne Manufacturing Company have made a pitch chain, of com- 
mon form but of uniform links, especially adapted to hoists, and Figs. 727, 
728, and 729 illustrate the construction of their chain-wheel. A is a pocketed 
chain-wheel, made of soft cast-iron, mounted on a frame B. C is the chain- 
guide enveloping the lower half of the chain-wheel. The inner curved surface 
of the chain-guide is grooved, and is of such a shape as to leave a space be- 
tween it and the periphery of the chain- wheel merely sufficient to admit the 





Fig. 730. 




Fig. 731. 



Fig. 732. 





Fig. 733. 



Fig. 734. 



C 



V, 



as 



7 



chain ; it must then enter properly and continue engaged with the chain-wheel. 
E is a chain-guide roller, that delivers the slack chain into the box or locker. 



336 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 




Fig. 736. 



D is the chain-stripper, bolted also to the plate B, with a tongue or rib pro- 
jecting into the centre groove of the wheel which disengages the chain. 

Forms of chain-cables are rep- 
resented by the open circular link 
(Fig. 730), the open oval (Fig. 731), 
-TT- oval with pointed stud (Fig. 732), 
)iii — oval with broad-headed stud (Fig. 
733), an obtuse - angled stud-link 
(Fig. 734), and the parallel-sided 
stud-link (Fig. 735). The usual 
proportions of chain -links are 6 
diameters of the iron in length by 
3^ in width. The end links, which 
terminate each 15 fathoms o| chain, 
are 6*5 in length to 4*1 in breadth, 
and the iron about 1-2 the diameter 
of the rest of the chain. 

Chain Couplings. — Fig. 736 is 
an ordinary coupling link of an 
anchor chain. The link is of 
wrought-iron, the bolt and pin of 
steel, both galvanized. The next 
link is made somewhat longer than 
other links of the chain, so that 
the coupling link may be more 
readily introduced. Fig. 737 is a coupling link in which one part is a swivel, 
so that the chain may have a rotation about its axis of length without twist- 




FiG. 737. 





Fig. 738. 



Fig. 739. 



Fig. 740. 



Fig. 741. 



ing. Figs. 738, 739, and 741 are sockets for wire-rope connections, shown in 
section. Fig 739, with a wrought-iron conical key ; often the wires of the rope 
are spread with wrought-iron wedges or nails, and in addition lead is poured in. 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



337 



In Fig. 739 the conical cone is formed over an iron core by unravelling the 
rope, passing the wires over it, and serving the ends to the rope below ; an iron 

socket fits over the core. Fig. 740 is 
a thimble in which the end of the 
rope is either spliced in or loose and 
served to the rope, with the end 
wires turned down. Fig. 741 is an 
open socket with a swivel hook, to 
prevent the tw^isting and untwisting 
of the rope and thereby weakening it. 
Fig. 742 is a loop-clamp. 

Hooks.— ¥igs 743 and 744 (from 
Redtenbacher) represent two wrought-iron hooks. The proportions of Fig. 
743 are : assuming the neck of the hook as 1, the diameter of journals of the 







Fig. 743. 



Fig. 744. 



Fig. 745. 



traverse are 1*1 ; width of traverse at centre, 2 ; distance from the centre of the 
hook to the centre of the traverse, 7*5 ; interior circle of the hook, 3*4 ; great- 
est thickness of the hook, 2-8. Assuming (Fig. 744) the diameter of the wire 
of the chain as 1 : interior circle of hook is 3*2, and greatest thickness of 
hook 3-5. 

Fig. 745 represents a hook of the Yale & Towne Manuf'g Company as fitted 
for a cross-head ; the diameter at A is that of iron from which the hook is 
forged, and the section shown hatched is equal to that of the round iron. Hooks, 
of the proportions but with a much greater load than given in the table below, 
yield by the gradual opening of the jaw, giving ample notice before rupture. 



Capacity of hook 

Dimensions of A. 
Dimensions of D. 

23 



Ton. 


Ton. 


Ton. 


Ton. 


Ton, 


To'n. 


Ton. 


Ton. 


Ton. 


Ton. 


Ton. 


i 


i 


i 


1 


H 


2 


3 


4 


5 


6 


8 


In. 


Id. 


In. 


In. 


In. 


In. 


In. 


In. 


In. 


In. 


In. 


f 


H 


f 


ItV 


li 


If 


11 


2 


H 


H 


n 


n 


If 


n 


If 


2 


H 


2f 


H 


H 


4i 


5i 



10 
In. 

H 

6i 



338 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



All parts of the hook are drawn in parts of A. 

Levers. — Figs. 746 and 747 are side and front elevations of an ordinary 
straight lever on a shaft ; both are shown broken, either because the length is 
indefinite, or because it is inconvenient to put on the paper. The handle 
should be from 5 to 6 inches long, and 1^" diameter. The bar beneath the 



n"T'"' 





A A A A 
A A A A 
A A A A 



D-^ 



Fig. 746. Fig. 747. 



Fig. 748. 



Fig. 749. 



.o; 

Fig. 750. Fig. 751. 



handle to be square, and of uniform width on one side of the lever and a taper 
on the other, as shown, of about Y i^i 4 feet on each side. The sides of the 
square at the handle to be ^ \/ length in inches, or say f " for 30'' lever, |-" for 
4 feet, and 1" for 5 feet. The neck of the shaft to be, as proportioned in the 
drawing, about -^ of the greatest width of the lever, and the diameter of hub 
1 j^. The stress exerted by a man may be from 75 to 100 pounds, and the size 
of the shaft will depend on the torsional stress between the hub of the lever 
and the point of resistance. 

Fig. 748 is a hand-lever forming one arm of a bell-crank — a bolt passing 
through a slot in the frame and the arm of the lever, and the two are clamped 
together by a tliumh-nut^ n^ by which the lever can be held in any position. 

The same purpose is often effected by notches in 
/^ "^ the frame, into Avhich the arm of the lever is caught, 

or by spring latches, as in Fig. 749. 

Figs. 750 and 751 are side view and plan of a 
foot-lever. The foot-plate is 8" X 5" X f ", and as 
the lever is subject to double the stress of the hand- 
lever above, the dimension should be somewhat in- 
creased. The side of square next the foot-plate 
should be, say for a lever of 30", I''; of 4 feet, 1^-, 
of 5 feet, 1^''; the form and taper as in the hand- 
lever. 
752 and 753 are views of a hand-crank. The diameter of the handles, 
for convenience in grasping, should not be less than IJ" ; if for the force of two 
men, ly, and from the diameter of the handle the rest may be proportioned as 



c:40 



Fig. 



(2) 



Fig. 753. 



Figs. 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



339 



-hZ5 hZ.B- 




in the figure. The length of handle for a single man should be from 10" to 
12"; for two men, from 20" to 24"; the crank from 15" to 18", and the height 
of shaft above the foot support for the men from 2' 10" to 3' 2". 

In the construction of steam engines the makers adopt simple rules of pro- 
portion between the diameter of cylinder and its connections. Thus, if that of 
the diameter of 
cylinder be 1, that 
of the crank-shaft 
at the journal is 
•50, of crank-pin 
•25, of crank-pin 
eye '6, that of the 
cylinder may be 
altered moderate- 
ly without change in that of con- 
nections which may be kept in 
stock. In large quick-running en- 
gines (Fig. 791) the crank-pin is of 
larger proportions than above. 

Figs. 754 and 755 are two views 
of a wrought-iron crank, and Figs. 
756 and 757 of a cast-iron crank,* 
both proportioned in their parts to 
the diameter of the large eye as 
unity, but, as shown by the diagram 

and rule following, these figures can only apply to a single throw of crank, as 
the diameters of the two eyes vary as their distances apart. 

Taking the diameter of the large eye of the crank as the unit, Redtenbacher 
gives in the table the relative sizes of cen- 
tral and end eyes of cranks, depending on 
the proportion between the length of crank 
and the diameter of central eye. The first 
column exhibits the number of times the 
diameter of eye is contained in the length 
of crank ; the second and third columns 
give the suitable diameters of crank-pins. 

The diameters of crank-pins as above 
given are on the basis of a length of from 1 
to 1^ of the diameter ; if the length be in- 
creased beyond this, the diameter should be 
increased in the ratio of 1 to the square root 
of the diameter. 

Disk-cranks are circular disks of cast- 
iron, with crank-pins of iron or steel, and 

as much strength of metal around the pin as in the crank. They are better 
than the crank, in that there is no unbalanced crank, and part of the weight 




Fig. 754. 



Fig. 755. 



DIAMETER OF EYE, BEING UNITS. 



I 
d 


For wrought- 
iron shafts. 


Cast-iron . 
shafts. 


2 


0-85 


0-62 


3 


0-69 


0-51 


4 


0-60 


0^44 


5 


0-54 


0-39 


6 


0-49 


0-36 


7 


0-45 


0-33 


8 


0-42 


0^31 


9 


0-40 


0-29 


10 


0-38 


0-28 


11 


0-36 


0^26 


12 


0-34 


0^25 


^ 13 


0-33 


0-24 



* " Elements of Machine Design," Unwin. 



340 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



of the connection can be balanced by a proper disposition of metal within 
the area of the disk. 

Fig. 758 is a plan of a double crank-axle, although by the projection the 
lower axle A appears as a straight shaft. The dimensions given are from an 
axle in use. In 
construction the 
cranks are rectan- 
gular in section, 
of which the 
width is j\ the 
depth, and the 
depth 1-5 the di- 
ameter of crank- 
journal. Double cranks are usually 
forged solid, and the slot for the 
crank cut out ; that shown in the 
figure was cast in steel for a double 
compound engine, 7 X 15 X 15, and 
has long worked satisfactorily. 

Fig. 759 is a drawing of a crank- 
axle adapted to a machine. 

Fig. 760 is an elevation and sec- 
tion of the driving wheel of a loco- 
motive, with a counterbalance op- 
posite the crank-pin, and Fig. 761 is a section of the trailing wheel. The crank- 
pin of the driver has two journals — one for the main connecting rod, the 
other for the coupling rod, for which there is a journal on the trailing wheel. 

Fig. 762 is a front and side elevation of a return crank, returning back and 




Fig. 757. 




Fig. 7.-38. 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



3^1 




342 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



having rotation about the main crank-shaft, used on small steam engines in- 
stead of an eccentric to give motion to the valve-rod. With its centre on the 




Fig. 759. 



central line of the main shaft there will be no motion, and used for the posi- 
tion of an oil cup, the oil flowing down the moving arm for the lubrication of 
the crank-journal. 

Eccentrics. — An eccentric is a modified crank ; the crank-pin is enlarged so 

as to include the crank-shaft ; motion 




is conveyed through the crank to the 
eccentric, and not through the eccen- 
tric to the shaft. 

Fig. 763 represents a front view, 
Fig. 764 the side view, and Fig. 765 a 
section, of a form of eccentric usually 
adopted in steam engines for giving 
motion to the valves regulating the ac- 
tion of the steam upon the piston. 
A ring or hoop, eccentric strap, is ac- 
curately fitted within projecting ledges 
on the outer circumference of the eccentric, so that the latter may revolve 
freely within it ; this ring is connected by an inflexible rod with a system of 
levers, by which the valve is moved. By the revolution of the shaft to which 



. 


' \ 



Fig. 762. 




Fig. 70.3. 



U ii il 

Fig. 764. Fig. 765. 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



343 



the eccentric is fixed an alternating rectilinear motion is impressed upon tlie 
rod, its amount being determined by the eccentricity^ or distance between the 
centre of the shaft and that of the exterior circle. The throw of the eccentric 
is twice the eccentricity E ; or the diameter of the circle described by the 
point E. The alternating motion is identical with that of the crank. 

The term eccentric is generally confined to the circular eccentric, all others, 
with exception of that last described, being called cams or loipers, but eccentric 
is often applied to curves composed of points situated at unequal distances 
from a central point or axis. 

Fig. 766. — Todraivthe eccentrical symmetrical curve called the heart^which^ 
when revolving ivith a uniform motion on its axis^ communicates to a movable 
point A, a uniform rectilinear motion of ascent and descent. 

Let C be the axis or centre of rotation upon which the eccentric is fixed, and 
which is supposed to revolve uniformly ; and let A A' be the distance which the 
point A is required to traverse dur- 
ing a half revolution of the eccen- 
tric. From the centre 0, with radii 
respectively equal to C A and C A', 
describe two circles ; divide the 
outer one into, say, 16 equal parts, / 
and through these points of divis- i 
ion draw the radii C 1, C 2, C 3, etc. ; 
divide the line A A' into the same "- - 
number of equal parts as in the \ 
semicircle, and through all the \ 
points 1', 2', 3', etc., draw circles '\ 
concentric with the former ; the ' 

points of their intersection B, D, E, 
etc., with the respective radii C 1, 
2, C 3, etc., are points in the 
curve required, its vertex being at 
the point 8. 

When the axis, in its angular motion, shall have passed through one division, 
the radius C 1 coincides with C A', the point A, urged upward by the curvature 
of the revolving body on which it rests, takes the position indicated by 1' ; and 
further, when the succeeding radius 2 shall have assumed the same position, 
the point A will have been raised to 2', and so on till it arrives at A', after a 
half revolution of the eccentric. The remaining half, A G F 8, of the eccen- 
tric, symmetrical with the other, enables the point A. to descend in the same 
manner as it was elevated. 

If the eccentric is turned vertically and the point of a weighted lever rests 
upon the curve, the lever will take a uniform motion from the curve ; but if a 
groove be cut in the face of a wheel with its outer edge like that of the curve 
and its inner one parallel to the outer one and a friction roll be inserted in the 
groove and attached to a lever or rod, the motion of roller and rod will be similar 
to that of the weighted lever resting on the eccentric. This construction is of 
frequent use, applicable to a great variety of motions, and is designated as a grooved 
cam. The grooves may be cut either in the face of a plate or of a cylinder. 




344 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



.-^^'' 

S 



v^V 



In the " Transactions of the American Society of Mechanical Engineers " is 
an illustration of a grooved cam cut on a machine of W. A. Gabriel, M. E., the 
motions being first laid out on paper and transferred to wooden or metallic forms, 
which act as guides to the cutting out of the grooves. The difficulty for the 

draughtsman is to comprehend 
the motions required and lay 
them out on the paper, which in 
lack of a machine may be trans- 
ferred to the metal surface and 
I cut by hand, with the aid of 
drills, chisels, and files. 

Fig. 767. — To draic a double 
^ and symmetrical eccentric curve^ 
' such as to cause the point A to 
7nove in a straight line, and ivith 
' an unequal motion ; the velocity 
of ascent being accelerated in a 
given ratio from the starting- 
point to the vertex of the curve, 
and the velocity of descent being 
retar^d in the same ratio. 

As in Fig. 766, take as the 
centre of motion and A A' the distance to which the point A is to be moved by 
a half revolution ; with C as centre and a radius C A' describe a circle and di- 
vide the semicircle into eight equal arcs, and draw the radii C 1, 2, C 3, etc. 
On A A' as a diameter describe a semicircle and divide it also into eight equal 
arcs and project the points of division 1', 2', 3', and 4' ; on the diameter A A', 
with C as a centre through the several points projected, describe circles ; the 




Fig. 767. 



A' 




Fig. 768. 



Fig. 769. Fig. 770. 



intersection severally of these circles with the radii C 1, 2, 3, will give 
points of the eccentric curve required. 

Fig. 768. — To construct a double and symmetrical eccentric, lohich shall pro- 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



345 




Fig. 771. 



346 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



duce a uniform rectilinear motion^ with periods of rest at the points nearest to, 
and farthest from, the axis of rotation. 

The lines in the figure above referred to indicate the construction of the 




Fig. 772. 

curve in question, which is simply a modification of the eccentric represented 
at Fig. "IQQ. In the present example the eccentric is adapted to allow the mov- 
able point A to remain in a state of rest 
during the first quarter of a revolution 
B D ; then, during the second quarter, to 
cause it to traverse, with a uniform mo- 
tion, a given straight line A A', by menus 
of the curve D G ; again, during the next 
quarter E F G, to render it stationary at 
the elevation of the point A' ; and finally, 
to allow it to subside along the curve B E, 
with the same uniform motion as it was 
elevated, to its original position, after hav- 
ing performed the entire revolution. 

Fig. 769 represents an edge view of 
this eccentric, and Fig. 770 a vertical sec- 
tion of it. 

If but one side of this were constructed, 
and the motion only equal to that of the 
arc and reciprocating, it would raise aud 
lower every point resting on it, and would 
'be called a wiper. The wiped surface is 
generally flat, an arm extending out from 
the rod to be raised, and a curve D G may 
be formed adapted to the height of lift, 
and action during the lift. 

Fig. 771 is a partial vertical section of 
the valve motion of one of the high-service 
pumping engines at St. Louis, Mo., show- 
ing the wiper A¥, or lifting toe, with its 
connection with the valves. The wiper 
shaft has a reciprocating motion by which 
the valve stem is raised and dropped. The valves are double-beat balanced ; 
the cut shows the arrangement of the steam jacket J, a space for live steam in- 
closing the cylinder, to aid in preserving the temperature and pressure within it. 




MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



34' 



Fig. 772 exhibits on a larger scale a portion of a section in plan and eleva- 
tion of the steam piston and mode of packing of the above engine. 

Fig. 773 is the elevation of a stamp mill in which a double wiper on a rotary 
shaft raises the stamp by its contact with a hub or collar on 'its shaft, and lets 
it fall suddenly by its weight. 

Machines like the above are often used in bleacheries to give a watered 
finish to goods. The battery of stamps is equal to the width of the cloth which 
turns in a roll beneath it, and the blows follow in quick succession. 

Connect mis. — Figs. 774 and 775 are sections of cottered joints of wrought- 
iron bars, the first made with a socket and the end of one of the bars ; the 






t— 11 —7 






Si 


m 


Lij 


c 

1— <.o-> 


life 


-*'"«ii^ 


^A 


^ 








latter by a sleeve connecting the two bars. The bars in the socket and sleeve 
are upset, to give more section than the bars themselves, so that the slots cut 
for the cotters c c will not reduce the strength below that of the bars. The 
cotters must have sufi^cient shearing strength and bearing surface, and at the 
same time diminish as little as possible the section of the parts connected. 
The proportions given in the figures are drawn to a scale of the diameter of 
the enlarged part as the unit, and the 
proportions given in figures are such as 
obtain in practice for wrought-iron. 
If the cotter be of steel, its breadth 
may be three fourths of that given, 
preserving the other dimensions the 
same ; the thickness is "25 of the unit. 

The knuckle-joint (Fig. 776) is 
given in dimensions of the bar as a 
unit, and adapted to usual work. If 
there is much motion at the joint, the 
wearing-surface should be larger, by 
increasing the wddth of the eyes and 
the length of the pin. The pin in the 
drawing is through the collar ; usually the pin is extended, and the pin passes 
through the bolt outside the collar. 

Connecting-rods^ in their application to steam engines, are the rods connect- 
ing the piston through the cross-head to the crank. When two cranks are 
connected it is called a coiqMng-rod. 




us 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



Fig. 777 is the side elevation of the eccentric and strap of a Reynold's 
20'^ X 48^ Corliss engine. The eccentric rod is made with a shoulder, the stem 
is fitted to the l^^*' socket, and held firmly by a nut in the 4" groove. 

Fig. 778 is a double eccentric, used 
in giving motion to the link in the cut- 
off. The eccentrics are made in halves 
for convenience in putting them on the 
shaft. 

Governors are used on quick-run- 
ning engines (page 407) to control the 
cut-off through movable eccentrics, but 
eccentrics adjustable by hand are con- 
venient as applied to pumps in modi- 
fying the stroke. With a uniform ac- 
tion of the motor the stroke of the 
pump is reduced, giving greater pres- 
sure on the plunger, say from a domes- 
tic to a fire pressure. 

Figs. 779 and 780 are plan and sec- 
tion of such an eccentric. The crank-pin is fastened on a slide-rest moving in 
guides attached to the power shaft by a long hub.-^ To hold the slide firmly to 
the shaft-hub there are three key-bolts, n n n. To move the crank-pin slide 
these bolts must be slacked, and by means of a hand lever (Fig. 781), using as 
a fulcrum the pins on one of the guides, and bringing the short end of the 
lever against a projection, p, attached to the crank-pin, it may be moved to any 
desirable position or stroke and clamped to the hub firmly by the key-nuts. 




Fig. 777. 















1 


1 1 

M- 




\ rn 


-M— 


— t--' 


1 1 




1 > V / / ' 


1 


t-l — ^ 





Fig. 778. 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



849 




Fig. 



Fig. 780. 



Fig. 782 is the elevation, plan, and section of an eccentric strap of a locomo- 
tive engine, of cast-iron, with very long bolts, and a very rigid construction. 
The strap forms a cup-section over the projecting ring on the eccentric, and 
retains the oil at the bottom for more efficient lubrication and prevents drip. 

Figs. 783, 784, and 785 is another cast-iron eccentric strap, in which a box 
is inserted, fitted with metallic disks, to prevent frequent oiling. The bolts at 
the large end are bored up to a sectional area of that of the screwed portion to 
secure equal elasticity. 







Fig. 783. 



350 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 




Fig. 787. 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



351 



In many marine engines the boxes of both crank and cross-head pins are 
connected with strong and heavy bolts without any other rod. 

Fig. 786 is a strap-end of a connecting-rod, from the Corliss Steam-Engine 
Company. The iDccnliarity is the adjusting-screws connected with tlie boxes. 

Fig, 787 is the strap-end of a locomotive connecting-rod in which the wear 
of the boxes is taken up by a cotter at the end of the strap. 




In Fig. 788 the key is between the bolts ; the weakness from bolt-holes or 
cotter-slot is compensated by the width of the strap. 

Fig. 789 is the box-end of a locomotive-rod, in which the strap gives place 
to a box forged on the end of the connecting-rod. 



352 MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 




MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



353 



Figs. 790, 791, and 792 are side, plan, and end views of a connecting-rod of 
the Southwark Foundry, of Philadelphia, used on their fast-running Porter- 
Allen engines. 

The cross-head end is a strap-end^ while that of the crank is a box-end^ and 
of larger diameter than the former on account of the extra wear and size of the 
crank-pin. The length of the page does not admit of the representation of the 
full length of the connecting-rod on the scale ; it is therefore shown broken, 
with the dimensions figured in. The sections of the two ends are drawn in on 
the rods ; the circular section A is the same as that of the piston-rod, and both 
are represented in the conventional hatching of cast-iron, but it is of wrought- 
iron. The gib g and key or cotter v at the strap-end are of steel, and the key 
is fastened when in position by a set-screw through the head. At the box- 
end, a wedge and screw forces the box into position. 




354 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



Figs. 793 and 794 are the sides and top elevations of the connecting- and 
coupling-rods of the express locomotives of the New York Central and Hud- 
son Kiver Eailroad, designed by Mr. Buchanan, and built at the Schenectady 
Locomotive Works, of which the drawing of driving wheels will be found 
at Fig. 760, of the frame Fig. 1301, and the boiler Fig. 926, with the gen- 
eral weights and dimensions of the locomotive. Fig. 795 is a section of the 
coupling-rod. 

Fig. 796 is a connecting-rod of the Eider hot-air engine, in which the ends, 
made of gun metal, are connected together by a tube in which is fitted a rod, 
extending from the upper to the lower brass, and so arranged that one key, E, 
capable of nice adjustment by nuts, at once takes up the lost motion on both 
upper and lower brasses. 




Fig. 796. 



Fig. 797 is the stub end of a coupling-rod. The bushes are solid, of brass, 
and kept from turning round by taper-pins, which are secured by set-screws 
pressing on the larger end ; taper, ^ig- in 3 inches. 

Cast-iron connecting-rods are now very seldom used. In some cases of 
vertical-beam pumping engines it is necessary that the weight of, the steam 
pistons should be counterbalanced by some mass of material, and it may be 
convenient to make use of a heavy pump-connection. 

The wrought-iron crank connections of American river-boat engines are 
peculiar in their construction. They are made as light as possible, with very 
great stiffness. Fig. 798 represents the side elevation of such a connecting- 
rod. The means adopted to give the required stiffness consist of a double- 
truss brace, a a, of round iron, which is fastened by bolts to the rod near each 
end ; struts Ij Z*, cut with a screw, and furnished with nuts, pass through the 
centre of the brace, by which means the braces are tightened. The connecting- 
rod at its smallest part near the extremities is of the same diameter as the pis- 
ton-rod ; the boss in the centre is from one to two inches more. 

Fig. 799 is the front view of the forked end of the rod, which is fitted with 
the usual straps, gibs, and cotters. Fig. 800 is the side view of the brace-rod. 

The working-beam (Figs. 801 and 802), of similar framed construction, was 
at one time largely used for river boats, but may still be applicable in many 
places for its lightness and stiffness. It is composed of a skeleton frame of 
cast-iron round which a wrought-iron strap is fitted and fastened. The strap 
is forged in one piece, and its extreme ends are formed into large eyes, which 
are bored to receive the end-pins or journals. The skeleton frame is a single 
casting, and contains the eyes for the main centre and air-pump journals ; the 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



355 





:: 


'\\> 


1 




\ \ 

\ 


JtL 1 






^11 1 


HC 7i L 




I 


1 




* 


^^ 


r 



centre hub is strengthened by wronght-iron hoops shrunk 
upon it. At the points of contact of the strap and skele- 
ton, key-beds are prepared. Small straps connect the frame 
and main-strap at these points, keyed to the frame — keys 
riveted over. The frame is further braced by wrought-iron 
straps, C C, which tie the middle of the long arms to the 
extremities of the shorter ones. The following are the gen- 
eral dimensions: From centre to centre of end-journals, 26 
feet; this is somewhat less than the usual proportion to 
length of stroke, being slightly less than double the 
stroke ; length of centre hub, 26", a a ; diameter of 
main centre eye c, 15f " ; of air-pump journal-eye d, 6|" ; 
of end- journals e e, 8-J-". 

Double plates or flitches of wrought-iron are often 
used in the construction of working-beams and side-levers. 
Fig. 803 is the section between the two plates of a beam 




Fig. 798. 



Fig. 797. 

of this kind, attached to the compound pumping engines 
at Milwaukee, Wis. The plates are each 30 feet long, 
by 6' 4" deep at centre, by If" thick. The connections 
between the two, shown in section in the figure, are 

cast-iron pipes with wide flanges at 

each end riveted or bolted to the 

plates. The main centre and other 

small journal -pins are rods of 

wrought-iron, passing through the 

pipes, and extending outside the 

plates to form the journals ; c is 

the section of the pin for crank 

connection, p for that of pump, h 

for that of high-pressure cylinder, I 

for that of low-pressure cylinder, 




Fig. 799. 



Fig. 800. 



356 



MACHINE DESIGN AND MECHANICAL CONSTP.UCTIONS. 



m for main centre-pin, and g for the parallel-motion links. This last is usu- 
ally the position of the air-pump centre, but in this engine the air-pump is 




Fig. 802. 



below the high-pressure cylinder, and its piston-rod is extended to the air- 
pump piston. The dimensions are — H. P., cylinder 36" X 62"; L. P., cylin- 




der 58" X 8 feet. The heads of the two cylinders are kept at the same levels 
by increasing the length of the H. P. piston. 

Working-beams with vertical steam engines are now seldom used except in 




IS 



i) 



v^ 



i=I] 



Fig. 804. 



connection with large pumps. For power the horizontal engine is now sub- 
stituted and connected closely with the fly-wheel. Fig. 804 represents such 
an engine and frame. 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



357 



The pin p is the connection in the cross-head (Fig. 804) between the piston- 
rod of the steam engine and the connecting-rod to the crank. 

Figs. 805, 806, and 807 represent the plan, end view, and section of the 
cross-head adopted by the Southwark Foundry for their high-speed engines. It 
is of cast-iron, with large, 
flat faces, the pin p for 
the connecting-rod being 
in the middle of the 
length. This pin is of 
wrought-iron, large and 
flattened on top and bot- 
tom, so that the boxes of 
the rod can never bind on 
the pin at the extreme of 
the vibrations of the rod ; 
usually these pins are 
round. The pin is formed 
with large squares at the 
ends, by which it is fitted 
into the jaws of the cross- 
head, where it is secured 
by a steel pin passing 

through the cross-head. The bearing surfaces of the head and those of the 
guide-bars are finished by scraping to true planes ; there are no means of ad- 
justment, as there is no wear if kept clean. 




Fig. 806. 



Fig. 805. 




Fig. 807. 



O 




Fig. 808. 















Fig. 809. 



It is to be understood that the piston-rod moves in a straight line, and that 
the stress on the connecting-rod pin is mostly oblique. Guides are to be pro- 
vided, between which the cross-head slides, to take the oblique stress oS the 
piston-rod. 



358 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



Figs. 808 and 809 are elevation and plan of guide-bars suited to the cross- 
head above, which are in common use for both vertical and horizontal engines. 
Lugs or ears are cast on the steam-cylinders, and on the frames to which the 
bars are bolted, and between which the cross-head slides. The grooves or 
notches across the guide-bars, at the ends of the stroke, are to throw off any 
grease or dirt that may be carried along by the head and prevent their accumu- 
lation. The stress on the guide-bars is due to the pressure of the steam on the 
piston acting obliquely on the crank through the connecting-rod, and is the 
greatest when the crank is at right angles to the piston. It can be determined 
by multiplying the pressure on the piston by the length of the crank, and divid- 
ing the product by the length of the connecting-rod, which will be the stress 
tending to separate the guides. If the connecting-rod be 3 times the stroke, or 
6 times that of the crank, which is the usual proportion, then the stress is -J- 
the pressure on the piston. Sometimes the proportion of connecting-rod to 




Fig. 810 



stroke is 2 J to 1. When a portion of the force of the steam is opposed directly 
to the resistance, as in direct-acting pumps, and only the irregularities in the 

steam-pressure are transmitted through the connect- 
ing-rods, the proportion of rod to stroke may be still 
smaller. 

Fig. 810 is the cross-head of the Harris-Corliss 
engine in which the bearing surfaces of guides are 
adjusted by bolts passing through wedges. 

On locomotives it is not unusual to have the 
guide on one side, as in Fig. 811, where the side-bars are of Avrought-iron and 
the slide-block is fastened between the two plates of the cross-head by bolts. 
It is the most common practice in this country to use guides with vertical en- 
gines, even when the connection is with working-beams. 




Fig. 811. 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



359 



St earn- Cylinders. — Fig. 812 is a sectional plan of a common form of small 
steam-cylinder. A is the cylinder, B the piston, h the piston-rod, D the slide- 
valve, ^ the valve-rod, C the valve- 
chest, c the chest-cover, s s the 
steam-ports, e the exhaust-port, S the 
stuffing-box of the piston-rod, s' that ^ 
of the valve-rod. H is the front 
head and H' the back head of the 
cylinder. The bolts attaching the 
heads to the body of the cylinder are 
not shown. 

Length of Cylinder. — It is the 
present practice, in the construction 
of stationary engines for driving ma- 
chinery, to make the stroke not over 
twice the diameter of the cylinder, and for diameters above 24" about IJ- time the 
diameter of the cylinder, and invariably to place the cylinders horizontally with 
a direct connection with the crank, without the intervention of a working-beam. 

Fig. 813 is a front view partly in section, and Fig. 814 is a transverse section 
through the centre of a Fishkill Corliss steam-engine cylinder, giving the steam- 




FiG. 812, 




Fig. 813. 



valves in section and outside view showing their connection with the wrist-plate 
and its motion, also the piston-rod and stuffing-box with a scale of reference. 
The thickness of shell Mr. Henthorne finds, by many examples in Corliss's large 
practice, to conform to the formula t = '268 V d., t and d being in inches. 



360 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



Thus the thickness of the shell of a 16" cylinder will be V 16 X '268 = 4 X '268 = 
1-072, a little more than 1". The thickness of flanges should exceed that of 
the shell by |^ to J its thickness. The bolts should not be less than f " and sel- 
dom more than 1". It is better to increase the number of bolts than their di- 




FiG. 814. 

ameter, the breadth of^ flange to be about 3 times the diameter of the bolts, and 
the pitch of the bolts, or the distance between centres, about 6 times the diam- 
eter of the bolts. 

Oast-iron is the material chiefly used for pistons, but those of wrought-iron, 
brass, bronze, and cast-steel are common. The wrought-iron pistons recently 
introduced in American locomotive practice follow the designs of the older 
cast-iron pistons. 

Fig. 815 is the cast-iron piston of a locomotive. The spring or snap-rings 
forming the packing are of cast-iron, 1^ wide by ^ thick, of uniform section. 
The split is made with a half lap, and 
the splits of the two rings are on oppo- 
site sides of the piston. The outsides of 
the rings are turned to a diameter slightly 
in excess of that of the cylinder, and are 
sprung into recesses of the piston fitted 
to receive them. 

Fig. 816 is a half plan and half sec- 
tion and Fig. 817 a full cross-section of 
piston of a steam-cylinder of Leavitt's 
design ; the packing is Wheelock's, in which the rings are in sections joined to 
adjust themselves to cylinders that have become worn. 




MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 361 



HALF SECTION C D 




Fig. 816. 
SECTION E F 

2i% 



7 It 




Fig. 817. 



Large cast-iron pistons are made hollow and strengthened by internal radial 
ribs. In Fig. 772 is shown the packing of the steam piston of the C3'linder of 
one of the St. Louis pumping-engines. Fig. 818 is a design from an English 
manual for a large cast-iron piston. The dimensions marked on the figure are 

T) /P 

in terms of the unit /^ , in which D is the diameter of the piston in inches 



362 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



and P the initial pressare per 
square inch. The junk-ring is 
secured by wrought-iron or steel 
bolts and brass nuts. The diam- 
eter of the junk-ring bolts may be 

•28Da/P , . -, 

— —7?? ^ 4 inch, and they may 

be placed at a pitch of seven to 
ten times their diameter. The 
number of ribs or webs may be 

about y- + 2 and their thickness 

•4DVP 

100 • 

j,jjj gjg for the packing will depend on 

the design of packing adopted. 
Fig. 819 is a sectional plan and Fig. 820 is a sectional elevation of the inte- 
rior of a piston-ring, showing another common form of ring packing, which 
consists of a single interior ring r and two exterior rings r" r", and each cut in 

r" F 




The size of the space 




Fig. 819. 



Fig. 8:20. 



two and so fastened that the joints are always broken. The packing is set out 
by springs s s, one of which is shown. F is the follower, which can be taken 
off for the admission of the rings and springs, and then replaced and bolted to 
the piston, making a close joint with the end of the rings. The depth of the 
piston at the exterior is from 3" to 9", varying with the diameter of the piston. 
Figs. 821, 822, and 823 are sections of the exterior rings of pistons adapted 






Fig. 821. 



Fig. 822. 



Fig. 823. 



more particularly to water-pumps. Fig. 821 depends on the closeness of fit of 
the exterior of the piston with the inner surface of the cylinder, and when accu- 
rately turned and fitted the leak is very inconsiderable, and by the use of grooves 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



363 



(Fig. 822) it is still less. In Fig. 823 the joint between the piston and the cyl- 
inder is made tight by a gasket, usually of hemp, compressed by a joint ring or 
follower, «, in the pocket between piston and cylinder. 

Wood-packing put in short staves, as shown in Fig. 824, is often used for 
pump-pistons and buckets. Make the diameter of the wood-packing a little 
less than the diameter of the barrel of the pump, to allow for the swelling 
which takes place when the wood becomes saturated with water. 





Fig. 825. 




Fig. 824. 



Fig. 826. 



Fig. 825 is a cup leather packing, and Fig. 826 is a U-packing for small 
cylinders of hydraulic presses. The application of the first will be understood 
from Fig. 827, in which the piston is packed with two cup leathers, in this case 
to withstand pressure in both directions. Were the piston single-acting, but 
one cup would be necessary — and if from beneath the piston, this would be the 
lower cup. The flexible flange is pressed against the inside of the cylinder, and 
the joint is perfectly tight. 




Fig. 827. 




Fig. 829. 



364 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



Fig. 828 shows the application of the U-packing ; it is put into a recess in 
the cyhnder by bending the packing into a saddle-bag form, and then allowing 
it to spring back into the recess. In English practice hemp packings serve 
the same purpose, and are necessary when the temperature of the water ex- 
ceeds 90°. 

Packings can be obtained from hydraulic-pump and press manufacturers, 
and are kept in stock of all the usual sizes. Their depths are from 1" to 1-J-" 
for diameters varying from 4" to 14", and the space occupied by the thickness 
in the U from ^" to f ". A filling of flat braided hemp is placed inside the U 
to keep it tight when not under pressure. The packings are made by steeping 
the leather in warm water, forcing them into a mould, and leaving them to dry 
and harden. The moulds (Fig. 829) are made of either metal or wood ; fre- 
quently the rings are of metal, and the piston over which the cup is formed, of 
wood. 




SECTION CC 
Fig. 831. 

The outer cylinder forming the exterior shell of the steam-jacket is fastened 
to the steam-cylinder, but is allowed to move under changes of temperature. 
In Figs. 830 and 831 are given longitudinal and transverse sections of a steam- 
cylinder with jacket, as constructed by E. D. Leavitt, M. E., in which the upper 
and lower end of jacket is cast with the cylinder, and the connection between 
the two is by a copper U-ring, which admits the necessary expansion and con- 
traction. All steam-cylinders, whether with or without jackets, should be 
clothed — that is, covered with some preparation to prevent the escape of heat 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



365 



from contact with air. The usual clothing is hair felt, with a lagging — that is, 
an exterior shell of some wood, usually black walnut. 





Fig. 832. 

Fig. 832 is a section and partial elevation of the air-chamber of one of 
Leavitt's pumps. It is of the Thames Ditton variety, in which the whole charge 
of water is drawn into the lower chamber, and a portion corresponding to the 
difference between the two plungers raised to the full head in the upper cham- 
ber ; in the down stroke a quantity of water eqiial to the displacement of the 
upper plunger is raised to the full head. The packing of the lower plunger is 
by grooves in the exterior ring ; this form of packing by proper fitting makes a 
tight joint without friction. With this packing the lower chamber of the pump 
can be drawn off and examined, leaving the water-load in the upper piston. The 
dash-pot of a Fishkill Landing Corliss engine, with a similar groove packing, 



366 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



was tested to a water pressure of 140 pounds and leaked very little. Like pack- 
ings are used in air-pump pistons with satisfaction. 

The pump-valves are not shown in the drawing, but are Riedler's controlled 
valves, which are opened by the movement of the water and closed positively by 
a mechanical connection. 





Tllllllllllllll 



Fig. &34. 



Fig. 833. 

Fig. 833 is a section of a single Worth- 
ington steam-pump, one of a pair always 
placed side by side (hence called duplex), 
combined to act reciprocally on the steam- 
valves of each other. 

In the form of pump shown, the length 
of barrel is about equal to the diameter 
of the piston, but the length of the piston 
is equal to that of the stroke of the pump 
plus that of the length of the barrel. 

In Fig. 834 the pump barrel is long 
and the piston short. 

The duplex was H. E. Worthington's 
invention and is now the general type of 
most makers for boiler feed pumps and 
small water supplies. For the boiler feed 
especially of locomotives the injector is 
largely used, and as supplementary to the 
pump. 

The hijector is an apparatus in which 
the momentum of a jet of steam issuing 
from the boiler is transferred to a body 
of water, producing a resulting velocity 
sufficient to force the water into the same 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



367 



boiler. Many shops mauufacture injectors. The section shown (Fig. 835) is 
from William Sellers & Co., one of the earliest makers, and the explanation of 
its working illustrates the principles of a good and successful machine. 

To start the injector the valve G is raised to permit the admittance of water 
into the chamber J ; the lever F is then opened sufficiently to allow the steam 
through the opening d d^ while the plug h still keeps the forcing nozzle a 
closed, thus admitting steam into the annular steam nozzle i, which, passing 
into the water-chamber J and the combining tube through the overflow cham- 
ber I and into the overflow E, producing a strong vacuum in the water-chamber 
J, into which the water from the source of supply is forced by the atmospheric 
pressure, the characteristic of a lifting injector. The combined jet of water 
and steam passes through the combining tube ; the valve F is then fully raised, 
admitting steam into the forcing nozzle a ; this steam, uniting with the jet in 
the combining tube, accelerates its velocity to sach an extent that the valve g 
is forced down, thus allowing the passage of water to the boiler. 




The issuing steam and water maintains its velocity by reduction of the areas 
of channel discharge till the last channel in connection with the boiler, which 
increases till it meets the valve g. 

The lower the temperature of the feed- water the greater the capacity of the 
injector. As the steam strikes the water its momentum is checked and trans- 
ferred to heat and at once absorbed by the feed, all the energy apparently 
wasted reappearing in the latent and sensible heat transferred to the feed. It 
is this absorption of heat that gives the great economy over the feed-pump, but 
for raising water it is not to be used except where simplicity of construction 
and convenience of application may offset the waste of power. 

To use the injector as a heater to prevent the freezing of the water in the 
water-tank, the valve Gr is opened and the eccentric lever H closed ; the steam 
will then have free admittance into the chamber I and the water-tank. 



368 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



Each size of injector is named from the diameter of the delivery tube in 
millimetres. In the table given by Strickland L. Kneass the diameter runs 
from 3'2 to ll'o millimetres; the steam pressure from 30 to 150 pounds, and 
the discharge 23*5 to 550 cubic feet per hour ; height of lift, 1 foot ; tempera- 
ture of water, 60°. 

Ejectors are also used as pumps for the raising of water by suction and 
pressure, of which Figs. 836 and 837 are of the simplest form. The steam is 





i! 



r, 1 !M 



.iil'iini 



\i I 



11 
11 




Fig. 836. 



Fig. 837. 



Fig. 838. 



ejected through a central nozzle a^ while the water is raised and discharged 
through the pipe inclosing it. The same principle of induced current is 
applied through a current of water, steam, or air in discharging earth from a 
caisson, the ashes from the boiler hold of a marine engine, water from founda- 
tions or from driven wells. 

Fig. 838 is a section of a Korting blower to improve the draft in the ash- 
pit, fire-box, or chimney of a boiler, and Fig. 839 is that of a larger size, show- 
ing the construction of the jet in which the force of the steam drawing the 
air through compound nozzles reduces the intensity of its flow, but increases 
its quantity to suit the purposes of draft. 

M. Mondesir, in the French Exhibition of 1867, effected the ventilation by 
means of reservoirs of compressed air. Around the exterior of the building 
there was a large underground gallery into which the exterior air was intro- 
duced by sixteen vertical shafts symmetrical in position, and from the main 
gallery the air was distributed by radial galleries into the interior of the build- 
ing, into which the air current was introduced by numerous jets of condensed 
air from the reservoirs. The air was supplied to the jets at a pressure of 29| to 
31^ inches of water. The vitiated air escaped through a ventilator in the roof. 

Clearances in cylinders include, in general signification, not only the spaces 
between the piston and cylinder-heads at the ends of the stroke, but ^Iso the 
spaces between the cylinder and the valves ; and as those spaces are voided in 
a steam-cylinder at each stroke for which adequate work from the steam is not 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



371 



Of the Size of Ports or Openings.— UndiQV " Steam-pipes " will be given the 
formula for the flow of steam, but the general rule of proportioning the ports 
of a cylinder is to consider the velocity of steam 100 feet per second, and of the 
exhaust 80 feet per second. With the slide-valve the opening and closing are 
made gradually, thereby throttling the flow of the steam. To avoid this, Mr. 
Corliss in his engine has made the ports long and narrow ; the steam-valves open 
quickly and close at once by a drop ; the exhaust- valves move rapidly from the 
wrist connection. From the great size and form of the common slide-valve there 
ensues a great pressure on the surface; various expedients have been adopted 
to relieve this pressure, which is especially desirable in quick-running engines. 

Fig. 843 is a horizontal section of cylinder, through steam- and exhaust- 
valves, of a Porter- Allen engine, and Fig. 844 a vertical cross-section through 




Fig. 844. 



cylinder and valves. The valves are four in number, one for admission and one 
for exhaust, at each end of the cylinder, and on opposite sides. They stand 
vertically to drain the cylinder. The valves work between opposite parallel 
seats ; the exhaust- valves nearly and the admission-valves wholly in equilibrium. 
The action of the back plate, and how the wear is taken up, will be understood 
from the section (Fig. -844), which passes through the middle of one pressure- 
plate. It is made hollow, and most of the steam supplied to two of the open- 
ings passes through it. It is arched to resist the pressure of the steam without 
deflection. It rests on two inclined supports, one above and the other below 
the valve. These inclines are so steep that the plate will move down under 
steam pressure; and that it may be closed up to. the valve with only a small 
vertical movement, the pressure-plate is held in its correct position by projec- 
tions in the chest on one side and tongues from the cover in the other, which 
bear against it at the near end, as shown. Between these guides it is capable 
of motion up and down and back and forth from yV to \". The pressure of 
the steam on thl^ plate tends to force it down the inclines to rest on the valve. 
By the means of the screw the plate is forced up and away from the valve, and 



372 



MACHINE DESIGN AND MECHANICAL CONSTHUCTIONS. 



can be so nicely adjusted that the valve works freely and perfectly steam-tight. 
When the pressure is greater in the cylinder than in the chest, the pressure- 
plate is forced back, to the instant relief of the cylinder. 

Cylindrical Valves. — Fig. 845 represents the section of the steam-cylinder 
of an Armington & Sims steam engine with a cylindrical valve. The steam- 



jm 



JTTL 



UTL 



JUL 




Fig. 845. 

chest S is central and incloses the valve ; the exhaust chambers E E are at the 
ends of the valve, and are connected through the hollow stem or body of the 
valve. The valve depends on its accuracy of fit for its tightness. The valve- 
chamber is bored out and ground, the valve is turned, ground, and carefully 
worked by hand, to so close a fit that there is no loss of steam in action, and 
the valve is completely balanced. 

There is a form of balanced valves, called the douUe-heat^ much used both 
for steam and water valves. Fig. 846 is a sectional elevation of a steam valve 





Fig. 846. 



Fig. 847. 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



373 



of this kind, and Fig. 847 a plan of the loAver seat a, with the valve-guides ^ ^ 
in section. There are two seats, a and h, and two faces on the valve corre- 
sponding to them. The balance depends upon the relative diameters of the 
bearinfr-lines of the two faces. In the figure, if the exterior of the bearing at 




\^ ^^ '^^ K^ 



Fig. 848. 



h and the interior at a are both tight, the valve is balanced under any pressure, 
except as to its own weight ; s is the valve-stem, and the hole r is for a bolt to 
fasten the valve-seat to the casting of the steam- chest. The scale is -J full size. 
Fig. 848 is another form of balance, consisting of two equal poppet-valves 
connected together — the steam passage to the cylinder being central, and the 
steam-chest at each end, connected. 

Automatic valves^ that are moved ty the action of the fluid i?i which they are 
placed. 

The double-beat valve (Fig. 846) is sometimes used in large pumping-en- 
gines. From its two beats, the lift is about one half that of a plain valve. 
There must be difference enough in the faces to admit of the lift of the valve 

by the pressure of water acting on this 

difference. The seats of the valves are 
often made of wood, set endways. 

Large valves, from their great weight 
and flow of water through them, are noisy 
in both seating and lifting. This is met 
in the balanced valves by slower move- 
ments of the piston ; but present practice 
is to obtain outlets by increasing the num- 
ber of valves, the total area of the aper- 
tures, and the speed. 

Fig. 849 is a single-beat direct lift- valve 

guided by three feathers on its under side, 

which slide in the cylindrical part of the pipe. The feathers are of a screw 

form, by which a rotary motion is given to the valve through the flow of the 

water, which prevents its beating on the same parts of the seat ; usually the 




\r . . .. 


^ 








Nj I- ■ ■ . 






■ 


1 ^ 


u 


1 




N £ 








Fig. 849. 



Fig. 850. 



374 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 





Fig. 851. 



Fig. 853. 



feathers are straight, and often four instead of three. Fig. 850 is a poppet-valve 
guided by a central stem ; both these valves have conical faces and seats, with 
generally an inclination of 45° to the axis of the valve. In many valves the 
faces and seats are flat, one or the other of which is of soft metal or rubber. 

Figs. 851 and 852 are elevation and section of a rubber disk- valve in very 
common use in direct-acting pumps and small pumping- engines ; sometimes 

with a thimble in the rubber as a 
guide ; usually, as in the figure, 
with a metallic plate on top of 
the rubber for the bearing of the 
spring ; valve-seat generally of 
composition, with spindle riveted 
or screwed into it. Sometimes 
the rubber is held in a metallic 
plate or cup. The springs at 
their backs cushion the blow on 
the lift, and start the valve down- 
ward promptly on the check of 
the waterflow at the end of the 
stroke. The great desideratum 
of r water - valves is that there 
should be little lift, but ample 
water-way. 

Fig. 853 is a section of Field's pump-valves, an English design for high-water 
service, as fire-pumps, of which the flaps are rubber disks. For lower pressures, 
as for the pumping of half-stuff in paper-mills, valves are made in the shape 
of a bishop's mitre slit lengthwise 
at the top and partly down the 
sides. The bottom flanges should 
be held loosely without bolts 
through them. 




Fig. 853. 





Fig. 854. 



Fig. 855. 



Fig. 854 is a ball-valve, guided in its movement by an open guide-cage, c, 
which is held down by a set screw in the cover. Globe-valves with this form 
are on sale. Ball- valves are usuallv small metallic balls on metallic or wooden 



MACHINE DESIGN" AND MECHANICAL CONSTRUCTIONS. 



375 



seats, or rubber balls on metallic seats ; and cylindrical valves have been made 
of the same section as in the figure ; the body of the valves of brass pipes with 
rubber jackets. 

In Fig. 855 the ball is of rubber and the seat is of composition, screwed 
into the pipe with a cage of the same metal, screwed 
to the seat. 

Fig. 856 is a section of a poppet-valve; the body 
is of cast-iron, but the valve and seat are of brass. 
The valve is guided by three feathers. The lift of 
the valve may be controlled by a set screw in the 
cover which admits of adjustment to varied lifts. 

Figs. 857 and 858 are the plan and section of a 
disk-valve for the air pump of a condensing steam 
engine. The valve consists of a disk of rubber ly- 
ing on a flat grating or perforated plate of brass, 
held in position between the grating and a spheri- 
cal guard by a central bolt. The shape of the guard 
gives a uniform flexure to the rubber in lifting, and 

an easy flow to the current of air and water. The rubber is not closely clamped 
between the guard and plate, as will be seen in the figure, 
being screwed home, is riveted, and 
the upper nut usually pinned to pre- 
vent turning. The size of the aper- 
tures in the grating are adapted to the 
thickness of the rubber. With an ex- 
ternal diameter of opening of 6", and 




Fig. 856. 



The lower nut, after 




°mm. 



lO 



c^ 



o 



^^ 



G/ 



Fig 857. 



Fig. 858. 



rubber ^" thick, the exterior ring of openings may be f " by f ", the la7ids or 

spaces between openings i" wide, and exterior lap of the rubber ^ inch. With 

larger diameters and larger openings thicker rubber must be used. This valve. 

is often made of a long strip or flap of rubber, on a suitable grating, with a 

curved guard attached on one side. For 

the common air-pump pressure, f" rubber 

is sufficient for apertures 1" X 4". With 

the use of backing and face plates on the 

rubber or leather flaps, gratings may be 

dispensed with (Fig. 859). Valves of this 

description— duplicate (Fig. 860) beneath 

the central pin and half circular in plan 

— are often used in pumps, and are called 

butterfly valves. It is the best practice to 

insert thimbles in the rubber (Fig. 859), fig. 859. 




374: 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 





Fig. 851. 



Fig. 853. 



feathers are straight, and often four instead of three. Fig. 850 is a poppet-valve 
guided by a central stem ; both these valves have conical faces and seats, with 
generally an inclination of 45° to the axis of the valve. In many valves the 
faces and seats are flat, one or the other of which is of soft metal or rubber. 

Figs. 851 and 852 are elevation and section of a rubber disk-valve in very 
common use in direct-acting pumps and small pumping- engines ; sometimes 

with a thimble in the rubber as a 
guide ; usually, as in the figure, 
with a metallic plate on top of 
the rubber for the bearing of the 
spring ; valve-seat generally of 
composition, with spindle riveted 
or screwed into it. Sometimes 
the rubber is held in a metallic 
plate or cup. The springs at 
their backs cushion the blow on 
the lift, and start the valve down- 
ward promptly on the check of 
the waterflow at the end of the 
stroke. The great desideratum 
of ^water - valves is that there 
should be little lift, but ample 
water-way. 

Fig. 853 is a section of Field's pump-valves, an English design for high-water' 
service, as fire-pumps, of which the flaps are rubber disks. For lower pressures, 
as for the pumping of half-stufl in paper-mills, valves are made in the shape 
of a bishop's mitre slit lengthwise 
at the top and partly down the 
sides. The bottom flanges should 
be held loosely without bolts 
through them. 




Fig. 853. 





Fig. 854. 



Fig. 855. 



Fig. 854 is a ball-valve, guided in its movement by an open guide-cage, c, 
which is held down by a set screw in the cover. Globe-valves with this form 
are on sale. Ball-valves are usually small metallic balls on metallic or wooden 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



375 



seats, or rubber balls on metallic seats ; and cylindrical valves have been made 
of the same section as in the figure ; the body of the valves of brass pipes with 
rubber jackets. 

In Fig. 855 the ball is of rubber and the seat is of composition, screwed 
into the pipe with a cage of the same metal, screwed 
to the seat. 

Fig. 856 is a section of a poppet-valve; the body 
is of cast-iron, but the valve and seat are of brass. 
The valve is guided by three feathers. The lift of 
the valve may be controlled by a set screw in the 
cover which admits of adjustment to varied lifts. 

Figs. 857 and 858 are the plan and section of a 
disk- valve for the air pump of a condensing steam 
engine. The valve consists of a disk of rubber ly- 
ing on a flat grating or perforated plate of brass, 
held in position between the grating and a spheri- 
cal guard by a central bolt. The shape of the guard 
gives a uniform flexure to the rubber in lifting, and 

an easy flow to the current of air and water. The rubber is not closely clamped 
between the guard and plate, as will be seen in the figure. The lower nut, after 
being screwed home, is riveted, and 
the upper nut usually pinned to pre- 
vent turning. The size of the aper- 
tures in the grating are adapted to the 
thickness of the rubber. With an ex- 
ternal diameter of opening of 6", and 




Fig. 856. 







O V 



Fig 857 



Fig. 



rubber ^" thick, the exterior ring of openings may be f " by f ", the lands or 

spaces between openings i" wide, and exterior lap of the rubber ^ inch. With 

larger diameters and larger openings thicker rubber must be used. This valve. 

is often made of a long strip or flap of rubber, on a suitable grating, with a 

curved guard attached on one side. For 

the common air-pump pressure, f" rubber 

is sufficient for apertures 1" X 4". With 

the use of backing and face plates on the 

rubber or leather flaps, gratings may be 

dispensed with (Fig. 859). Valves of this 

description— duplicate (Fig. 860) beneath 

the central pin and half circular in plan 

— are often used in pumps, and are called 

butterfly valves. It is the best practice to 

insert thimbles in the rubber (Fig. 859), fig. 859. 




3Y6 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



and the rivets connecting the plates pass through these thimbles, so that the 
rubber may be held but not tightly fastened — a rule applicable to all such valves. 
Check-valves (Figs. 861 and 862) are placed outside of large pumps to pre- 
vent the return of water in cases of accident to the pumps, and for facility of 




SPACE OCCUPIED BY THE 
VALVES. 



Fig. 860. 





Measure- 


Measure- 


SIZE. 


ment from 


ment from 


face to face 


end to end 




of flange. 


of hub. 


Inches. 






4 


llf 


13f 


5 


14i 


16 


6 


IH 


16 


8 


17f 


19 


10 


21i 


24 


12 


24i 


26i 


16 


29 


31 


18 


33 


35 


20 


35i 


38 


24 


39f 


39 



their examination. Valves of this kind open from the pressure of water be- 
neath, and, from a state of rest, with some suddenness and shock. To prevent 
this in large valves, there is a valve and small by-pass pipe, from one side to 
the other of the valves, by opening which the pressure on the two sides of the 
valve may be equalized, and the excess due to the starting of the pump dis- 
tributed. At many pumping works the by-pass is kept open except when 
necessary to get at the pumps. In case of accident to the pumps the flow 
through the by-pass would be comparatively small, and readily shut off. 




Fig. 861. 




Fig. 862. 



Valves controlled hy Hand. — Fig. 863 represents a side view of a water Mb- 
cock^ called a 7iose-bib, because the outlet end is fitted with a screw to adapt it 
to a hose. Without this screw it is a plain tib. If both ends of the cock are 
in the same line, it is called a stop-cock. The ends may not be fitted with 
screws, as in the figure ; the screws are sometimes female screws, and often 
with taper ends, to solder lead pipe to, or to drive into a cask. These cocks 
come under the common designation of plug-cocks, from their interior con- 
struction, which will b^ readily understood from the section given in Fig. 864. 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



377 






Fig. 863. 



Fig. 864. 



Fig. 865. 



They are used in both steam and water pipes, but not in the former when the 
use is frequent and daily, and then usually not over 2" in diameter of passage. 





Fig. 867. 

Fig. 865 is the side view of a compression water-bib, used when the pres- 
sure of the water is great. The section is somewhat similar to that of Fig. 
870, in which a rubber disk is forced against a metallic seat to shut off the 
flow. 

Fig. 866 is a side view of a common air-cock for boilers and steam work ; 
they are plugs in their construction, as are the cocks used in gas-fitting ; size of 
vent of air-cocks, -J to J inch diam- 
eter. 

Fig. 867 is an air-cock in which 
the valve is a plug of Jenkins's pat- 
ent composition, mostly rubber and 
graphite, on a flat seat of small sur- 
face. 

Figs. 868 and 869 are front 
views of globe - valves, so called 
from the shape of the body inclos- 
ing the valve. Fig. 868 is an an- 
gle globe-valve ; Fig. 869, a cross 
globe- valve used for cutting off the 
steam supply through the vertical fig. sgs. fig. f^w. 




378 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



pipe from the horizontal one ; the same purpose is attained by putting a 
straightway valve on the vertical pipe. The valve seats of all globe- valves, 
kept in stock and on sale, are now made of soft metal or of rubber, or of some 
mixture of it vulcanized ; soft rubber for cold water, hard rubber for hot water 
or steam. Fig. 870 is a front view of a globe-valve, with one side turned off 



DIMENSIONS OF GLOBE-VALVES 
IN COMMON USE, WITH SOFT 
SEATS. 



Diameter 

of opening 

in seat. 


Length 
over all. 


Diameter 
of globe. 


Body 
metal. 


i 


2i 


If 


Brass. 


i 


2i 


If 


" 


1 


2i 


n 


" 


i 


2f 


If 


(( 


f 


3i 


2i 


a 


1 


3f 


3i 


a 


n 


H 


3 


'■ 


n 


41 


^ 


" 


2 


51 


41 


" 


2i 


8 


6i 


Iron. 


3 


9f 


7i 


" 


3i 


10 


SI 


li 


4 


m 


H 


" 





13f 


m 


" 


6 


14f 


m 


" 


7 


16i 


14 


u 


8 


m 


14 


a 



c 



r^^ 



) 




to show its interior construction. 

The diaphragm <^ 6^ is in the form 

of a I — i, which divides the interior 

of the globe ; through the flat part fig. 870. 

is the aperture for the passage of 

the fluid covered by the valve, controlled by the handle and screw on its stem. 

The arrows show the direction of flow. 

Fig. 871 is a perspective of the valve, showing the grooves through which 
it is slipped on to the head on the steiji and held. The composition or rubber 
is in the form of a ring slipped into a circular groove in the bottom of the 
valve. In some valves the rubber ring is slid into a straight groove and re- 
tained by a nut on the stem, and the head of the stem is held to the valve by a 
nipple. 

When the seat is of soft metal it is run into a groove in the case, faced, and 
the valve formed with a circular chisel edge is forced down by the hand wheel 
into the soft metal. On account of the loss of head by the change of direction 
in flow — through the valve aperture — it is better to make it of a little larger 
diameter than that of the pipe. 

Figs. 872 and 873 are the plan and section of a steam valve of the South- 
wark Foundry pattern ; the seats and faces are of metal ground to a fit. The 
valve is guided by three wings, to w. The flow through globe-valves, as will be 
seen by their sections, have three changes of direction ; to avoid this, straight- 
way gates are almost invariably used on water mains. 

If the double-beat valve (Fig. 846 or 848) be mounted with a screw (like the 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 379 




380 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



above), as the pressure on the valve may be nearly balanced throughout its 
movement, it can be made of large area, and still be under the control of a 
hand wheel. 

GATE-VALVES. 

When the pressure is always on one side of the valve, it may be made as a 
plain gate, sliding in grooves, and raised up into a chamber ; but it is the usual 
practice to make these gates double, each being forced positively against faces. 

The earliest of these 
forms of gates are the 
Peet (Fig. 874) and the 
Coffin valve (Fig, 875). 

The first were usually 
made of small sizes, and 
for steam - pipes, it is 
shown in the figure shut ; 





Fig. 874. 



Fig. 875. 



the two side valves or disks are forced against their respective faces by the cone 
suspended between the disks, forced upward by its stem coming in contact with 
the bottom of the case ; as the gate is raised, the cone drops, the pressure is re- 
leased, and the valve easily drawn up into the chamber above, giving an un- 
obstructed passage through the body of the valve. 

In the Coffin valve the disks are suspended by two pivots in their backs to 
a wedge connected with the same. The wedge by its downward movement 
forces the disks outward against the seats, while by the upward motion this 
pressure is relieved. 

In the Pratt and Cady valve (Fig. 876) the seats are of soft metal which 
are cast in a mould and forced into position, making a tight fit with the body 
of the valve and a seat for the valve with smooth faces. In case of a cutting 
of the soft metal, it can be readily withdrawn and replaced by a new one. 

The above forms of gates, especially those of large sizes, are used as w^ater 
gates. Steam-valves are mostly of the globe pattern. 

Between the boilers and the steam-chest of an engine there should be a 
valve that can be shut promptly. The simplest is the damper-valve (Fig. 877), 
which is also used for the control of the draft in the smoke-pipe, but for a 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



381 



steam-pipe it is made with a closer 
nt; it never can be close, but 
sufficiently so to control or slow 
down the engine. A better valve 
is the usual Corliss steam-cylin- 
der valve, moved by a handle, or 
the register - valve (Fig. 878), 
which is held down by a spring, 
and is opened and shut like a 
register. These valves may be 
connected to a governor. 

Fig. 879 is a valve used in 
Nasmyth's works for steam ham- 
mers. Opposite the ports there 
are false ports or slight recesses 
in the shell. The steam enters 
at the end of the valve into the 
spaces a a ; the endwise pressure 
is received by a thrust bearing. 
This valve is so nearly balanced 
that it is readily moved by hand. 
To prevent excessive pres- 
sures, either of steam or water, a 
safety-valve is used (Fig. 880), 
which consists of a poppet-valve 
held down by a lever and weight. 
To determine the weight coun- 
terbalancing the pressure, put 
the valve and lever in position, 
attach the valve to the stem, and 
with a spring balance attached to 
the lever at its connection with 
the stem, find how much weight it takes to lift the valve-stem and lever ; this 
is a constant, which if divided by the area of valve at its lowest bearing diame- 






FiG. 877. 



Fig. 878. 



382 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



ter will give the constant pressure per square inch. The moyable weight is the 

P of a steelyard, and is to be estimated by multiplying fjp by the weight and 

dividing it by/ 5 and the 

area of the valve, to which 

is to be added the constant 

weight per square inch 

found above. 





Fig. 879. 



Fig. 880. 



The safest and simplest way is to put a blank flange on below the valve and 
with a force pump inject water to certain pressure, as shown by a steam gauge ; 
balance this pressure by a weight P on the lever ^and mark its distance from 
the fulcrum, which will give the weight per square inch on the valve at the 
position bf the P ; in the same way determine other points on the lever. 

Fig. 881 is what is termed a 
pop safety-valve ; the steam issu- 
ing as the valve rises, impinges on 
a cup surface to force the valve 
farther open. The valve is held 
down by a spring, but can be 
raised by the lever I. Valves of 
this kind are often inclosed in a 
locked box, that they may not be 
tampered with. 

To determine the weight on 
the spring, test it by raising the 
pressure in the boiler, as shown by 
the gauge, to. the height which is 
deemed safe ; adjust the valve to 
the lifting point by the nuts on 
the side bolts. If not in position 
on a boiler, test by a pump. 

Hydrants. — For water-service 
in connection with high-pressure 
mains. 

Fiff. 882 is a section of a post- 

Fir 881 • i» 

hydrant. The valve v consists of 
a series of leather disks bolted together and turned conical, which is brought in 
contact with a corresponding seat by the valve-rod and its screw at the top of 




MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



383 



the hydrant. The valve is opened by being forced down into the cavity of a 
branch of the pipe-main ; n is the nozzle for the coupling of the hose ; outside 

the main pipe of the hydrant there is a 
case, extending from near the line of valve 
to the ground line, called the hydrant 
or frost case, which prevents the hydrant 
from being lifted by the frost. Were 
the water left in the hydrant, it would 
freeze in most exposures during winter; 
the hydrant, when not in use, is therefore 
kept empty. This is effected by a small 
hole at a, which, when the valve is closed, 
is opened, and the water in the hydrant, if 
any, is discharged. This vent is closed by 
a slide attached to the valve-rod, when this 
last is moved down to open the main valve. 
Instead of leather for the valve-face, many 
valves are fitted with rubber ; there is also 
a great variety of valves for hydrant pur- 
poses — slides, poppets, disks — but in the 
arrangement of hydrants the illustration is 
the common one, although often without 
the frost case. 






Fig. 889. 



Riveted Joints^ as used in the Construction of Boilers. — Figs. 883-889 are 
forms of rivets with their proportions referred to the diameters next the heads. 
The thickness of the plate connected by rivets will be given in tables here- 



384 



MACHrN"E DESIGN AND MECHANICAL CONSTHUCTIONS. 




Fig. 890. 



after. Figs. 884 and 885 are the usual finish of rivets in hand-riveting ; Figs. 
886 and 887, when made by machines, in which, as the rivet-hole is slightly 

counter-sunk, the strength of the head is increased. 
Fig. 888 is a counter-sunk rivet, the head being 
flush with the outside of the plate. Fig. 889 is the 
head of a rivet, in, which a narrow strip at the edge 
is burred down by a chisel, or calked^ to make the 
joint between rivet and plate tight. 

Fig. 890 is a plan and section of a single-riveted 
lap-joint. Joints of this kind fail from the tear of the plate on the line of 
rivets if the rivets are too close, or the distance of the rivet to the outside of 
the plate too small, or by the shear of the rivets if they are too few. 

Rivet-holes. — Punching has an injurious effect upon plates ; but this injury 
(if the plates are not cracked by the process) is removed by afterward annealing 
them, or by rymering or drilling to the extent of y^ inch on the diameter. 

It is difficult to insure the correct spacing of the holes when they are made 
by punching. In the best boiler work the rivet-holes are drilled after the 
plates have been bent or flanged and put together in their proper places. This 
insures that the corresponding holes in the different plates shall be exactly op- 
posite to one another. After drilling, the plates are taken asunder and any 

burr that has been formed at the edges of the 
holes is removed. Eiveting may be performed 
either by hand hammering or by a machine. 
Hydraulic riveting machines are the best. 

For wrought-iron plates a tenacity of 47,000 
pounds is estimated per square inch in the di- 
rection of the fibre, and 40,000 pounds per 
square inch across the fibre ; steel plates, a te- 
nacity of 65,000 pounds per square inch. 

Shearing resistance of wrought-iron rivets 
is about equal to the tenacity of wrought-iron 
plates ; the shearing resistance of steel rivets is 
about eight tenths the tenacity of steel jolates. 

Fig. 891 shows the connection of two plates 
by means of single-riveted lap-joint. When 
the plates are arranged as shown in the lower 
section, the tension in the plates causes a bend- 
ing action on them at the lap. To avoid this, 
the plates have sometimes a set at the lap, as shown in the upper section. 

DIMENSIONS OF SINGLE-RIVETED LAP-JOINTS FOR BOILER WORK. 




Fig. 891. 





IRON PLATES AND IRON RIVETS. 


STEEL PLATES AND STEEL RIVETS. 


Thickness of Plate. 


Diam. of rivet. 


Pitch. 


Diam. of rivet. 


Pitch. 




.1 ' 


2f ^* 




2f 2. 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



385 



The eflSciency of the joint in the percentage of the strength of the plate is 
to be taken at the lowest figure, whether in tear or shear. In the above table 
it is 55 per cent. The distance between the edge of the plate and the centre 
of the outer rivet, as shown in the figures by /, is invariably one and a half time 
the diameter of the rivet. 




Fig. 892. 



The arrangement of the rivets in Fig. 892 is known as zigzag riveting, while 
that of Fig. 893 is chain riveting. 

DIMENSIONS OF DOUBLE-RIVETED LAP-JOINTS. 





IRON 


PLATES AND IRON RIVETS. 


STEEL 


PLATES AND STEEL RIVETS. 


t. 


d. 


P- 


c. 


cl. 


d. 


P- 


c. 


cl. 


t 


■H 


n 


11% 


n 


f 


2f 


If 


2 


iV 


f 


n 


If 


2 


if 


2f 


It^^ 


2i 


i 


If 


H 


H 


2i 


1 


2|f 


H 


2i 


A 


i 


3 


ii% 


2i 


II 


2| 


ii% 


2f 


i 


If 


H 


If 


2| 


1 


3 


If 


21 


li 


1 


3i 


If 


2i 


ll\ 


3i 


i-H 


2| 


f 


lA 


3-/^ 


m 


2f 


H 


3i 


If 


2f 


II 


li 


3A 


n 


2f 


ii% 


3f 


lit 


21 


i 


lA 


3f 


2 


21 


i| 


3i 


m 


3 


■H 


11 


31 


2tV 


3 


lA 


3| 


2 


3i 


1 


^~h 


4 


2-1% 


3i 


i| 


3f 


2i 


31 



The efficiency of joints in the above table is for iron plates 68 per cent, 
and steel, 04 per cent. 

In all riveted joints the distance between adjacent rivets, measured from cen- 
tre to centre, whether in the same or different rows^ should not be less than 2d. 

On the results of experiments on riveted joints, Professor'Kennedy has stated 
that the net section of metal in the plate, measured zigzag, should be from 30 
to 35 per cent, in excess of that measured straight across. This gives a diago- 
2pJ-_d 

3 * 

26 



nal pitch of 



386 



MACHIXE DESIGN AND MECHANICAL CONSTRUCTIONS. 



Treble-riveted Lap-joints. — In Fig. 894 the riveting is zigzag, and in Fig. 
895 chain. 




Fig. 894. Fig. 895. 

DIMENSIONS OF TREBLE-RIVETED LAP-JOINTS. 





IRON- ] 


PLATES AN! 


IROX RIVETS. 


STEEL PLATES ANE 


STEEL RIVETS. 


t. 


d. 


P- 


C. 


cl. 


' d. 


P- 


C. 


cl. 


f 


it 


3i 


If 


2i 


1 


3i 


1| 


2i 


\\ 


1 


3i 


If 


2i 


if 


3| 


If 


2f - 


f 


if 


3ii 


1| 


2| 


1 


3i 


lit 


2^ 


^ 


1 


3i 


lif 


2i 


ll\ 


3U 


lif 


2f 


1 


It^. 


4i 


2tV 


■ 2f 


H 


31 


2 


2f 


if 


H 


4A 


2tV 


21 


1^ 


4 


2tV 


21 


1 


lA 


4i 


2i 


21 


H 


4A 


2-^ 


3 


lIV 


li 


4ii 


2t 


3 


It^ 


4f 


2i 


3i 


H 


lA 


4| 


2i 


3i 


If 


4i 


21 


3i 



The efficiency of joints for iron plates is 74 per cent, and that of steel 70 per 
cent. The strength of a treble-riveted joint (Figs. 896 and 897) may be increased 
by making the pitch of the inner row of rivets one half that of the outer. 

d — I'llt for iron plates and iron rivets. 

d = 1*59^^ for steel plates and steel rivets. 

The pitch of a quadruple lap-joint will be the same. as in the last example. 

A butt joint with a single cover-strap (Fig. 898) is composed of two lap- 
joints, and is proportioned by the rules previously given for lap-joints. With 
this form of joint, the tension on the plates will tend to bend the cover-strap. 
For that reason the cover-strap is made thicker than the plates. If t^ = thick- 
ness of cover-strap and t = thickness of plates, then ^^ = l^t. For single- 
riveted butt-joints (Fig. 899), with double cover-straps, the usual rule for the 
thickness of each butt-strap is t^ = ^t. 

The diameter of the rivets for different thicknesses of plates may be as fol- 
lows : 

d =^ t -\- \ for iron plates and iron rivets. 

d =^ t -\- ^^ for steel plates and steel rivets. 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 387 




^r-1 : r--r-1 



Fig. 898. 



-l-^-e^~£l-^^c--*-l- 



FiG 899. 




Fig. 900. 



Fig. 90]. 



388 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



Double-riveted Butt-joints with Double Cover-straps (Fig. 900). — The pitch 
of the rivets are the same in each row. If alternate rivets in the outer rows be 
removed, as in Fig. 901, the arrangement is stronger. 

The diameter of the rivets (Fig. 900) for different thicknesses of plates may 
be as follows : 

d = t -{- ^-^ for iron plates and iron rivets. 

d =^ t -\-\ for steel plates and steel rivets. 

The diameter of the rivets (Fig. 901) for different thicknesses of plates may 
be as follows : 

d = t -\-^iov iron plates and iron rivets. 

d — t -{- ^-^ for steel plates and steel rivets. 

Fig. 902 is a triple-riveted butt-joint with double cover-plate, as butt-joints 
with double covers, one on each side of the plates, increase the shearing resist- 



^/^'r^^'^-^'^r^'/^'M \ M 



I 


o 




© 




o 


o 


© 


© 


© 


o 


o 




© 




o 


- 1 




Fig. 902. 



Fig. 905. 



ance of the rivets, so that rupture always takes place in the plates ; and as these 
can not bend, and there is considerable frictional resistance between the plates, 
the strength of the joint has been found to be more than that due to the net 
section of the plates between the rivets. 

Fig. 903 is a plan and section of a combined lap- and butt-joint. The pitch 
of the exterior rows is double that of the central one ; for a f " plate, 4" for the 
former and 2" for the latter. 

Fig. 904 is a section of joint, showing a better arrangement than Fig. 903, 
requiring less work, more easily calked, and of as much strength. 

Fig. 905 is the plan and section of a butt-joint when the cover is of T-iron— 
a not uncommon form of strengthening flues to resist collapse. 

Junction of more than Two Plates, shotvn in Plants and Sections (Figs. 906, 
907, and 908).— These become necessary when cross-joints intersect longitudi- 
nal ones. At these joints one or more of the plates are thinned or drawn out 
by forging. 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



389 



Fig. 909 is the plan and section of an angular connection of plates by the 
means of angle-iron ; this should be a little thicker than the plates, and its 
width four times the diameter of the rivets. 




Fig. 906. 




J 


©i 


m 


©r 



^^1^ 



■o.^.o^.r^.^. 



Fig. 908. 



Figs. 910, 911, and 912 are sections of angular connections by flanging the 
plates. The iron should be good and the curvature easy ; inside radius at least 
four times the thickness of the plates. 



r\ ^-^ r~\. 






Fig. 909. 



Fig. 910. 



Fig. 911. 



Fig. 912. 



Figs. 913 and 914 are sections of joints of cylinders of unequal diameters, 
or surfaces not in line with each other. 

Figs. 915, 916, and 917 are sections of fire-box legs. 




Fig. 913. 




Fig. 914. 



Fig. 915. 



Fig. 916. 



In all connections provisions are to be made for the means of holding the 
head of the rivet, and for riveting and for calking the joints. 

Fig. 918 is the perspective view of a horizontal tubular boiler, very largely 
used with anthracite as a fuel, but with bituminous coal the tubes should be of 
the larger diameters. 

The proportions of the boiler vary with the requirements of their position, 
and with the views of the mechanical engineer or maker constructing them. 
Many use a dome, but it is the better practice to increase the diameter of the 
boiler an inch or two for more steam space, if necessary, and insert a dry pipe 
in the space. Those in most extensive use are with shells of 4 to 5 feet inside 
diameter and 3" to 3^' tubes, 14 to 16 feet long. The line of the top of the 
upper tubes is usually about y^ of the diameter of the boiler above its centre ; 
tubes arranged in vertical rows, with distance between tubes ^ of their diam- 



390 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



eter. By keeping the average distance the same, but making them farther 
apart at the top row, say -|- diameter, and the lowest J diameter, so that the line 
of tubes is radial instead of vertical, the outside of the tube will meet the flame 
better, and at the same time be more readily cleaned with a brush. 




Fig. 918. 



The following table is from Barr, showing the greatest number of tubes 
which should be put in a given head, no tube to come nearer to the shell than 
2" for boilers of small diameter, 2^" for medium, and 3" for the larger series : 



Diameters of 


Number of Tubes (outside diameter). 


bodies inside, 
















in inches. 


3 in. 


3iin. 


3iin. 


3f in. 


4 in. 


4iin. 


5 in. 


36 


26 


23 


20 


19 


16 


12 


10 


40 


34 


34 


25 


23 


20 


14 


14 


44 


48 . 


36 


32 


25 


25 


20 


16 


48 


50 


38 


36 


30 


26 


21 


18 


52 


57 


50 


48 


38 


32 


26 


21 


56 


72 


57 


55 


48 


41 


32 


23 


60 


80 


68 


62 


55 


46 


36 


30 



A is the man-hole^ to enable the mechanic to get into the boiler to examine 
it. It consists of a cast-iron frame, bolted to the shell of the boiler, with an 
elliptical opening usually 9" X 15" in the clear ; the valve laps about 1" on each 
side. In closing the opening the valve is passed down into the boiler, and is 
brought up against the valve-seat, where it is held by its stem passing up 
through a movable yoke, and brought up tight by a nut and screw. The joint 
is made with a gasket or with sheet-rubber. The man -hole is often placed in 
one of the boiler heads, or at one side, above the tubes, for convenience of 
access. B is the hand-hole, of the same general construction as the man-hole, 
but smaller, to enable the fireman to clean the boiler. Formerly this hand- 
hole was quite small, but of late the practice is to place a hand-hole at the rear 
end of the boiler and a man-hole at the front in the position B. This is for the 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



391 



readier cleaning and repairs of the boiler ; it reduces the number of tubes by 
four, but without detriment to the evaporation of the boiler ; and by taking off 
both covers one can look directly through the boiler. As the hand-hole is ex- 
posed to the flame and products of combustion, it is well to make it small, say 
3" X 5" ; III are lugs by which the boilers are supported on the brickwork, 
but they are in the way in getting the boiler through a confined space, and 
rest so solidly on the brickwork that it often becomes cracked by the expansion 
of the boiler. It is preferable that the boiler should be hung as in Fig. 
1252. In the head above the tubes there are rivet-heads, and also in the sides 
back of the first seams at each end. These are for the attachment of diagonal 
stays. The tubes themselves serve as stays in the lower part of the boiler, but 
above, the flat surface needs somethiug to prevent the head from moving out 
under pressure. The stays are made of round or flat iron (see Fig. 1249), 
bolted directly to the shell, the round part being flattened, and connected by 
a yoke and pin to a crow-foot or piece of angle-iron attached to the head. 
The stays are from f " to 1 J" diameter or equivalent sections. 

To determine the diameter of stays in square inches multiply the area sup- 
ported by the stays and divide the product by 7,000 for wrought-iron stays not 
welded ; and for steel stays, under same condition, by 9,000 ; but if welded or 
otherwise worked after heating, take three fourths of above. 

Forms of Boiler Stays. — Fig. 919 is a direct stay in which a hole is drilled 
through the head of a boiler ; the stay has an outside nut of a thickness equal 





Fig. 919. 



Fig. 920. 




Fig. 922. 



to the diameter of the screwed part, and the inside 

or locked nut three fourths of this thickness. The 

plates are stiffened by inside and outside washers. 

If the stay is diagonal it is usual to increase its area in the, proportion of the 

length of the diagonal to that of the horizontal. 

The flat parallel surfaces surrounding the fire-boxes of locomotive and 
marine boilers are secured by means of screwed stays, so called because they 
are screwed into the plates (Figs. 920, 921, and 922). After being screwed 
into the plates their ends are riveted. The fracture of the stays is detected by 
the escape of steam through the small holes which are sometimes drilled through 
the screwed parts. The screwed stays for locomotive boilers are usually placed 
about 4 inches apart, centre to centre, and vary in diameter from f inch to 1 
inch. 

In marine boilers the screwed stays are made of steel, and they vary in 
diameter from 1^ inch to l-f inch. They are provided with washers and 
nuts at each end, as shown at Fig. 919. The nuts have a thickness of from 
five eighths to three fourths the diameter of the stay. 



392 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 




Fie. 923. 



In the steel-screwed stays the ends of these stays 
are drilled as shown, and after they are screwed into 
place a steel drift is driven into the holes by slight 
blows to expand the ends tightly into the plates to 
make steam-tight joints. 

Fig. 923 is a gusset stay, used in angles, consist- 
ing of a triangular plate with the edges flanged and 
riveted to the shell. 



BARR'S 


PROPORTIONS FOR STAY-BOLTS FOR 


FLAT SURFACES. 




CENTRE TO CENTRE OF STAY-BOLTS IN 


SQUARE INCHES. 


Pressure per 
square inch. 






i" plate. 


-^" plate. 


r' plate. 


^" plate. 


i" plate. 


60 


5f 


n 


n 


8i 


9 


80 


H 


^ 


Qh 


n 


n 


100 


4i 


4f 


5J 


^ 


7 


120 


3| 


4i 


5 


5| 


n 


140 


3f 


^ 


4f 


5J 


6 




Fig. 924. 



Stationary boilers as 
designed and built un- 
der the direction of 
John E. Codman, M. E., 
for the Philadelphia" 
Water- Works, of which 
Eig. 924 is a transverse 
section and one half 
cross - section through 
fire-box, and one half 
front view without the 
doors. Fig. 925 is a 
longitudinal section. 
These boilers have inside 
fire-boxes, and the out- 
side is protected by a 
covering of brick or 
some clothing of a non- 
conducting material to 
prevent radiation. The 
corrugated furnaces are 
made in this country 
by the Continental Iron 
Works, Brooklyn, of an 
inside diameter of from 
30" to 60" and up to 32 
feet long. 

Rules for calculat- 
ing the pressure allowa- 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 393 



i ( 




394 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



loans xg 




MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



395 



ble on corrugated furnaces adopted by the Board of United States Supervising 

Inspectors : 

Corrugations to be 6 inches pitch and H inch deep. 

14000 ^ , . ... . . 

— yy— X T = working pressure in pounds per square inch. 

T = thickness in inches. 

D = mean diameter in inches. 

Example. — Given a corrugated 
furnace 40 inches mean diameter 
to carry 175 pounds working pres- 
sure, required the thickness of 
metal. 



P. XD. 



= thickness. 



175 X 40 




Fig. 927. 



__U_10i^ 



14000 ""' 14000 

= \ inch thickness of metal. 
* Figs. 926 to 929 are drawings 
of a locomotive boiler as designed 
and constructed by Mr. Buchanan 
for express passenger locomotives 
for the N. Y. C. and H. E. R. R, 
Fig. 926 is a longitudinal section 
Fig. 927 a transverse section of 
one half the fire-box and an eleva- 
tion of one half of that end. Fig. 
928 of the fire-box with cover off, 
and showing one half of tlie tubes. 
Fig. 929 are details of the riveting. 

Figs. 930 and 931 are drawings 
of a marine boiler of the United 
States steamer Minneapolis, show- 
ing longitudinal and cross-section 
of fire-box end. When locomo- 
tive or marine boilers are used as 
stationary their outsides should be 
protected as the Codman boiler 
(page 392). 

Water-tube boilers are now in 
extensive use, economical in evap- 
oration, and popular from the 
comparative safety from explosion. 
Some of the numerous and varied 
forms will be found illustrated in 
the Appendix. 

Flue Boilers.— Where bitumi- 
nous coal is used, small tubes be- 
come clogged with soot; it was 
therefore customary to construct boilers with large tubes or flues of boiler-iron 
riveted together, which sometimes failed from collapse. It may be considered 




Fig. 928. 



396 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



ample to make the tubes subject to outside stress 50 per cent thicker than for 
bursting, especially for the large drawn tubes now made. Mr. Fairbairn, from 
his experiments, considered it necessary to make the joints of tubes subject to 
collapse as in Figs. 932 and 933. 




Fig 929. 

Fig. 934 is a section of the Shapley boiler, as made by the Knowles Steam- 
Pump Works — a good form of upright- boiler, with the head of the boiler 
stayed by rods directly to the crown-sheet, beneath which short tubes or nip- 
ples connect the fire-box with a cast iron smoke-box around the boiler and the 
draft is downward through vertical tubes to a smoke-5ox in the base. The 
crown-sheet and downward draft tubes are well covered by water. It is an ad- 
mirable illustration for the draughtsman of how a boiler in action may be 
represented. 

The usual form of upright boiler consists of a fire-box, extending a little 
above the door, and tubes extending from the crown-sheet to the top-head, 
over which there is a bonnet to receive the smoke, which is led off by a smoke- 



MAC^IXE DESIGN AND MECHANICAL CONSTRUCTIONS. 397 




398 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



pipe. It is a convenient form for furnishing steam for a small power, but not 
as economical in combustion, and apt to prime — that is, take up water with 
the steam, and leak at the top of the tube exposed in the smoke-box. 

The common vertical boilers are 
from 2 feet 6" to 4 feet 6" outside 
diameter of shell, with water space in 
of ^" to 3" ; extreme height of 
boiler from 2 to 2-|- times the outside 
diameter of fire-box ; tubes from 2" to 
2^" diameter, and spaced from 1" to 
ly apart. Water-line from 10" to 15" 
above crown-sheet. 

There is supposed to be a propor- 
tion between the tube sectional area 
and the grate-surface, say from \ in 
the horizontal to ^ in the verti- 
cal ; but this rule is entirely em- 
pirical. There is also a propor- 
tion of grate to heating surface ; 
but only the same class of boilers 
can be compared with each other, 
as fire-box surface — and that ex- 
posed directly to the flame — is 
much more effective than that of 
the tubes, and the products of 





l^^^y 1^ M 



Fig. 932. 




Fig. 934. 



Fig. 933. 



combustion escape at much different temperatures in different boilers. 

Flange Connections for Steam and Water Pipe. — Fig. 935 is a section of a 
flanged connection of a cast-iron pipe of the most usual form, but some thick- 
en or re-enforce the pipe a little for 1" to 2" in length next the flange ; but if 
there is a good fillet in the angle of the fiange it is unnecessary. 

The flanges are almost invariably faced, and joints made with red and white 
lead, or a sheet-rubber washer, or with corrugated copper gaskets (Fig. 936) 
of very thin sheet copper, which are used of full diameter of flanges on rough 
boiler joints and red-lead putty ; but for faced surfaces thin paint will insure a 
perfect joint inside the bolts. 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



399 





Fig. 935. 



Fig. 936. 



DIMENSIONS OF PIPE FLANGES AND CAST-IRON PIPES. 
J. E. Codraan, M. E., Pro. Engrs. Club, Philadelphia. 



Diam. 


DIAMETER OF 
FLANGK. 


Diameter 


Diam. 


No of 


Thick- 


THICKNESS OF PIPE. 


Weight per 


Weight 


of 






of bolt 
circle. 


of 
bolt. 


bolts. 


ness of 
flange. 






foot with- 
out flange. 


of flange 


pipe. 


Diagr. 


Form. 


Inches. 


Dec. 


and bolts. 


2 


^ 


6J 


4f 


f 


4 


1 


1 


0-373 


6-96 


4-41 


3 


n 




5| 


f 


4 


1 


M 


0-396 


11-16 


5 93 


4 


9 


81 


7 


f 


6 


h 


iV 


0-420 


15-84 


7-66 


5 


n 




8 


f 


6 


f 


^ 


0-443 


21-00 


9-63 


6 


lOf 


11 


9i 


f 


8 


f 


if 


0-466 


26-64 


11-82 


8 


131 




llf 


f 


8 


H 


i ' 


0-511 


39-36 


16-91 


10 


m 


15i 


13^ 


f 


10 


i 


1% 


0-557 


54-00 


23-00 


12 


17| 


.... 


15f 


1 


12 


if 


if 


0-603 


70-56 


30-13 


14 


20 


. . . 


18 


1 


14 


1 


u 


0-649 


89-04 


38-34 


16 


22 


221 


20 


i 


16 


H, 


H 


0-695 


109-44 


47-70 


18 


24 


24i 


221 


i 


16 


n 


f 


0-741 


131-76 


58-23 


20 


27 


26f 


24i 




18 


ii% 


If 


0-787 


156-00 


70-00 


22 


28| 


29 


26i 




20 


n 


u 


833 


182-16 


83-05 


24 


31i 


.... 


28f 




22 


h\ 


i 


0-879 


210-24 


97-42 


26 


33i 


33J 


31 




24 


If 


¥e- 


0-925 


240-24 


113-18 


28 


35^ 


35| 


331 




24 


ii^ 


U 


0-971 


272-16 


130-35 


30 


38 





35i 




26 


ii^ 


1 


1017 


306-00 


149-00 


32 


40 


m 


37i 


n 


28 


If 


ll^. 


1-063 


341-76 


169-17 


34 


421 




40 


n 


30 


if^ 


n 


1-109 


379-44 


190-90 


36 


45 


44f 


42 


H 


32 


If 


h%- 


1-155 


419-04 


214-26 


38 


47 




44 


H 


32 


ll6 


i-fV 


1-201 


460-56 


239-27 


40 


49 


49i 


46 


n 


34 


H 


n 


1-247 


504-00 


266-00 


42 


51J 


51i 


48i 


H 


34 


lit 


iiV 


1-293 


549-36 


294-49 


44 


53^ 




50i 


n 


36 


2 


m 


1-339 


596-64 


324-78 


46 


55f 


56 


52f 


n 


38 


2iV 


If 


1.385 


645-84 


356-94 


48 


58 


58i 


55 


n 


40 


2i 


iiV 


1-431 


696-96 


391-00 



Fig. 937 is a section of the joint used by Sir William Armstrong for the 
pipes of his accumulator. For a working pressure of 800 pounds per square 
inch, pipes of 5" diameter are made 1" thick and tested to 3,000 pounds per 
square inch. The flange is elliptical, and there are but two bolts ; one pipe 
slightly enters the other, forming a dovetailed recess in which is placed a gutta- 
percha ring J" in diameter. 

Figs. 938 and 939 are sections of two other forms of cast-iron flanged pipes, 
both with projections fitting into grooves. The packing in Fig. 939 is a ring 
of lead. In Siemens's air reservoirs, where the pressure sustained by steel rings 
is 1,000 pounds per square inch, the joint is made by turning a V-groove in 



400 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



the face of the rings, and placing in it a ring of annealed copper -f-^" diameter. 
This form is adopted by many mechanics for forming flanged joints even for 
steam purposes. 




Fig. 937. 




Fig. 938. 



Fig. 939. 



Figs. 940, 941, and 942 are steam-pipe joints, as used at the works of the 
Narragansett Electric Lighting Company, where it is essential to maintain the 




CALKING EDGE 





Fig. 940. 



Fig. 941. 



Fig. 942. 



full boiler pressure permanently. Fig. 940 is a joint between two wrought-iron 

pipes ; Fig. 941 that between a wrought-iron and cast-iron pipe. In both these 
the joints are calked. In Fig. 942, between two cast- 
iron pipes, the joint is made by a gasket of vulcanized 
asbestos placed in a recess of the female joint. 

Fig. 943 is a connection between wrought-iron plates, 
in which the joint is made by a copper ring brazed to- 
gether. 

Wrought -Iron Pipe Connections. — With the present 
cost of wrought-iron pipes, they are almost invariably 
used for the conveyance of steam, but are more liable 
to rust for water purposes than . cast- iron. Wrought- 
iron pipes are either butt-welded or lap- welded. It is a 

mere question of manufacture. It is difficult to make a lap-welded tube less 

than 1^" diameter, and therefore below this size they are usually butt- welded ; 

but this size and above, lap-welded. 

Wrought-iron j^ipes of the smaller 

diameters are connected by socket-sleeve 

couplings (Fig. 944), of wrought-iron, 

of large diameters, by cast-iron flanges 

screwed to the ends of the pipes to be 

coupled. The screw in the coupling is 

tapped parallel usually, but the ends of 




Fig. 943. 




MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



401 



the tubes are cut with a taper thread, uniform with all makers, of 1 in 32 to 
the axis. The length of the screwed portion varies with the diameter. 




Fig. 944. 



Fig. 94.5. 



Fig. 945 is the longitudinal section of tapering tube-end with the screw 
thread as actually formed, and considered standard by the late Robert Briggs, 
C. E., in his " Treatise on Warming Buildings by Steam." It is shown in the 
figure double full size for a nominal 2^" tube. 

DIMENSIONS OF WROUGHT TUBES AND COUPLINGS. 



DIAMETER OF 


TUBE. 


CIRCUMFERENCE. 


SCREWED ENDS. 


Weight 
per foot 
in length. 


COUPLINGS. 


Nomi- 
nal in- 
side. 


Actual in- 
side. 


Actual out- 
side. 


Inside. 


Outside. 


No. of 
threads 
perend. 


Length of 
screw. 


Outside 
diameter. 


Length. 


In. 

i 


In. 

0-27 


In. 

0-41 


In. 

0-85 


In. 

1-27 


lu. 

27 


In. 

0-19 


Lts. 

0-24 


In. 

0-55 


In. 

1 


i 


0-86 


0'04 


1-14 


1-70 


18 


0-29 


0-42 


0-70 


1 


f 


0-49 


0-67 


1-55 


2-12 


18 


0-80 


0-56 


0-88 


1 


+ 


0-62 


0-84 


1-96 


2-65 


14 


0-39 


0-84 


1-01 


lA 


1 


0-82 


1-05 


2-59 


8-30 


14 


0-40 


1-18 


1-24 


If 


1 


1-05 


1-81 


8-29 


4-18 


Hi 


0-51 


1-67 


1-53 


If 


n 


1-88 


1-66 


4-88 


5-21 


IH 


0-54 


2-26 


1-89 


H 


H 


1-61 


1-90 


5-06 


5-97 


m 


0-55 


2-69 


2-17 


2 


2 


2-07 


2-87 


6 49 


7-46 


IH 


0-58 


3-67 


2-68 


2i 


2i 
8 


2-47 
8-07 


2-87 
8-50 


7-75 
9-64 


9-08 
11 00 


8 
8 


0-89 
0-95 


5-77 
7-55 


8-19 

3-87 


3 


3i 
4 


8-55 
4-08 


4-00 
4-50 


11-15 
12-65 


12-57 
14-14 


8 
8 


1-00 
1-05 


9-06 
10-78 


4-40 
4-99 


H - 


4i 

5 

6 

7 


4-51 
5-04 
6-06 

7-02 


5-00 
5-56 
6-62 

7-62 


14-15 
15-85 
19-05 
22-06 


15-71 
17-47 
20-81 
23-95 


8 
8 
8 
8 


1-10 
1-16 
1-26 
1-36 


12-49 
14-56 
18-77 
23-41 


5-49 
6-19 
7-24 
8-86 


3| 
3i 
3f 
4 


8 


7-98 


8-62 


25-08 


27-10 


8 


1-46 


28-35 


9-49 


4i 


9 


9-00 


9-69 


28-28 


80-43 


8 


1-57 


84-08 


10-54 


41 


10 


10-02 


10 -7,5 


81-47 


33-77 


8 


1-68 


40-64 


11-72 


5 



Figs. 94G, 947, 948, also from Briggs's treatise, give the dimensions of the 
parts of elbows, tees, crosses, and branches. Fig. 947 shows the parts of an 
elbow designated by letters in Fig. 946, and Fig. 948 shows the applicability of 
the same to tees and crosses. The scale is one quaT-ter full size ; if much used, 
it would be better for the draughtsman to construct one of full size. The 
dimensions are obtained by measuring from the base or zero to the inclined 
lines, on ordinates corresponding to the inside diameter of pipe required. 

When pipes are thus put together in lengths, with couplings, it is frequently 
impossible to take out a length of pipe for repairs or alterations without break- 
27 



402 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



ing a coupling or fitting ; provision is made for disconnections by the insertion 
of a union or unions in the line. 




Fig. 946. 



Fig. 949 is an exterior view, and Fig. 950 a section, of the common mal- 
leable-iron union ; p and p' are the halves into which the tube is screwed, and 
the joint is made by a male and female coupling. The male, h, turning on a 
flange on the tube p^ is screwed to the other half of the coupling, and the joint 
is made tight by a rubber washer, shown in black. These unions are used only 




Fig. 949. 





Fig. 951. 



in the smaller sizes of pipes. The flange coupling (Fig. 951) is preferred by 
most fitters, and they are made of diameters up to 14" ; the thickness is about 
one half that of the length of a coupling of the same diameter. The bolts are 
from f " to f ", and spaced somewhat larger than that given for cast-iron flanges. 
The width of flange is such as to admit of the head and nut of the bolt without 
projection beyond the edge of the flange. 

Fig. 952 is a common cast-iron flange, and with about the same proportions 
as in Fig. 951. When the lines are long, and provision can not be made by 
bends for the expansion and contraction of pipes under changes of temperature, 
a fitting like a stuffing-box is often used, the end of one of the tubes being 
attached to the box, and the other sliding in and out like a piston-rod; some- 
times expansion is permitted by two flexible flanges, admitting of a sort of bel- 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



403 



lows-like movement ; sometimes by a U-connection between pipes, as in Fig. 
933, or a succession of corrugations. 

Fig. 953 is a soldering union ; the ring, I, is like that of the male coupling 
(Fig. 950), which is screwed directly to the wrought-iron pipe, while a is a 
brass tube, with a shoulder on the bottom on which the coupling, a, turns, and 
a lead pipe is soldered to the tube. If it is not necessary to break the joints, a 
soldering nipple (Fig. 954) only is necessary, one end of which is screwed into 
the wrought-iron pipe, and the other soldered to the lead pipe. 







Fig. 952. 



Fig. 953. 



Fig. 954. 



Fig. 955. 



Fig. 955 is a close nippile ; Fig. 956 is a shoulder nipple. 

If the uncut part of the tube is longer than in the figure, it is called a long 
nipple ; they serve the purpose of short pipes. 

Fig. 957 is a husliing. There is a thread cut inside. It is screwed into a 
coupling, and the pipe that is screwed into the bushing must be smaller in 
diameter than that connected with the coupling. The service of the bushing 






Fig. 956. 



Fig. 957, 



Fig. 958. 



Fig. 959. 



is to connect pipes of different diameters, but the reduction of one side or arm 
of a coupling tee, or cross is better. 

Fig. 958 is a plug to close up the end of a pipe by screwing it into the 
coupling ; caps are used for the same purpose ; half-couplings with one end 
closed, or hlanlc flanges — that is, flanges covering the aperture in the pipe — 
bolted to a flange on the end of a pipe. 

It will be seen by Fig. 947 that the cast-iron elbow makes a very short turn, 
with considerable obstruction to the flow of the fluid through it. Fig. 959 is 
an elbow in which the obstruction is very much reduced. It consists of a 
piece of wrought-iron pipe curved to an easy radius ; and, as a general rule, it 
may be said that for the connection of pipes not in a line with each other, it is 
better to bend the pipe, if possible, than make angles by cast-iron elbows. 

Figs. 960, 961, and 962 are oblong, spiral, and flat coils, showing the extent 
to which pipe can be bent by machinery, and are used largely for heaters and 
in refrigerating plants. 



404 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 




Fig. 960. 



Figs. 963 and 964 are a tee and a cross, as used in connections of hj^draulic 
presses, made of composition. The tubes are of wrought-iron, extra thick. 
The usual dimensions for such are as follows : 



Outside diameter 


f" 


7" 
8 


1" 


Inside diameter 


r 





The joints are made by leather washers, square ends on square seats. 




Fig. 965. 



Fig. 966. 



Fig. 964. 



In Leland's lead-pipe coupling (Figs. 965 and 966) a double-cone ring is 
inserted between the ends of the pipes to be coupled, and they are brought to- 




. <=^ 



^F» . 



IT 



Fig. 967. 



Fig. 970. 



gether by the common wrought-iron pipe-union, the inner surfaces of which 
are adapted to the surfaces of the lead pipe, compressing it between the pipe 
and the cone. 

Figs. 967 and 968 are a section and plan for a similar joint of steel water 
pipe. 



MACHIXE DESIGN AND MECHANICAL CONSTRUCTIONS. 



405 



Figs. 969 and 970 are Petit's pipe joint used in the water system of the camp 
at Chalons. A rubber ring is inserted in the short bell, one clamp being con- 
nected ; the other is brought over and secured, compressing the rubber, making 
a tight and a slightly flexible joint, easily taken apart and put together. 

Fig. 971 is a flexible steam joint consisting of a ball and socket carefully 
turned and then ground to a close fit, to be connected with wrought-iron pipe. 

The earlier flexible joints for water mains were turned and fitted, but about 





Fio. 971. 



1870 John T. Ward, C. E., introduced a ball-and-socket pipe in which the 
socket was turned but the ball was fitted by a lead packing run in. There was 
some danger to the socket by the stress of the ball if the movement was in ex- 
cess of that contemplated. Mr. Ward in his late designs made stops o o (Fig. 
972) to prevent this. Other engineers have re-enforced the ball by a hoop, of 
which Fig. 973 is an example, from the "Transactions" A. S. C. E., designed 
by James C. Duane, C. E., and laid beneath the East Eiver from New York 
city to Ward's Island. 

Fig. 974 is a section and elevation of a flexible joint for a submerged steel 
water main used at Toronto, Ontario. This joint is 5 feet in diameter, con- 



^3lJ WroTight lifon */] 
■/,/,///,■///{ Band ^ 3. 




note: 

a band seat to be turned 
truly cylindrical and 
band securely shrunk on 

b corners to be rounded 
off as shown , 

Fig. 973. 




sisting of two parts, one part having a turned spherical section riveted to the 
sti-aight pipe ; the other part is a socket, on the inside of which are two U- 
shaped sections, one riveted to the sheet-iron of the socket and the other to a 
flange fastened to another flange on the end of the socket ; these U-shaped 



406 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



rims are filled with soft pig lead projecting I of an inch beyond the rim ; the 
lead joint bears against the spherical section and makes a close yet flexible 



JYood P^ck/rTg 




f/snae 



^_ 






f 


^ 




< 


o^ 




-^ 


»^ 


^ 


1 


«: 






■3 


p 






io 


o ^ 








1 







o 






3 


b 




» 


o 















o 






>| 


P 







o 




^ 


3 
3I 



1 


.1 


O 




^ 












o 




'^ 





P 







O 




c: 


















•^ 






00 0000 0000 





o 




^ 







1 







o 




'k. 


b 







o 




I 


oC 


b 









o 









L 




Q 








D 







o 














o 






oi 


P 






















%l 


oo 

















U 




^ — 


i 





: -" 


■^ 



Fig. 974. 




joint. The space between the two flanges on the socket end is made tight 
by a wood packing. 

Fig. 975 is the section of a ball-joint used as a connection for the 12" steel 
pipe for a temporary supply of water to Liverpool and sunk beneath the Mer- 
sey, which was connected for a length of 
800 feet on the shore and drawn across 
the river by the united forces of horses 
and a steam winch in twenty-eight min- 
utes. The ball is of cast-iron, turned, and 
has a socket of the same material, with a 
joint of cast lead, for which two holes are 
shown — one for running the metal and 
the other for the vent. 

Governors. — In the running of all ma- 
chinery there are variations of speed, due to varying powers and resistances 
caused by increase or decrease in the pressure producing the power, as of 
steam or water, or in the resistances of the machinery, from more or less being 
brought into action, or through inequalities of work done. To maintain the 
speeds at as much uniformity as possible, governors are used, which, applied 
to steam engines or wd^ter- wheels, open or close valves or gates, and increase or 
reduce the supply of steam or water to the cylinders or wheels, according to 
the varying necessities. The ordinary governor (Fig. 976) consists of two 
heavy balls, suspended by links from a spindle, and caused to revolve by some 
connection with the shaft of the motor. In the figure the governor is driven 
by a belt-connection to the pulley, ;?, bevel-geared to the governor. When at 
rest, the balls hang close to the spindle, but when in motion the balls rise by 



Fig. 975. 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



407 



the centrifugal force. When the motor is running at its established speed, for 
which the pulley is to be adjusted, the links assume a position nearly at 45° 
with the spindle. If the speed falls off, the balls fall, and, acting on the lever, 
as shown in side view, open the valve or gate controlling the passage of steam 
to tlie cylinder or water to the wheel ; if the speed rises, the balls rise and close 
the valve or gate. The lever does not always connect directly with the gate, 
nor is there always a lever, but the rise or fall of the balls acts on some mech- 
anism which performs the function of reducing or increasing the supply of 
steam or water. 

The size of the balls depends somewhat on the work to be done, the resist- 
ance to be overcome in the movement of the gate and connections, and may be 
much reduced if this work is thrown on some other mechanism, which is usu- 
ally the case in the regulation of water-wheels ; while for steam engines the 





Fig. 9' 



Fig. 977. 



work to be done by the governor is reduced by balancing the steam- valve, or 
to the merely releasing of a trip, cuts off the movement of the valve at any 
point of stroke. 

The common governor (Fig. 976) is sufficient for the regulation of drop 
cut-off engines like the Corliss (Figs. 422, 423), but for slide-valve engines with 
throttle regulation the Porter governor (Fig. 977) is better adapted; the balls 
of this governor are comparatively light, but they are connected to a heavy cen- 
tral weight by levers, the same as those connecting the balls with the spindle. 

Of late it has become very common to run engines at very high speeds, be- 
yond that possible to be obtained by drop cut-offs ; and light slide-valves are 
used in which the governors act by shifting the cams (actuating the valves) 
placed within the pulley or fly-wheel. Fig. 978 is an elevation of one of this 
class of governors — the Westinghouse. The disk A is cast solid and keyed to 
one of the cranks. The loose eccentric is suspended by the arm c from the 
pin fZ, around which it has a motion of adjustment ; B B are the governor 
weights, pivoted on the pins l b ; one of the weights is connected to the ec- 



408 



MACHINE DESIGX AND MECHANICAL CONSTRUCTIONS. 



centric by the link /, and both weights are connected to operate in unison by 
the link e. Coil springs, D D, furnish the centripetal ot returning force. The 
eccentric encircles the shaft S, the opening being elongated to admit of the 




Fig. 978. 




proper motion. The stops s s limit the motion of the weights. Fig. 979 shows 
the governor in the position of latest cut-off. The^^overnor weights are shown 
in the position of rest, whereby the eccentric is thrown over to its position of 
greatest eccentricity, giving a maximum travel to the valve corresponding to a 
cut-off of about f stroke. The parts of the governor remain in this position 
till the engine is within a few revolutions of its full speed. The centrifugal 
force of the Aveights then overbalances the tension of the springs, and the 
weights move outward, reducing the travel of the eccentric and valve, conse- 
quently shortening the cut-off and closing the exhaust earlier, thus increasing 
the compression curve and preserving greater economy in running the engine. 

Fly- Wheels. — In most machinery there are great inequalities of movements, 
from the great difference in power exerted or resistances overcome, and in the 
application of the force, as through cranks. To obviate this, fly-wheels are 
used, which absorb energy in one part of their revolution and give it out at 
another, or by their mass in movement overcome resistances, as in the punch- 
ing, shearing, and rolling of metal, which comes only periodically, and is much 
in excess of that usually required. In addition, fly-wheels give governors time 
to act, and consequently the motion is more uniform and constant. 

All shafting, pulleys, and machines in movement act as regulators, and 
where the resistances vary largely on machines they require independent fly- 
wheels. In addition, friction, hygrometric, and other conditions vary so much 
at different times, even with the same engines, that it is impossible to get data 
for an estimate by any mathematical formula embracing the conditions. From 
the experience of the best mechanical engineers, and from published examples 
of constructions, are deduced the following rules, applicable to common prac- 
tice for the fly-wheels of steam engines : The diameter of fly-wheel to be 4 
times that of the stroke of the engine, and the entire weight of the wheel 40 
times the square root of the diameter, its exterior velocity being about 5,000 
feet per minute ; if less or more, increase or reduce the weight inversely as the 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



409 



velocity. The rim is generally a little less than f of the whole weight, but the 
arms should be made strong in view of the fact that a great strain may be 
produced in them by any suddenly interposed obstacle. For rolling-mill en- 
gines, Prof. C. B. Richards takes the weight of the fly-wheel at 60 times the 
square of the diameter of the cylinder, and the diameter of the wheel 5 times 
that of the stroke, and rim velocity not to exceed 125 feet per second. 




Fig. 980. 



In most stationary engines the fly-wheel is a pulley or band-wheel or gear 
driving the machinery, but often the fly-wheel is independent. Fig. 980 is the 
elevation and section of a fl3^-wheel built by the Southwark Foundry. The 
construction will be understood from the drawings, but the wrought-iron links 



410 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 




MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



411 



connecting the segments, shown on a larger scale (Fig. 981), do not project, 
but are countersunk in the sides of the rim. 

The cast-iron fly-wheel of a steam engine 36" X T2", built for the Amos- 
keag Manufacturing Company in 1883, 30 feet diameter, 110" face, with one 
set of 12 arms, and total weight 116,000 pounds, making 61 revolutions per 
minute ; exploded in 1891, and was replaced by a wooden-rimmed pnlley with 
two sets of arms (Figs. 982 and 983). The counterbalance of the cranks and 
connecting-rods was obtained by placing heavy cast-iron plugs in the outer ends 
of the three arms directly opposite each crank. Though the total weight of 
the wheel is not much less than that of the old one, the weight of the rim 
(31,855 pounds) is only about one half, but has shown itself ample for a very 
steady speed at much less cost and greater security. 

Fly-wheels, and in fact all wdieels that have a rapid motion, should be bal- 
anced, and if driven by cranks their connections should be balanced dynamic- 
ally to make the motion as uniform as possible. 

Air-Cliamhers. — The action of the air-chamber is very similar to that of a 
fly-wheel ; it tends to make the outflowing or inflowing pressure of the fluid 
uniform, and cushions or prevents the reaction that takes 
place from the fluid in reciprocating pumps, especially 
crank-pumps ; but pumps in which the pistons or plung- 
ers start very slowly and stop equally so require but little 
air-chamber. Cornish engines are usually provided with 
a stand-pipe instead of an air-chamber — that is, a vertical 
pipe of considerably larger diameter than that of the 
pump, and high enough to contain the water-column. 

Fig. 984 is the section of a copper air-chamber for the 
smaller size of steam or hand-pumps. It is screwed into 
the top of the pump-chamber. Fig. 985 is the elevation of 
an air-chamber for power pumps of larger size of cast-iron 
or a cast-iron base with a copper chamber. A flange is 
cast on the top of the pump-chest, and the chamber is 
bolted to it. 

Fig:. 986 is the elevation of an air-chamber of one of 
the older Brooklyn pumping-engines. 

The lower end of the small air-chamber (Fig. 984) is 
necked, or of smaller diameter than the main part of the 
chamber. This prevents a too sensitive reaction of the air 
and retards its escape ; for the same purpose a diaphragm 
perforated with holes is put across the inside of the cham- 
ber. When the inlet column is long, whether suction or 
under pressure, put an air-chamber on it. 

Air-chambers should be from ten to fifteen times the 
capacity of the pump-cylinder, with glass gauges- to show 
the quantity of air in them for large pumps, and some pro- 
vision to supply and maintain the air at such levels as will be found by experi- 
ment suited to the easiest working of the pump. A large air-chamber can in 
this way be reduced in capacity, while that of a too small chamber can not be 
increased. Air-chambers are made of wrought-iron or steel and the heads 




Fig. 985. 



412 



MACHINE DESiaX AND MECHANICAL CONSTRUCTIONS. 



are bumped up or dished. The thickness of the cylindrical part is to be deter- 
mined by the rules on riveting (page 383). The dished head, struck up on a 

spherical radius (Fig. 987) equal 
to the diameter of the cylinder 
and of the same thickness of 
plate, is of equal strength. 

In the earlier application of 
water to the distribution of power 
the air-chamber held the reserve 
of force, but since the use of 
power in this form has become of 
general application, the accumu- 
lator (Fig. 988) is the form 
adopted, in which the pressure of 
the water in the pipe A raises the 
piston B from which is suspended 
the dead weight sufficient to 
maintain the pressure required. 
For the distribution of power 
throughout the city of London 
the pressure is about 700 pounds 
to the inch. At the Forth Bridge 
Works there are two forms of 
accumulators in use through 
which the high-pressure water is 
pumped ; in one form a 16" cylin- 
der is loaded with dead weights, in 
the other an 8" cylinder is loaded 
with steam. 




iL =3 



•m 



LULildJUJiULLI HI jJJUi.LUliJlliLilJ 




tifTi [ii in fti iti fTi 



LULLI U LU 111 LU LLJIi 




Fig. 986. 



Fig. 987. 



To make a hydraulic riveting machine that could be introduced into some 
of the more complex parts of the structure, it was necessary to increase the 
pressure of the riveter and reduce its dimensions. This was effected by the 
multiplier (Fig. 989), in which the usual high pressure is introduced into a large 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 413 




Fig. 991. 



414 



MACHINE DESIGN AND MECHANICAL CONSTRUCTIONS. 



cylinder with its piston connected with a plunger of smaller diameter, and the 
pressure from the smaller cylinder is connected with the riveter. 

For hydraulic cylinders the common rules are for cast-iron to a pressure up 
to 2,000 pounds per square inch and cast-steel to 6,000 pounds per square inch, 
rarely exceeding 8,000 pounds. For the resistance of thick shells Eankine gives 
the bursting strain — 

_ E^-r^ 

in which /is the tenacity of the metal, R and r exterior and interior diameter 
respectively. 

Figs. 990 and 991 are the elevation and plan of a common form of hydraulic 
press for the baling of goods. The dimensions of the bolts at the four corners 
should be estimated from the hydraulic pressure, with a factor of safety of 5. 

As tools the hydraulic punch, riveter, and jack are in general use. 




Fig. 992. 



Fig. 993. 



Fig. 994 



Fig. 992 is the section of a common jack-screw in which the screw is turned 
by a lever of which the hole beneath shows where its end is inserted. The whole 
weight is taken by the extended base. 

Figs. 993 and 994 are side and end views of a cast-iron housing ; the screw 
exerts a pressure on the roll box journals to be resisted by the frame. 

Fig. 995 is the side elevation of a cam punch and shear, the action being to 
spring the jaws, which are reinforced. 

The above drawings of machines, not shown elsewhere in the work, are given 
as illustrations of forms adapted to the str.esses for which they are designed. 



ENGINEERING DRAWING. 

There is no part of engineering more important than that of securing a 
good foundation for the structure. Where likely to be disturbed by frost, the 
structure should start below it, unless, as in the extreme northern regions where 
frost is permanent at certain depths, the support should be in it. In preparing 
the foundation for any structure, there are two sources of failure which must 
be carefully guarded against : viz., inequality of settlement, and lateral escape 
of the supporting material ; and if these radical defects can be guarded against, 
there is scarcely any situation in which a good foundation may not be obtained. 
It is therefore important that, pi'evious to the commencement of the work, 
soundings should be taken to ascertain the nature of the soil and the lay of the 
strata, to determine the kind of foundation ; and the more important and 
weighty the superstructure, the more careful and deeper the examination. But 
it must be understood that in general it is not an unyielding but a uniformly 
yielding stratum that is required, and that a moderate settlement is not objec- 
tionable, but an inequality of settlement. 

In good sand or gravel, the load on foundations per square foot is usually 
from three to five tons. Many soils are very compressible, not supporting one 
ton per square foot ; if the structure is important, the bearing resistance of the 
strata should be tested by experiment. The base of the wall is extended to 
secure the requisite area of bearing-surface, either by a base-stone (Fig. 996), 
by a bed of concrete (Fig. 997), or by extending the w^all by steps (Fig. 998), 





Fig. 997. 




with or without concrete base, or the weight may be distributed by inverted 
arches between walls and piers. 

Wooden platforms are often used for foundations, but must be laid beneath 
the water line where they are kept wet, otherwise rot will take place. These 
platforms may be of a single course of plank or plank and timber, as in Fig. 999, 
or may be very much extended, forming rafts or grillages of many courses. A 
similar foundation has been introduced in Chicago, where the great depth of 
clay requires extended areas of foundation, but instead of timber it consists 

415 



4:16 



ENGINEERING DRAWING. 



of a combination of masonry with common rails or I-beams, affording greater 
length of offsets and less depth than by timber or masonry. The length of 

offsets may be calculated from the insistent weight, 
by the formula of beams fixed at one end and uni- 
formly loaded or one quarter that given in the tables 
(pages 243 and 244). 

Fig. 1000 is a section of one of these foundations 
beneath a pier, but equally applicable to the support 
of walls. The space between the beams is filled 
with cement, mortar, or concrete, which adds to the 
stiffness of the structure and is a preservative of the 
metal. The iron grillages for piers are distinct, and 
each proportioned in bearing-surface to its proposed load. In astronomical 
observatories it is especially necessary that the foundations for the large and 




Fig. 999. 



STEEL I BEAMS 



'iiii!LiiTzs^s,iiiii3LiJLJLiJLiij^s:YJ3r '^^y^ 




*i4X«*4LAAXAAJLAXXAX«4A4p«4k««il^4iAi^A* 






Fig. 1000. 



delicate instruments should be detached from those of the building, and also 
where the noise and jar of the machinery might interfere with the occupancy of 
the building for other purposes. 




Fig. imz. 



Walls on party lines and confined to these lines are often partially supported 
by cantilever beams reaching over interior posts. Such a construction is shown 
in Figs. 1001 and 1002. 

It is the safer construction to lay walls in air and open to inspection, and 



ENGINEERING DRAWING. 



417 




therefore important that their foundations should be freed from water, which 
can be done by inclosing them with a bank of eartli or by a curb of sheet-piling 
(Figs. 1003 and 1004). Sheet- 
piling is usually of plank two to f i j T 
three inches thick, set or driven. ^ 
For driving, the bottom of the 
plank should be sharpened to a 
chisel-edge, a little out of centre 
toward the ranging timber side, 
and cornered slightly at the outer 
edge, that it may hug the timber -g 
and the plank while being driven- 

Fig. 1005 is the section of a 
timber sheet-piling, in which a 

tongue and groove forms the \ \ \ 

guide, the grooves being either p^^ jqq3 

made in the timber, as shown at 

a rt, or planted on, b h. The pile should be of uniform thickness, but the 

widths may be random ; six inches thick is a good practical thickness, driving 

well under short and frequent blows of a ram ; the tongue should be of hard, 

straight-grained wood, 2 inches by 2 inches, and well spiked to the pile. 

Frequently, to secure the foundation from water, a wall is constructed of 
two rows of sheet-piling, driven one within the other, and the space between the 

two filled with clay or some compact earth. 
This is called a coffer-dam ; the two rows 
of piling are stayed to each other by bolts, 
and if the wall is wide enough no other 
stays or braces will be necessary. 

Pile-drivers are now constructed to drive 
sheet-piling in panels of 6 to 8 feet wide, which serves to preserve the line and 
make tight joints. 

In quicksands it is very common to secure a foundation by consolidation 
with small stones or rubble worked down by iron bars or driven bv rams of a 
pile-driver, till sufficient resistance is secured for the structure. Some success- 
ful experiments have been made in compacting such sands bv forcing down 
cement mortar through pipes. In soft earths piles are generally used for this 
purpose, and if a firm bottom can be secured at a reasonable depth they are the 
most economical expedient. 

Piles are used either as posts or columns driven through soft earth to a hard 
bottom, or depending on their skin resistance to give the necessary support, 
either in earth naturally compact or made so by the driving of the piles. In 
the first case care must be taken that the piles be driven sufficiently deep into 
the lower strata to secure their ends from slipping laterally, and soundings 
should be made carefully to ascertain the dip and character of these strata. In 
many places, from the hardness and the inclined position of the lower strata, 
this kind of foundation is inapplicable and unsafe. 

For a foundation where no firm bottom can be found within an available depth, 
piles are driven, to consolidate the mass, a few feet apart over the whole area of 
28 




418 



ENGINEERING DRAWING. 



the foundation, which is surrounded by a row of sheet-piling to prevent the escape 
of the soil ; the space between the pile-heads is then filled to the depth of several 
feet with stones or concrete, and the whole is covered with a timber platform. 

It is very difficult to establish a rule of general application for the load which 
a pile will sustain. It is well in untried soil to drive a few piles, noting the set- 
tlement under blows, and then load the piles in excess of what they will be re- 
quired to bear, noting the results from time to time ; and if settlement con- 
tinues, drive deeper, or more piles with less spaces. 

Major Saunders, in the " Journal of the Franklin Institute," gave a rule for 
the safe load of piles depending on the skin resistance, which has been of general 
application, but of which the factor of safety is unnecessarily large, and is given 
below modified to 4 instead of 8. 

Multiply the weight of the ram in pounds by the distance in which it falls 
in inches at the last blow, and divide the product by four times the depth 
driven in inches at this blow. 

Weight of ram 2,000 pounds, fall 15' or 180", set If. 

^ . , , 2000 X 180 . . nn^^ 1 

Safe load = — -^i : — = 60,000 pounds. 

li X 4 ^ 

In driving piles the effect of the ram should be carefully noted, the rate of 
fall under successive blows, the brooming or splitting of the head of the pile, 
and the rebound of the ram after the blow. E&pecial note should be taken 
toward the close of the driving to determine the last set when the formula 
above given is used. 

The usual weight of the ram or hammer employed on our public works va- 
ries from 1,400 to 2,400 pounds, and the height of leaders or fall from 20 to 35 
feet ; but there is a great advantage in reducing the fall, increasing the weight 
of the hammer, and the frequency of the blows. As generally driven, and of 
average size, when the whole weight is to be supported by the pile, ten tons 

may be considered a usual load, but when 
additional support is received from com- 
pacted earth, broken stone, or concrete be- 
tween piles and caps, this bearing surface 
should also be taken into consideration. 



o 



o 



.^.- 



.o 



o 



o 



fvr^ 



X 



ff=??=f 



f=F 



t r-H 



1 1 
n 



n 



rr~n 



I I 



I 



U 



e; 



n'. 



■^',\\\\\',\K.\' 



^ 



8 



:s 




Fig. 1006. 



Fig. 1007. 



Figs. 1006 and 1007 represent plan and elevation of a pile foundation ; the 
piles are usually from 10" to 14" top diameter, and driven at about 3 feet be- 
tween centres. The tops are cut off square and capped with timber the caps 



ENGINEERING DRAWING. 



419 



treenailed or ragbolted to the piles, and plank spiked to the timber. In the 
figure a sheet-piling, s 5, is shown, inclosing the piles ; the spaces between piles 
and timbers are often filled with concrete, small stone, or closely packed earth. 

In compacting some soils it has been found that good results may be ob- 
tained by drawing the pile and filling the hole with sand. It would seem that 
the best result would be obtained by forming these piles of a uniform taper 
downward, as the consolidation would be more uniform, the withdrawal easier, 
and less disturbance of the sides of the hole. The consolidation might be still 
further increased by ramming the sand in thin layers, owing to the ability of 
the latter to transmit pressure laterally. The sand should be fine, sharp, clean, 
and the grains of uniform size. 

It is often difficult to obtain or drive piles of sufficient length, and they 
must be spliced. After the first pile is driven, its head is cut level ; a wooden 
dowel or iron pin, penetrating each pile about a foot, is inserted in the centre ; 
the upper pile is then fitted to the low^er one, or a cast-iron collar or ring of 
plate iron 6" to 12" wide may be used to strengthen the joint and protect the 
pins from splitting either head of the piles. 

Spliced in this way, the pile is deficient in lateral stiffness. In most posi- 
tions it is safer to re-enforce the splice by flatting the sides of the piles and 
nailing on with, say, 8-inch spikes, four pieces 2 or 3 inches thick, 4 or 5 inches 
wide, and 4 to 6 feet long. In the erection of the bridge over the Hudson 
River at Poughkeepsie, IN. Y., two piles were thus spliced together to form a 
single one 130 feet long. 

Piles may be made of any required length or cross-section by bolting and 
fishing together, sidewise and lengthwise, a number of squared timbers. Hol- 
low-built piles 40 inches in diameter and 80 feet long were used as guide- 
piles in constructing the St. Louis bridge. To protect the head of the pile 
against brooming or splitting it is usual to drive on a tight-fitting wrought- 
iron ring or cap (Fig. 1008) by a blow of 
the hammer. In driving into compact 
gravel or shingle the point of the pile 
should be protected with iron straps, as 
shown in Fig. 1009. 

Fig. 1010 is a section of a bulkhead 
wall on the North River front, in positions 
where the mud is deep, as designed and 
constructed by George S. G-reene, Jr., Chief 
Engineer for the Department of Docks, 
New York city. 




Fig. 1008. 



Fig. 1009. 



The site of the wall is first dredged to hard mud compacted with sand. The vertical 
piles are then driven, and small cobble-stones mixed with coarse gravel put around and 
among the piles to the height of the under side of the binding frames, and rip-rap stone 
placed outside the piles, in front and rear. 

The binding frames, then slid down to their places, were made of two pieces of spruce 
plank 5 X 10 inches, placed edgewise one over the other, and running frcm front to 
rear of the piles between the rows. An oak beam 8x8 inches is let through these 
planks in front of the front row and in rear of the rear row of piles, and an oak wedge 
block fitted and placed by the divers between the oak beam and each pile nearest it. 



420 



ENGINEEKING DRAWING. 



o 

m 



^ 



P ^ g 







:'''*jl"|!ffi,.,^ 



•i'il!' ^ 



111 



mm 



''tHili'f'llii 



fe^il 




i«!iji;;ii:r 



ENGINEERING DRAWING. 



421 



These frames hold the front rows of piles firmly, in case there should be any tendency in 
them to tilt outward. More cobble-stone is then put in to the height of the bottom of 
the base blocks of the wall, weighting the binding frames and preventing any tendency 
to floating. 

The bracing piles are then driven on a slope of 6 inches horizontal to 12 inches ver- 
tical, between tlie rows of vertical piles, and spaced 3 feet from centre to centre longi- 
tudinally and transversely. All the piles are staylathed and adjusted in position as soon 
as they are driven. 

The bracing piles are cut off at right angles to their axis, about 1 foot below mean 
low water, and capped with 13-inch square timber, running longitudinally. The sides 
of the caps are kept horizontal and vertical, and a sloping recess or notch made to re- 
ceive the head of each bracing pile, and give it a good bearing. 

The six rear rows of vertical piles are cut off at 2 inches above mean low water, and 
notched front and rear to give an 8-inch -wide bearing across their tops for the trans- 
verse caps. 

The three front row^s of vertical piles are cut off by a circular saw, suspended in the 
ways of a pile-driver, at 15 '3 feet below mean low-water mark, to receive the concrete 
base blocks of the wall. It being impossible to cut off piles at this distance below the 
surface of the water to exactly the same height, and as the bottom of the concrete base- 
blocks would rest only upon the highest piles of those under them, a mattress of burlap, 
containing freshly mixed soft mortar, in a layer about 2 inches thick, placed on a net- 
work of marline stuff, supported by a plank frame about its edges, is lowered upon the 
tops of these piles immediately before setting the base-blocks uj^on them. The diver 
then cuts the netting between the edge of the mattress and the plank frame, and the 
frame floats to the surface of the water. 

The base-block is then immediately placed in position upon the mattress of mortar 
resting on the piles, and the excess of mortar is pressed out from between the head of the 
pile and the bottom of the base-block, until each pile has a well and evenly distributed 
portion of the load to carry. 

The concrete base-blocks for this section are 7 feet wide at the bottom and 5 feet 
wide at the top; on the front the vertical height is 13 feet, and on the rear 14 feet. The 
top has a step on the rear of 1 foot height and 1^ foot wide, extending the entire length 
of the block, for the purpose of giving the mass concrete backing of the granite super- 
structure a good hold upon the block. For handling, grooves for chains are moulded in 
the end, and a longitudinal hole, 2 feet in the clear above the 
bottom, connects them, with the corners rounded, to enable the 
chain to render easily. The face is curved inward, to save ma- 
terial while giving a broad base ; their length is 12 feet. 

After the blocks are set, the vertical chain-grooves in each 
block, coming opposite to each other, are filled in with concrete 
in bags, well rammed into place. This closes the joints between 
the blocks, and also acts as a tongue set into the grooves in the 
blocks. 

Fig. 1011 shows a block in section with the central- 
and side-groove spaces, which are deep enough to admit 
of the easy slipping in and withdrawal of the chain. 




Fig. 1011. 



As soon as the base-blocks are set, and the groove filled in, 
the cross-caps resting on the tops of the vertical piles, and on 
the longitudinal caps of the bracing piles, reaching about half 
way across the base-blocks, are placed and fastened. Oak treenails are used in all fast- 
enings. The small cobbles are then filled in around and among the piles to the top of 
the caps, and the rip-rap placed in the rear of them. 



422 



ENGINEERING DRAWING. 



Figs. 1012 and 1013 are the elevation and plan of a crib with dock or pier. 
Below the level of the water, as here shown, the logs are round and locked 




Fig. 1013. 



to the cross-timbers ; above the water the timber is squared, the exterior walls 
presenting a tight, smooth surface into which the cross-timbers are dovetailed. 

A quarantine station, built for the port of ]^ew York, on the west bank con- 
sists of an exterior wall of cribwork, of which Fig. 1014 is a section ; the in- 
closed space is filled with sand, comprisiug an extent of about 228' X 448'. The 
base to low water consists of cribs about 80' in length, sunk, and loaded with 
stone ; above it the construction is continuous. The base timbers 14" X 14", 
upper 12" X 12", interties 12" X 12", at intervals of 7 feet centres ; the 
ranging timbers to be secured at every joint to these below, and at every cross- 
ing by 1" square bolts 21" long. The exterior is close-fendered with oak plank, 
iron bolted, with three iron bands at the corners. 

Fig. 1015 is a transverse section of the river-wall Thames embankment, 
Middlesex side ; a wall of concrete, etc., faced with granite, with a sewer and 
subway within the same, lined with, brickwork. The different material is rep- 
resented by different shadings and letters : g, granite ; h h, brickwork ; c c, 
concrete. 



ENGINEERING DRAWING. 



423 



Extracts from specifications : 

"The embankment-wall is to be formed within iron caissons or coffer-dams. As 
soon as the excavations shall have been made to the requisite depths, and the works 
cleared of water, the trenches shall be filled up with concrete to a level of 12^ feet be- 
low datum, and a bed dressed to the proper slope and level for the footings of the brick 
wall. This wall to be formed thereon, generally in courses at right angles to the face 
of the wall. The subway shall be formed 7 feet 6 inches high by 9 feet wide in the 
clear, generally; the side-walls to be 18 inches, the arch 1 foot 1^ inch thick. The sub- 
way sewer and river-wall shall be tied into each other, at intervals of 6 feet, by cross or 




Fig. 1014. 



counterfort walls 18 inches thick, extending from the brickwork of the wall to a vertical 
line 9 inches beyond the side of the sewer farthest from the said wall, and from footings 
9 feet below datum, which are to be bedded on a concrete foundation 12 inches thick, 
up to the under side of the subway. The upper arch of the subway, and all other simi- 
lar arches, shall be coated on their outside circumference with a 1" layer of Claridge's 
patent Seyssel asphalt. The whole of the stones above 11^' datum to be dowelled to- 
gether in bed and joints with slate-dowels, not less than 5 for every foot run of wall; 
each 2| inches square at least, let fully 2^ inches into each stone, very accurately fitted, 
and run in with neat cement; the stones to be bedded and jointed in cement, and the 
joints struck with neat cement." 

Fig. 1016 is an isometrical view of the overflow and outlet of the Victoria 
and Regent Street sewers in the Thames embankment. S is the main sewer, 
and W the subway shown in Fig. 1015 ] s s s the street-sewers, discharging into 
the overflow basin ; lu w the weirs over which the water is discharged into 
the weir-chamber c c, p is the penstock-chamber, which is but a continuation 
of the weir-chamber. Whenever, from storms, the discharge from the street- 
sewers (s s s) is greater than can be carried off by the main sewer (S), the water 
rises in the overflow-chamber (0), passes over the weirs {w w) down into the 
weir-chamber (c), then into the penstock-chamber, and through the flap-gates 
(g) into the river. 



424 



ENGINEERING DRAWING. 



Extracts from the specifications : 

"The foundation to be of concrete, not 
less than 2 feet in thickness ; upon this 
brick- work shall be built for the flooring of 




the chambers, and for the side- 
end and weir-walls. The weir- 
chamber shall be divided in the 
direction of its length, by a brick 
wall, into two rectangular over- 
flow-channels, covered with cast- 
iron plates, 6 feet S^ inches long, 
3 feet wide by | inch general 
thickness, with strong ribs and 
flanges on the under side, prop- 
erly bolted together and jointed 
with iron cement, and bolted Fm. 1015. 

down to stones which are to be built into the under side of the brickwork of the base- 
ment chamber. Arches on either side, running parallel thereto, and communicating with 
this chamber and with the weirs which are to be formed, upon which weir- walls, divided 
so as to correspond with these arches, are to be built in brickwork, capped with granite 



ENGINEERING DRAWING. 



425 




426 EXGINEERIXG DRAWING. 

blocks, 4 feet long, 2 feet deep, and 2 feet 3 inches in the bed. The floor of the pen- 
stock-chamber to be formed with York landings, 6 inches thick, having a fall of 3 inches 
to the river. The outlets for the penstock-chamber through the river-wall shall be 
formed by an arch-recess in granite, and fixed with two tidal flaps, well hung, and firm- 
ly secured to the masonry by strong bolts and screws. 

' ' The subway is to be continued over the low-level sewer, and across the overflow- 
chamber, by cast-iron plates, curved to the form of the arch, |- inch general thickness, 
with strong ribs and flanges on the upper side, properly bolted together, and strongly 
bolted down to the brickwork ; jointed with iron cement, and covered with brickwork, 
to form the floor of the subway. From a point of 10 feet 3 inches on either side of the 
central longitudinal line of the chamber, where the sewer and subway are farthest from 
the river- wall, these are again to be brought into their general position by two curves, 
each not less than 80 feet in length. 

"The wliole of the cast-iron shall receive one coat priming of red lead and linseed 
oil, and three coats best coal-tar, before fixing ; and the accessible surfaces one further 
coat best coal-tar, when fixed." 

Fig. 1017 is the section of the dike or jetty forming a breakwater for the 
harbour of Boulogne, France. It may be considered in two distinct parts, cor- 




FiG. 1017. 

responding to the substructure and the superstructure. The substructure is 
formed by a mass of natural and artificial rip-rap, with a central core of stones 
weighing about two hundred and fifty pounds each, resting on the bottom, and 
rising to a level of one metre above low tide. The shore side is protected by a 
pitching of stone, each about twelve hundred pounds weight ; the sea-side 
slope, by one of heavy rubble of about seven tons each, 'and covered by beton- 
blocks w^eighing uniformly thirty-three tons each ; on the above is built the 
masonry superstructure. On each side of the wall, on a level with the lower 
platform, the slopes are consolidated by masonry bermes formed of isolated 
blocks, which protect the foot of the wall and afford a path for the workmen 
and materials at low tide. 

The water-jet is extensively employed on sandy shores for the sinking of 
piles for foundations of lighthouses, wharves, etc., and in the Southern States 
it renders the palmetto available, which resists the ravages of the teredo, but is 
too soft to withstand the blows of the pile-driver. In a simple and effective 
application it consists of a pile to which a small iron pipe is attached, extend- 
ing below the bottom of the pile. A flexible hose is attached to the top of the 



ENGINEERING DRAWING. 



427 



10 



pipe and, water being forced through, the earth is washed away from the bot- 
tom and side of the pile, which falls by its own or superadded weight or light 
blows of a maul or hammer. 

The jet has also been employed in a great variety of ways to facilitate the 
passage of screw and disk piles, cylin- 
ders, etc., through earthy material, and ^ ^ ^ 
as an ejector to remove earth from the 
inside of caissons, and relieving stranded 
vessels by removing the sand from their 
bottoms and sides. 

Cast-iron or wrought-iron is used for 
piles, and, at the present prices of iron, 
with economy. They can be driven by 
the pile-driver, the interior earth removed 
by an augur, by sand-pump, or water-jet. 
The blows of the ram should be cush- 
ioned by a wooden block. For the con- 
struction of the iron pier at Coney 
Island, N. Y., to the bottom of the 
wrought-iron pipes 8f" in diameter, in 
lengths of from 12 to 20 feet, cast-iron 
disks were fastened by set screws and 
sunk by an inside water-jet to a depth of 
17 feet in the sand. 

In Chili iron piles were sunk 14f" 
diameter with bottom flange of 42" ; the 
pump discharged 12,000 gallons per hour 
through two 2" pipes extending 8" below 
the base, and would sink two piles 28 feet 
on an average in 18 hours. The bottom 
was of coarse compact sand and the pile 
was worked down by an endless cable 
passing around a pulley on the pile and 
giving it a motion of rotation. 

Tlie screw pile usually consists of a 
wrought shaft from 3" to 8" diameter to 
which is keyed a cast-iron screw from 2 
to 5 feet in diameter sunk by turning 
the shaft by hand or power, mostly used 

for marine purposes, for the foundations p^^. j^^oq 

of lighthouses, or anchors for buoys 

where they resist the upward motion of the waves. As they are sunk without 
jar or disturbance of the soil, they are adapted to positions where the neigh- 
bouring structure mighl be injured by other methods of sinking foundations. 

Figs. 1018, 1019, and 1020 are sections of masonry curbs sunk by water-jets 
for a quay at Calais, France. 

The base is of concrete made in a mould, the rest of the masonry laid in 
cement mortar. 




428 



ENGINEERING DRAWING. 



The sand surface beneath the blocks was exposed to the action of strong 
jets, and the mixture of sand and water was pumped up by centrifugal pumps ; 
the suction-pipe nozzle was just below the level t)t the bottom of the block ; 
care was taken that the quantity of water forced in should be the same as that 
pumped out, and the level of the water in the curb should be just below that 
in the surrounding sand. When the curb had reached the bottom after a de- 
scent of about 15 feet, the sand was allowed to settle and the opening was filled 
with concrete up to a level where it could be filled with masonry. 

The blocks 1, 3, 5 are sunk alternately, 
and then 2, 4, 6, the blocks being cemented 
together as shown in Fig. 1021. 

It has lon.2: been common in India to ^^ __ ^ 



sink brick wells in clusters by hand labour, 





Fig. 1021. 



Fig. 1022. 



excavating and pumping for the foundations of bridges, but by substitution of 
bucket-dredges to remove the inner cores of earth greater facility in work and 
depth of sinking has been secured. This system has been successfully applied 
to the sinking of iron caissons. 

In the sinking of small curbs for wells it is common to make circular plank 
curbs supported by segmental ribs inside, and load them so that they will sink 
as the earth is removed from the inside and then lining with masonry. 

Fig. 1022 is a partial section of a shoe of the 50-foot diameter well sunk at 
Long Island City, N. Y. It consists of timber segments bolted together on 
the top of which a brick wall was laid ; on the outside is a board sheathing. 
As the earth is removed from the inside the curb settles from the weight of the 
brick masonry, which is built up and settles again and again till the required 
depth is reached. As the boards are set at a batter of 2" to 1 foot, the struc- 
ture settles readily as the earth is removed. Were it not for the batter the 
earth would press against the sheathing and masonry, and vertical bolts would 
be necessary in the latter to anchor the courses together and prevent rupture. 
The sheathing of boards is planed on the outside and firmly attached to the^j 
shoe with bound wooden segments above to preserve the form, which are re- 
moved as the brickwork reaches them. 

Fig. 1023 is a joartial section of a steel caisson, exhibiting the cutting edge 
re-enforced by steel plates and supported by beams to the bottom girder. 

Foundations for the abutments of piers and bridges may be constructed on 



ENGINEERING DRAWING. 



429 




Fig. 1023. 



any of the systems illustrated, but as it is generally necessary that they should 

not extend in width so as to obstruct the current of the stream and increase its 

velocity, it is usual to inclose the site of 

the foundations within a coffer-dam, 

freeing it from water and preparing the 

foundation ; but this is expensive in deep 

water, and other means are adopted. 

Figs. 1024, 1025, and 1026 are plans 
and sections of the foundations of one 
of the Poughkeepsie bridge piers, which 
may be designated as a crib, although its 
walls are tighter than usual in such con- 
structions. 

It is built of 12" X 12" white hemlock 
timber, except the bottom or cutting 
course of the shoe, which is white oak. 
The shoe is carried up in a triangular 
section of solid lumber around the sides 
and a central longitudinal division to 
the height of 20 feet. Top surface at 
sides 10 feet wide, at ends 9 feet, central 
16 feet ; above the shoe there are hollow 
spaces. Cross-timber walls 2 feet thick 
divide the spaces into pockets, of which those above the shoe are weighting 
pockets and those open at the bottom are dredging pockets D. The earth is 
dredged from the pockets D and discharged into the pockets W, and acts as a 
weight to sink the crib, care being taken to distribute the load to equalize 
the sinking. As the earth is dredged from the pockets D the crib sinks, and 
when it reaches the bottom they are cleared out and the space filled with con- 
crete lowered into place in boxes of one cubic yard capacity and unloaded by a 
trip. 

The top of the crib was sunk to a level of 7 feet below water mark and the 
concrete brought to within 2 feet of this level; this space was filled with broken 
stone and levelled by divers; a floating caisson, or tight box with timber bottom 
and sides, was floated over the crib and sunk and the masonry begun. When 
complete above water the sides of the caisson was removed. 

The Chinese anchors used in mooring the cribs of the Poughkeepsie bridge 
as shown in Fig. 1027 is composed of 3" X 8" hemlock planks 10 feet long 
piled to make the interior dimensions 6' X 6' X 6', which is filled with broken 
stone, each anchor holding 8 cubic yards ; the eye-bolts shown at the corners 
serve the double purpose of holding the framework together and carrying the 
slings to which the cable is fastened. 

Open caissons, as shown in the description of the Poughkeepsie bridge, are 
useful when a suitable foundation can be secured either in a uniformly yield- 
ing material or by preparing one by means of piles or divers. 

Figs. 1028 and 1029 are illustrations of the means adopted by G. A. Parker, 
C. E., in lowering the caissons for the erection of some of the piers of the Sus- 
quehanna bridge. 



430 



ENGINBERIi^G DRAWING. 



He commenced by dredging away as much as possible of the material in the bed of 
the river at the pier site. A f -inch-thick boiler- iron curb was then sunk and secured in 
place. The curb was about 30 feet wide and 50 to 60 feet long, and of sufficient 
height to reach above the bed of the river. The material was then pumped by sand- 
pumps out of the curb, which gradually undermined, and settled down to the estab- 
lished depth, or to the bed-rock. When stumps, logs, or boulders were met with they 
were removed by divers working in a bell. After the rock had been thoroughly 
cleaned off, it was brought to a uniform level by a solid bed of concrete extending over 
a greater space than the size of the bottom of the pier by the use of the diving bell. 

Three guide-piles on each side, and one at each end, were fixed firmly in position. A 
strong platform of solid timber, the size of the bottom of the pier, was then placed in 
position over the curb and at the surface of the water. On this was placed a caisson of 
iron large enough to contain the pier, and with sides and ends high enough to reach to 




the level of high water after the caisson 
was landed on the bottom. The caisson 
was then made water-tight. The bottom 
was then floored over with masonry and 
stone, and laid in mortar up the sides of 
the caisson to the top, thus constituting a 
stone caisson inside of an iron one. This 
was secured to the guide piles, and the 
masonry of the pier proper was laid up, the caisson sinking as the weight of masonry 
inside increased, until it finally settled upon the bottom which had been prepared for 
it. At some of the piers (Figs. 1028 and 1029) screw-rods were used to suspend the 
pier and gearing attached, governed by one man, who could raise or lower without assist- 
ance the whole pier. Wooden piles were driven for some piers and cut off by machinery 
just above the ground, and the platform, with its masonry, lowered upon them. 



Fig. 1026. 



ENGINEERING DRAWING. 



431 



Piers are sometimes made by sinking a wrought-iron curb, extending from 
the bottom to above the level of the water, driving within it the usual propor- 
tion of piles, and then filling the 
spaces entirely with concrete. 
This process was adopted in form- 
ing some of the piers of the bridge 
of the Shore Line Railroad across 
the Connecticut Eiver at Say- 
brook, under Cushing's patent. 

Pneumatic Piles. — The vac- 
uum process in which the hollow 
pile of cast- or wrought-iron was 
sunk, by capping it and exhaust- 
ing the air within, and thus load- 
ing it with the pressure of the ex- 
terior atmosphere, gave place to 
the plenum process, which was 
adopted for the old piers of the 
Third Avenue bridge across the 
Harlem River, of which Fig. 1030 
is a section. It conists of a pipe 

in two sections ; the upper one is called the air-lock, which can be connected 
with either the lower chamber or the atmosphere. The lower chamber being 
under pressure and shut off from the air-lock, the workman passes from the 
outer air into the lock, closes the door, opens the pipe connection between the 
two compartments, and, when the pressure becomes equal, opens the lower door 
and passes down. 




Fig. 1027. 




Fig. 1028. 



Fig. 1029. 



Mr. McAlpine enlarged the bottom of the cylinder to a conical form, and 
also added largely to the bearing surface by poling-boards driven obliquely out- 
ward. After the excavation was completed, a strong course of concrete was 
laid, and, when set, the air-lock was taken off and the balance of the concrete 
filling was done in open air. 



432 



ENGINEERING DRAWING. 





tfjy 



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ENGINEERING DRAWING. 



433 



u 



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The pneumatic caisson has superseded the pneumatic pile. The system of 
air-lock is the same, but, instead of sinking several piles and then combining 
them with a structure, the caisson em- 
braces the whole pier and starts from 
the bottom. The pneumatic caisson 
is an inverted boat or diving bell of 
timber, which forms the working or 
air chamber, connected with the upper 
air by pipes and air-locked shafts for 
the ascent and descent of the work- 
men and for the removal of waste 
from, and the delivery of material 
into, the working chamber. 

Figs. 1031, 1032, and 1033 are the 
plan and partial sections of a late form 
of the framing of a caisson. The ceil- 
ing of the working chamber is of 
plank, and between the first and sec- 
ond courses of beams there is a double- 
plank floor, which are calked and then 
coated with pitch, and the spaces be- 
tween the timbers filled with concrete. 

Fig. 1240 is a section of the pier 
of the Bismarck bridge. The sand 
was removed from the air chambers 
by water ejectors. As it is removed 
from the chamber, the masonry sinks 
the caisson, and when it reaches the bottom the space is filled with concrete 
or with sand. If the top of the caisson, when first sunk, does not reach the 
surface of the water, a curb is formed on the top to a height sufficient to per- 




FiG. 1030. 




Fig. 1034. 



Fig. 1035. 



mit the construction of the masonry in the open air. To preserve the position 
of the air-lock during the whole construction there is an offset in the pipe at 
29 



434 



ENGINEERING DRAWING. 



Q 








<'1.?.- 



4; 



'v_/"r 







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Fig. 1037. 



ENGINEERING DRAWING. 



435 



this point, and necessarily an inconvenience in the change of movement of ma- 
terial and workmen, but in later constructions this is avoided. 

Fig. 1034 is a recent plan and section of a main shaft, through which access 
to the caisson is obtained by the workmen ; each length consists of a cylindrical 
shell 4 feet in diameter and 8 feet long, flanged at the bottom, with a head hav- 
ing an opening in it; these lengths are added as fast as the caisson sinks 8 feet. 
The head of the top and second section are provided with doors (Fig. 1035), 
thus making the air-lock. When a length has been added the top door is re- 
moved and placed on the top of the new length ; the lower door may then be 
taken off and placed where the other has been removed. 

Figs. 1036 and 1037 are plan and section of the Barr-Moran air-lock on the 
excavating shaft. The top doors are double slides, tight-fitting and working 
on cast-iron guides, operated by pistons driven by steam or by compressed air 
from the caisson. The lower door is a flap-valve, balanced by a counterweight 
and operated through a rocker-shaft extending through the air-lock, and a 
quadrant and chain attached to the piston-rod of a steam or of a pneumatic 
cylinder in connection with the caisson. In the figures both doors are shut. 
Under atmospheric pressure the upper doors can be opened for the clear move- 
ment of the bucket by a rope attached to the bail, the rope passes through a 
stuffing-box, around which the doors close when shut. With the upper doors 
shut, and the air in the lock brought to caisson pressure, the flap-door can be 
opened and the bucket lowered to the bottom. At the bottom of the shaft 
there is a flap-door which can be raised when it is necessary to repair the air- 
lock or to raise it by adding another length of pipe. 

The air-lock at the top of the shaft adds to the security of the workmen 
and to the easier supervision of the machinery, while the single straight pipe 
gives greater facility to the movement of men and materials. 

In the freezing process^ invented by F. H. Poetsch, of Austria, the site of 
the foundation is inclosed with large vertical pipes sunk by a water jet ; within 
these p%)es, which are closed at the lower end and sunk to the proper depth, a 
small pipe open at the bottom is inserted, through which is forced a freezing- 
mixture (as chloride of calcium), returning through the outer pipe. In this 
way a curb of ice is formed, inside which the earth is removed for the foundation. 
In Finsterwalde, Austria, 12 
tubes of 8-2-" diameter were 
sunk through 115 feet of 
quicksand, in a circle of 
about 14 feet diameter, for a 
shaft 8-|- feet diameter. After 
the brick lining was laid the 
tubes were withdrawn, a hot 
circulation freeing them from 
the ice. 

This process has been used 
successfully in this country. 

Betai7ii7ig-\\a\\s are such 
as sustain a lateral pressure 
from an embankment or head of water (Figs. 1038 and 1039). The width of 




436 ENGINEERING DRAWING. 

a re taming- wall depends upon the height of the embankment which it may 
have to sustain, the kind of earth of which it is composed (the steeper the nat- 
ural slope at which the earth would stand, the less the thrust against the wall), 
and the comparative weight of the earth and of the masonry. The formula 
given by Morin for ordinary earths and masonry is b = 0-285 h + h' ; that is, to 
find the breadth of a wall laid in mortar, multiply the whole height of the em- 

* 0Q.5 
bankment above the footing by ; for dry walls make the thickness one 

fourth more. 

Most retaining- walls have an inclination or batter to the face, sometimes 
also the same in the back, but offsets (Fig. 1038) are more common. The 
usual batter is from one to three inches horizontal for each foot vertical. To 
determine the thickness of a wall having a batter, "determine the width by 
the rule above, and make this width at one ninth of the height above the base." 

The formulae for the thickness of retaining-walls are very complicated. En- 
gineers make use of some general rules as above, and depend on their experi- 
ence for any modification. The top of the wall should not be less than 2 feet, 
and in climates subject to frost it will be impossible to secure permanently the 
upper part. Where the soil is saturated with water, it is usual to put weep- 
holes at or near the bottom to relieve the pressure against the back of walls laid 
in mortar. 

Buttresses and counterforts in the rear of a wall of which the construction 
requires a uniformity of thickness are only considered equivalent to increasing, 
the strength by the mean amount added to the horizontal section of the wall ; 
but when the buttresses are on the line of the bridge trusses, they add to the 
strength by the better distribution of the weight of the truss and by the secu- 
rity which the weight of the truss gives at this point to the wall. The but- 
tresses should be well bonded to the wall. 

Dams are constructed to pond water for the supply of cities and towns ; for 
inland navigation, by deepening the water over shoals, and the feeding of ca- 
nals ; for power in its application to mills and workshops ; and for irrigation. 
To whatever purpose the water is to be applied, there are two questions to be 
settled : Whether the level will be raised high enough by the construction, and 
whether the flow of the stream is sufficient for the purpose required ; and, fur- 
ther, it may often be important to know how large a pond will be thus formed, 
how ample a reservoir to balance unequal flows or intermittent use. If the 
pond be small, so that the water can not be retained, and the supply is only 
the natural run of the stream, then the minimum flow of the stream is the 
measure of its capacity. 

The rule that obtains on the Merrimac River, at Lowell and Lawrence, 
where the pondage is more than the average, is that 1 cubic foot per second 
per day of 12 hours per square mile of water-shed can be depended on for per- 
manent mill-power. On small streams it happens that comparatively large 
pondage may be secured, and the supply be equal to one half the rainfall. 

Blodgett, in his " Climatology of the United States," says that " in this 
sense of permanence as a physical fact we may consider the quantity of rain 
for a year as a surface-stratum, on the Alantic slope and in the Central States 
of 3i feet, which may be diminished to half this quantity, or increased to twice 



ENGINEERING DRAWING. 437 

as great a depth in the extreme years. The evaporation from a water surface 
is now usually considered equal to that of a rainfall ;- therefore in the estimate 
of the water-shed available for pondage the area of the reservoir is not taken 
into account ; the quantity of rain falling upon it is offset by the evaporation. 

The usual form of dams for small streams and but little fall is to build a rub- 
ble wall across the stream and secure the up-stream side with an earth of loamy 
gravel puddled Avith water to the consistence of mortar or rammed in, the top 
where the water is to flow over or through being protected by tight planking, 
around or beneath which the water can not leak. 

Lake McMillan dam, built across Pecos River, Colorado, intercepting its 
entire flow for the purpose of irrigation, is 1,686 feet long, 54 feet high, with 
an estimated water capacity of 1,000,000,000 cubic feet. Fig. 1040 is a section 




Fig. 1040. 



showing its construction, a heavy rock fill with a puddle slope in reservoir 
front. There is an ample spillway or waste channel by which all surplus water 
will be discharged, wdth no flow over the dike. The South Fork, Pa., dam, 
similar in construction to the above, gave way from a flow over the top of the 
dam, due to an insufficient waste and an extreme freshet. 

In the " Transactions " of the A. S. C. E., December, 1892, James D. Schuy- 
ler, a member, gives a description of the asphalt lining of reservoirs for the city 
of Denver. The excavation consisted of 2' to 3' sandy loam, 12' to 15' hard clay 
impregnated with alkali, and 8' to 12' of shale. On the completion of the em- 
bankment the slopes were sprinkled and rolled with a roller of 5 tons, drawn up 
and lowered by an engine. Beginning at the bottom, the slopes w^ere laid in 
horizontal strips of asphalt 10' wide and about If" thick spread with hot rakes, 
tamped with hot tampers, and smoothed with hot smoothing-irons. While the 
sheet was still w^arm anchor spikes of strap iron 1" X -J", 7" to 8" long, were 
driven through it into the bank, in rows about 12" centres, alternately flush 
with the surface and projecting 1^-" ; lumber strips of 2" X 4" were placed loosely 
above them on the slope for the workmen. After the finishing coat was applied, 
the projecting spikes were driven flush and painted over. The bottom thick- 
ness was 1", spread, tamped, and rolled with a cold roller of 5 tons. The finish- 
ing coat of refined Trinidad as|)halt, fluxed with residuum oil, w^as poured on 
from hot buckets, and ironed over with smoothing-irons heated to a cherry-red. 

Dikes or dams over which there is no flow of water can be made entirely of 
earth. It is sufficient that the material be made more compact than the natu- 
ral earth in which the dam is built, that it be of sufficient section to resist the 
pressure, and width to obstruct the flow of water through it, and reduce the 
percolation to a safe and economical limit, the passage of water between the 
particles of earth being like that through very small broken and crooked pipes. 



438 



ENGINEERING 
'5 




DRAWING. 

Dikes across salt marshes are 
made of material taken from the 
marsh at some distance from the 
site of the dike, well packed in thin 
layers on a base prepared on the 
soil without excavation. Sand and 
gravel, being heavier than the moist 
material, break through it and set- 
tle to the bottom, involving often 
the construction of a large em- 
bankment, while by the use of a 
homogeneous material the founda- 
tion is not displaced but compressed. 

Fig. 1041 is a section of the 
dike or embankment for the Ashti 
Tank or Reservoir, constructed for 
retaining water for irrigation pur- 
poses in India. The following is 
an abstract of the description of 
the work given in the " Minutes 
of the Proceedings of the Insti- 
tute of Civil Engineers," vol. Ixxvi : 

' ' The net supply available for irri- 
gation may be calculated thus : 
Available capacity 

of tank 1,348,192,450 cub.ft. 

Deduct loss by 

evaporation, etc. 233,220,240 " 
Net supply availa- 
ble for irrigation 1,114,972,210 '' 

' ' Area of catchment basin nearly 92 
square miles." 

The total length of the dam is 
12,709 feet ; the breadth at the top, 
which is uniform throughout, 6 
feet ; breadth at full supply-level, 
42 feet; height of the top of the 
dam above full supply-level, 12 feet ; 
greatest height of dam, 58 feet. 
The seat of the dike throughout 
was cleared of vegetable mould, 
stones, and loose material, all trees 
and shrubs with their roots being 
completely grubbed or dug out. 
The puddle-trench laid in the nat- 
ural ground is rectangular in cross- 
section, 10 feet in width, excavated 



ENGINEERING DRAWING. 



439 



through various materials to a compact water-tight bed, and then filled in with 
puddle material, consisting of two parts of sand and three parts of black soil, 
carefully mixed and worked by treading with the feet, and then kneaded into 
balls and thrown or dashed into the trench in layers up to 12 inches in thick- 
ness. The puddle was brought to a level of 1 foot above the ground. Across 
the river the trench was cut down to the rock and filled with concrete. 

The general distribution of the material of the dam is shown in the figure. 
The central core is formed of the best black soil attainable ; on each side, ex- 
tending to the surface of the mixed material, brown, reddish, or white earth is 
used. The outer part of the dike is formed of a mixture of equal parts of 
black soil and sand. The black soil may be described as a clayey earth, tena- 
cious and adhesive when wet — a pi'oduct of the decomposition of volcanic rock. 
The brown and reddish soils are of a clayey nature, but contain admixtures of 
fine sand, nodules, and thin layers of fine grains of lime. The white soil con- 
sists of finely powdered particles of 
a grayish color, similar to wood 
ashes, which when dry possesses lit- 
tle adhesion, but when wet is ad- 
hesive. 

The various soils were laid in the 
work in layers 8 inches in thickness, 
every layer being thoroughly watered 
and rolled with iron rollers. The 
outer slope was protected by a mix- 
ture of equal parts of soil and sand, 

and with sods of grass, laid about 3 feet apart, which in time extended over the 
whole slope. 

The inner slope is protected from the action of the waves by being pitched 
or faced with dry stone, set by hand, and laid on a layer of coarse sand. The 
stones of the pitching were bedded on the slope, and were laid with their 
broadest end downward (Fig. 1042), each stone being roughly squared with the 
hammer, and touching for at least 3 or 4 inches. The interstices were then 
packed with small stone-chippings, and finished off with sand. 

P 




Fig. 1042. 




Fig. 1043 is the section of a crib-dam in northeastern Colorado for the 
pondage of water for the purposes of irrigation. The crib- work is of round 
logs, 10" at least in diameter, joined at the end as in ordinary log huts, with 



440 



ENGINEERING DRAWING. 



dovetail or tongue. Each crib is 18 feet long on the face, and the fastenings 
are 2" X 18" treenails. The cribs are set radially, forming a cnrve up-stream 
of 200 to 238 feet radius. The crib gives the stability, but the water-tightness 
depends on a shutter, ^, or vertical panel of timber, and the filling of earth on 
the up-stream side. 

For dikes where water does not flow over the top a construction similar to 
Fig. 1043 is very strong and in many places the most economical, but without 
any wood, which is likely to decay or rot when exposed to the air. In con- 
struction it consists of a mass of masonry laid dry, with a nearly vertical up- 
stream face pinned and pointed with cement mortar and again faced with a 
concrete or cement wall in close connection with the wall face and mortar 
bonded with it. The face of the concrete or cement wall is plastered with a 
light coat of cement and protected against the wash of the water or thrust of 
the ice by an earth embankment. This embankment adds to the security of 




Fig. 1044. 



the dam by cutting af[ seams in the rock foundations and to the stanchness 
of the cement wall. 

Fig. 1044 is a section of the dam across the Connecticut Eiver, at Holyoke, 
Mass. This dam is 1,017 feet long between abutments, averages 30 feet high 
by a base of 80 feet and is constructed of timber crib- work, loaded with stone 
for about one third its height. The foot of each rafter is bolted to the ledge, 
and all their intersections are treenailed together with 2" white-oak treenails. 
The inclined plank face is loaded with gravel, and the joint at the ledge cov- 
ered with concrete. The lower or base tier of ranging timbers are 15" X 15", 
the other timbers 12" X 12". The rafters are placed vertically over each other, 
in bents of 6 feet between centres. The planking is of hemlock 6" thick, with 
oak cross planking at crest of dam 4" thick at bottom and 8" at top. The crest 
is plated with iron ^" thick, 5 feet wide. During the construction the dam 
was planked first about 30 feet on the incline ; a space was then left of about 
16 feet width by sufficient length, through which the water flowed ; and the 
balance of the dam was then completed. A plank flap was then made for the 
opening, and when everything was ready it was shut down and the pond filled. 
The objection to the flap construction is that the space left for the waterway 
through the dam, after its completion, serves as a duct for air from below 
which softens and rots the timber-work. 



ENGINEERING DRAWING. 



441 



When the dam was first contemplated the longer time and extra cost re- 
quired for a masonry construction turned the scale in favour of crib-work. 
Some twenty-five years after its completion it was found that the water over- 
fall from the crest was cutting out the ledge beneath the dam, and a crib-apron 
was constructed, entirely across the river, sheathed with plank on a slope of 
about 2^ to 1 from the crest downward. From the decay and weakening of the 
timbers of the old dam, continual repairs have been required, and it is now de- 
cided to put in a masonry dam, the wooden dam having served its purpose for 
some fifty years. 

Fig. 1045 is a section of the dam across the Croton River, constructed under 
the direction of Mr. John B. Jervis, for the supply of the aqueduct for the city 
of New York. This dam was built on an earth foundation, with curved roll in 




Fig. 1045. 



cut stone, extending by a timber-apron some 50 feet, supported by strong crib- 
work. Originally there was a small supplementary dam farther down to set the 
water back on to tlie crib-apron, but this was washed out, and the crib-w^ork is 
replaced by heavy rock pave. In the erection of this dam all loose material was 
removed, and then the cribs C and D were built up and the tops were planked ; 
on this planking were carried up the cribs F and' G. Between these piers the 
space E, as well as e below and on the cribs, was filled in with concrete ; on this 
the body of the dam was erected in stone-masonry, laid in cement. The face- 
work of granite is cut to admit of a joint, not exceeding j\ of an inch. The 
radius of the granite face is 55 feet, and the dam 38 feet high from level of 
apron to crest of dam. This dam has been in use fifty years and is in very good 
condition and tight. 

Fig. 1046 is a section of a, part of the dam across the Merrimac River, at 
Lowell, built under the direction of Mr. James B. Francis. It was laid dry, with 
the exception of the upper face and coping, which was laid full in cement. 
The horizontal joints at the crest were run in with sulphur. The coping- 
stones were dowelled to the face and together, and clamped to an inclined stone 



442 



ENGINEERING DRAWING. 



on the lower slope ; the end-joint between these stones was broken by making 
every alternate lower stone longer, and the upper shorter, than shown in the 
drawings. 

The Cohoes dam (Fig. 1047) was built by W. E. Worthen, C. E., directly 
below an old dam of somewhat similar construction to that of Holyoke. The 



Scale : k inch - 1 foot. 




Fig. 1046. 

old dam had become very leaky and worn, and the overfall had in many places 
cut deep into the rock, and in some places within the line of the dam. It was 
therefore proposed to make the new dam, as a roll to the old one, to discharge 
the water as far from the foot of the dam as possible, and to keep the old dam 
for the protection of the new. The exterior of the dam was of rock-faced ash- 
lar ; the caps were in single lengths of 10 feet, and none less than 15" thick and 
2 feet wide ; they were dowelled together with two galvanized wrought-iron 
dowels each. The whole work was laid full in cement ; the 20" face was laid 
first to divert the leak of the old dam from the new work. The whole was 
brought up to the outline, to receive the cap-stones, which were bedded in ce- 
ment ; the top-joints were then run or grouted in neat cement, to within about 
6" of the top of the stone, which was afterward run in with sulphur. Entire 
length of overfall, 1,443 feet ; average depth below crest of dam, 12 feet. 

Where the body of water which may at any time discharge over the dam is 
large, and the fall high, it is especially desirable to secure a location Avhere the 
overfall can be upon solid rock. If there be a ledge at the side of the river, and 
none can be found in the channel, it is often better to make a solid dike across 
the river and above the level of freshets, and cut the overfall out of the bank. 



ENGINEERING DRAWING. 



443 




Fig. 1047. 

When the dam can have only an earth foundation, an artificial apron, or plat- 
form of timber or rock, is to be made, on which the water may fall, or the high 
fall may be broken up by a succes- 
sion of steps. In some cases a roll 
or incline, like that given in the 
Croton dam, is extended to the bed 
of the stream, and continued by an 
apron. The water thus rolls or 
slides down, and takes a direction, 
as it leaves the apron, parallel with 
that of the bed of the stream. But fig. io48. 

care must be taken to protect the outer extremity of the apron by sheet-piling 
and heavy paving, as the current, by its velocity, takes with it gravel and all 
small rocks, and undermines the apron. 











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i| 




1 


il 


■1 


1 

1 




1 











Fig. 1049. 



444 



ENGINBERING DRAWINa. 




^F^^^ 



Fig. 1051. 



To retain the floAV of rivers in dry seasons when the ponding will have little 
or no effect on works farther up the stream, flash-boards are used, which usually 

consist of an iron bolt driven 
into the crest of the dam, 
against which common boards 
are raised to be swept off when 
the river rises unexpectedly. 
To control the levels of the ca- 
nal, hand flash-boards are used, 
as in Fig. 1048, sliding in per- 
manent grooves. 

Figs. 1049, 1050, and 1051 
are plan, elevation, and section 
of the Beetaloo dam. South 
Australia. The dam is built of 
concrete, 580 feet long, 110 feet 
high, 110 feet thick on a level 
with the bed of the creek, and 
14 feet thick at the top. The 
cross-section is in accordance with Prof. Eankine's formula, the horizontal 
curvature having a radius, of 1,414 feet. The structure is founded on rock 
and has a spillway 200 feet long by 5 feet deep, its channel below being di- 
vided by walls into three sections, as shown by the drawings. 

Head-gates are constructions necessary to control the flow from the river- 
pond or reservoir into the canal or conduit by which the water is to be con- 
veyed and distributed for the purposes to which it is to be applied. The top 
of the works should therefore be entirely above the level of the highest freshets, 
that no water may pass, except through the gates ; and it is better that the 
opening of the gates should be entirely below the level of the top of the dam, 
to prevent as much as possible the passage of drift and ice, which are often ex- 
cluded by booms and racks placed outside the gates. 

Figs. 1052, 1053, and 1054 are drawings, in plan and detail, of the head- 
gates, and the machinery for hoisting them, at the Cohoes Company's dam. 
There are ten gates, four 8' x 6' 6" and six 8' x 9' in the clear ; all can be 
hoisted by machinery connected with a turbine-wheel at «, or separately by hand. 
At b there is an overfall, at the same height as the dam, over which any drift 
that is brought against the gate-house is carried. At c there is a similar over- 
fall within the gates, and another at d, by which any sudden rise of the level 
of the canal is prevented. At e there is a gate for drawing down the pond, and 
another at /, for drawing off by the canal, both raised and lowered like the 
head-gates. The head-gates are of solid timber bolted together, moving in 
cast-iron guides set in grooves in the stone ; in front of these grooves there is 
another set of grooves {g g), which are intended for slip-planks or gates, to be 
put in whenever it is necessary to shut off the water from the gates themselves 
in case of repairs. 

Hoisting Apparatus.— To each gate there are strongly bolted two cast-iron 
racks, geared into two pinions on a shaft extending across the gate-space, and 
supported on cast-iron standards on the piers. At one extremity of this shaft 



ENGINEERING DRAWING. 



445 




446 



ENGINEERING DRAWING. 




ENGINEERING DRAWING. 



MY 



there is a worm-wheel, driven by a worm or screw on a shaft perpendicular to 
the pinion-shaft. The worm-shaft can be driven either by a hand-wheel at one 
end, or by ihe friction-bevel at the other. The friction-bevel can be driven in 
either direction by being brought in contact with one or other of the friction- 
bevels on a shaft extending the whole length of the gate-house, and in gear 
directly with the small turbine at a. The small turbine draws its supply through 
a pipe, built in the walls, and opening into the space between the gates and the 
slip-plank groove. 

In the guard gates at Lowell, instead of racks attached to the gates they are 
supported by strong rods with screws cut at the upper ends and are raised by 




Fig. 1055. 

nuts in the hubs of a pair of horizontal gears driven by a pinion between the 
two on an upright shaft, connected with the gearing of a turbine water-wheel. 
In late constructions the gates are raised by hydraulic jacks in connection 
with the city water mains. 

Small gates in canals are usually made of wood, with wooden starts on which 
a rack or racks are planted and hoisted by hand through a crank and pinion 
shaft. Fig. 1055 is a perspective of the hoisting apparatus of such a gate with 
a single stem or start. The pinion is driven through a horn wheel and lever. 
The lever is pressed down and the gate raised ; when this movement is stopped 
a dog catches a ratchet on the back of the wheel and the gate is held. The 
lever is slipped outward, and is brought in contact with another horn, with 
another depression and raise of gate. The fulcrum of the lever is the centre 
pin of the wheel. In dropping the gate the lever holds it in position, the dog 
is thrown out, the lever thrown out from the horn, and the gate drops from its 
own weight; if it sticks, it can be forced down by the reverse movement of the 
lever. 

Gates seldom used are raised by chains over a barrel by handspikes, and 
held by ratchet and dog and dropped as above ; but for gates at the head of 



448 



ENGINEERmG DRAWING. 




ENGINEERING DRAWING. 



449 



flumes leading to wheels the provision for their movement must be positive in 
both directions, as they are of frequent use. 

Figs. 1056 and 1057 are the elevation and section of flume head-gates as 
manufactured and used at Holyoke, Mass., for such positions. G G are plank 
gates sliding laterally, moved by two pinions working into racks at the top and 
bottom of the gates, turned by a capstan bar on a horn wheel head. F is the 
flume, circular, of wooden staves or wrought-iron plates. P is a paddle gate by 
which the flume must be filled slowly, and A the pipe for escape of air from 
the flume during fllling. 

The Cheney head-gates (Figs. 1058 and 1059), as applied to several of the 
water gates of the canals at Lowell, are gates supported by wheels, which run 




Fig. 1058. 



Fig. 1059. 



on upright cam shafts on each side of the gate ; when the gate is moved either 
up or down, the cam shafts are turned to raise the gate from the flat-closing 
surface, and take the whole water pressure, which is, in a measure, relieved by 
the opening of this joint, and the whole friction is transferred to the wheels 
and the gate readily raised. 

Fig. 1060 is the elevation of a circular tube of plate-iron, as used for a 
waste gate in the canal of the Connecticut River 'Company at Windsor Locks. 
It is of the form of a hollow plug, largely used for bath tubs, and now called a 
standard waste. The tube is 8 feet diameter and 9 feet high. The joint be- 
tween the plug and the pipe extending to the river, is made by angle irons A A. 
The movement of the plug vertically is controlled by radius bars working in 
30 



450 



ENGINEERING DRAWING. 




Fig. 1060. 



ENGINEERING DRAWING. 



451 



centres on the back wall ; they are made of channel bars, each set braced hori- 
zontally. The plug is raised by a differential pulley-block suspended at C from 
a wooden beam across the water. The hoist chain is carried by a yoke to the 
two radii bars at B ; when eased, the plug drops readily to its seat. The level 
of the canal is about 35 feet above that of the river, and the discharge is so 
large that it produces a scour in the canal. When the level of the canal rises 
above the crest of the tube it forms an overfall ; a depth of a little over 2 feet 
will take the whole capacity of the tube. 

Figs. 1061 and 1062 are the front elevation and section of the gates of Farm 
Pond, Sudbury River Conduit, Boston Water- Works. The main web or plate 





Fig. 1061. 



Fig. 1062. 



of the gate is H" thick, the ribs 6" deep, the gate-stems 2^" diameter. The 
nuts by which the gates are raised are geared together, and actuated by a 
double crank. The gates and guides are faced with brass, about -^" thick. 

Similar gates are very common, plates of casf-iron strengthened by ribs ; 
the guides are also of cast-iron, bolted to the masonry, with faces of the gates 
and guides usually of brass plates, as iron faces become rusty and stick. 

Canals. — The sections of canals depend upon the purposes to which they 
are to be applied, whether for navigation or for power ; if for navigation, ref- 



452 



ENGINEERING DRAWING. 



erence must be had to the class of boats for which they are intended ; if for 
power, to the quantity of water to be supplied, and sundry precautions of con- 
struction. 

Fig. 1063 is a section of the Erie Canal : width at water-line, 70 feet ; at 
bottom, 28 feet; depth of water, 7 feet; width of tow-path, 14 feet. The 




Fia. 1063. 



slopes are gravelled and paved, the edge of the tow-path is paved with cobble- 
paving, and the path gravelled. The smaller canals of this State and of Penn- 
sylvania are generally 40 feet wide at water-line, and 4 feet deep ; the Delaware 
and Karitan, 75' x 7' ; the Chesapeake and Delaware, 66' x 10' ; the ship-canals 
of Canada, 10 feet deep and from 70 to 190 feet wide. 

The dimensions for canals for the supply of mills depend — first, on the 
quantity of water to be delivered. Their area of cross-section should be such 
that the average velocity of flow should not exceed two to three feet per second, 
and in northern climates less velocity than this would be still better ; it should 
always be such that during the winter the canals may be frozen over, and re- 




FiG. 1064. 



main so, to prevent the obstruction from drift and anchor-ice in the water- 
wheels. The usual depths of the larger canals are from 10 to 15 feet ; with 
such depths the cover of ice which reduces the section by the amount of its 
thickness does not materially decrease the velocity of flow, nor diminish very 
perceptibly the available head. 

Fig. 1064 is a section of the Northern Canal, at Lowell, Mass., which may 
be considered a model for large works. The width at water-line is 103 feet 
and the depth 16', and is intended for an average flow of 2,700 cubic feet per 
second. The fall in the whole length of 4,300 feet is between 2" and 3" ; when 
covered by ice, about 4". The sides are walled in dry rubble, and coped by 
split granite. The portion above, and about three feet below, the water-line, or 
between the limits of extreme fluctuations of level, is laid plumb, that the ice 
may have as free a movement as possible vertically. 

Fig. 1065 is a section, on a scale of -J" = 1 foot, of the river-wall of this 
same canal, where the canal passes out into and occupies a portion of the river 
channel. The main wall is in dry masonry, faced on river-side with rough- 
faced ashlar, pointed beds and end-joints. The inside lining is of two courses 
of cement- wall, to the dry rubble wall pointed with cement, against which is 



ENGINEERING DRAWING. 



453 



laid the first cement lining, plastered on the inside, and the interior wall is 
then laid ; the granite inside wall, above lining, is laid in cement. 




Fig. 1065. 



Lochs of Canals. — Figs. 1066 and 1067 are portions of plan and vertical 
section of locks, taken from the general plans for timber locks on the Chemung 
Canal. They represent the half of upper gates. Fig. 1068 is a section of one 
side of the lock of the same. Fig. 1069 is the plan of a portion of one of the 




Fig. ]066. 



enlarged locks of the Erie Canal, showing one of the upper gates and the side- 
walls. Fig. 1070 is a cross-section of one of the same locks, showing the cul- 



454 



ENGINEERING DRAWING. 



vert in the centre between the locks, used for the supply of the waste of the 
lower level. The proper height of water in this level is controlled by gates in 
the upper level. 




Fig. 1067. 



ScAiE : rz" =\ foot. 




Fig. 1068. 




ENGINEERING DRAWING. 



455 



Fig. 1071 is a drawing, in outline, of the hollow quoin of the lock-gate, on 
a scale of -^ full size (Chemung Canal). 



^ V -»r- 




FlG. 1070. 



Scale : ro" = 1 foot. 



Fig. 1072 is a plan and elevation of pintal for heel-post of lock, with a sec- 
tion of the bottom of the post. The pintal is imbedded in bottom timber or 
stone, as the case may be. 






Fig. 1071. 



is full size. 



Fig. 1072. 



Fig. 1073 is a plan and elevation of the strap for the upper part of heel-post. 
Extracts from lock specifications (" N"ew York State Canals," 1854) : 

" Locks to be composed of hydraulic stone masonry, placed on a foundation of 



ber and plank. The chamber to be 18' 
level, and 110' long between the upper 
and lower gate-quoins. The side-walls 
to extend 21' above the upper gate- 
quoins, and 14' below lower gate- 
quoins. If the bottom is of earth, 
and not sufficient to support the foun- 
dation, then bearing-piles of hard 
wood, not less than 10" diameter at 
small end, shall be driven. The foun- 
dation timbers to be 12" x 12", and of 
such lengths as will extend from and 
cover the outside piles, and to be tree- 
nailed with a 2" white-oak or white- 
elm treenail, 24" long, to each pile. 



tim- 
wide at the surface of the water in the lower 




Fig. 1073. 



456 ENGINEERING DRAWING. 

''If without bearing-piles, the foundation to be composed of timber, 13" thick and 
not less thari 10" wide, counterhewed on upper side, placed at uniform distance, accord- 
ing to their width, to occupy or cover at least f of the area of the foundation, and 
under the lower mitre-sill to be placed side by side : in all cases to be of sufficient 
length to extend across the lock to the back line of the centre buttresses, and at the 
head and foot to the rear or back line of wing-walls. The timber under the lower 
mitre-sill to be of white oak, white elm, or red beech, the other foundation and apron 
timber to be of hemlock. The foundation to be extended 3' above the face of the main 
wall at the head of the lock, and at the foot from 25' to 30' below the exterior wing — 
that portion of the spaces between the timbers in all cases to be filled with clean coarse 
gravel, well rammed in, or concrete. Where rock composes the bottom of the lock, and 
is of such a character that timber is not required for the foundation, the same shall be 
excavated smooth and level, and the first course of stone well fitted to the rock, 

*' Sheet-Piling. — In all cases where rock does not occur, there shall be a course at the 
head of the foundation, under each mitre-sill, and at the lower end of the wings, and at 
the lower end of the apron, to be from 4' to 6' deep as may be required — in each to ex- 
tend across the whole foundation. 

'■'■Flooring. — A course of 2V pine or hemlock plank to be laid over the whole of the 
foundation timbers, except a space, 3' wide, under the face-line of each wall to be 2^" 
white oak; the whole to be well jointed, and every plank to be treenailed with two 
white-oak treenails at each end, and at every 3' in length, to enter the timber at least 5", 
or with wrought-iron spikes, treenails to fill ly bore. Platform for the upper mitre-sill 
to be 5' 10" wide, and 6' high above foundation, and to extend across from side-wall to 
side-wall, to be composed of masonry, coped with white-oak timbers, extending 6" into 
each side- wall. Mitre-sills to be of best white-oak timber, 9" thick, to be well jointed, 
and bolted to the foundation or platform timbers with bolts 20" long, 1" x 1", well 
ragged and headed. 

" Masonry. — The main walls, for 21' 6" in length, from wing-buttresses at the head, 
and 32' at lower end, to be 9' 8|^" thick, including recesses, and for the intermediate 
space, 7' 81" thick, with three buttresses projecting back 2^', and 9' long at equal dis- 
tances apart. The quoin-stones, in which the heel-post is to turn, shall not be less than 
5' 6" in length in line of the chamber, to be alternately header and stretcher. The 
recesses for the gates to be 20" wide at top of wall, 12' long, with sub-recesses, 9" wide, 
6' high, 10' long, for the valve-gates. 

" Culvert Ijetween Locks. — The sluice-way shall be made in the head- wall with cut- 
stone jambs, grooves to be cut in the jambs for the sluice-gates, the bottom of the aper- 
ture to be of cut stone, with lower corner beveled off, over which the water will fall into 
the well, the bottom of which shall be covered with a sheeting of cut stone, 6" thick. 

'-'■ Second flooring of seasoned 2" first-quality white-pine plank, to be well jointed, and 
laid on the foundation between the walls, from the breast-wall to lower end of main wall, 
and also on the floor of the wall. 

" Gates. — The framing to be made of best quality white-oak timber; the cross-bar to 
be framed into heel and toe posts with double tenons, each tenon to be 7" long, and se- 
cured with wrought-iron Ts, well bolted. The heel and toe posts to be framed to the 
balance-beam by double tenons, and secured by a wrought-iron strap and balance-rod, 
from the top of the beam to the under side of the upper bar. The lower end of the 
heel-posts to be banded with wrought-iron bars ; the collar and other hangings to be of 
wrought-iron, secured together with a double nut and screw, and to the coping by bed- 
ding the depth of the iron in, and by screw-bolts fastened with sulphur and sand-cement. 
The pivots and sockets which support the heel-posts to be of best cast-iron; a chilled 
cast-iron elliptical ball, 1\" horizontal, and 1" vertical diameter, to be placed on the 
pivot and in the socket of each heel-post, gates planked with seasoned 2" white-pine 
plank, jointed, grooved, and tongued — tongues of white oak." 



ENGINEERING DRAWING. 



457 




Fig. 1074. 



Water, ponded by dams, and conveyed by canals for use as mill-power, is 
carried within the workshops or manufactories, to be applied on water-wheels, 
by some form of covered channels usually designated as fltcmes. The common 
form of a flume for the conveyance of water to breast, overshot, or undershot 
wheels, is of a rectangular section, framed with sills, side-posts, and cap, and, 
if a large section is required, with intermediate posts. The sills are set, and 
earth well rammed in the spaces between them ; the bottom plank is then laid, 
posts and cap framed with tenon and mortice, set and pinned, and the plank is 
then firmly spiked on the outside of posts and caps. The planks are usual- 
ly partially seasoned and 
brought to close joints ; 
the size of timbers will 
depend on the depth be- 
neath the soil, or the in- 
sistent load. Within the 
mill, and just above the 
wheel, the flume is framed 
without a cover, and the 
posts and side-planks are 
brought above the level of 
the water. This open 
flume is termed the penstock, especially necessary, in the class of wheel above 
referred to, to secure the full head of water. 

For the conveyance of water to turbine-wheels, wrought-iron pipes are 
almost invariably used. Cast-iron is also sometimes used, with flange, or hub 
and spigot- joints. Plank-pipes (Fig. 1074) are also used, made with continu- 
ous staves, and hooped with wrought-iron; these constructions are much 
cheaper, and serve a very good purpose. The head-gates of flumes are placed 
at the head of the flumes, in a recess back from the face of the canal, with 
racks in front to prevent the passage of any drift that might obstruct or injure 
the wheel. The total area of passages through the racks should liberally exceed 

the area of cross-section of the flume, not 
only on account of the extra lateral fric- 
tion of the rack-bars, but also on account 
of their liability to become obstructed. 
Sometimes two sets of racks are placed 
in front of the flumes, especially for 
turbines and reacting wheels : a coarse 
rack outside, with wide spaces, say 2" 
and a finer one inside, say of f" to f" 
spaces. 

Conduits for the supply of water to 
cities and, towns are of masonry, or cast- 
or wrought-iron pipes. Their capacity to 
deliver the required quantity depends upon 
the area and form of cross-section, and 
the velocity of flow due to the loss of head or of pressure permissible ; this 
velocity being due primarily to gravity, but largely modified by conditions of 




Fig. 107,5. 



458 



ENGINEERINa DRAWING. 



structure, as the kind and amount of wetted surface, and length and directness 
of line. 

. Fig. 1075 is a cross-section of the main conduit of the Nassau Water- Works 
for the supply of the city of Brooklyn, Long Island. The width is 10' at the 
springing of the arch ; the side- walls 3 feet in height ; versed sine of invert, 
S" ; height of conduit in centre, 8' 8" ; fall or inclination of bottom, 1 in 
10,000. 

The foundations to be of concrete, 15' wide, on earth, or, if the water was trouble- 
some, on a platform of plank. The side-walls of stone, with an interior lining of 4" 
brick; arch brick, 12", and the invert 4" thick. The outside of arch, and each wall, 
were plastered over on the outside with a thick coat of cement mortar. In both cuttings 
and embankments the arch was covered with 4' of earth, with a width of 8' at top, 
and slopes on each side of 1^ to 1, covered with soil and seeded with grass. 

Fig. 1076 is a section of the conduit of the Boston Water- Works. The 
inside section is equal to a circle 8|- feet diameter, and is uniform throughout 
except in tunnels. The section given is the general one, resting on concrete, 
brick lining at sides and invert at bottom, with an 8" arch at top for a 4' cover, 
and 12" for exceptional depths or under railway-tracks. The lower corners 
were of special brick. 

The inclination of the conduit is 1 foot per mile, and the flow 80,000,000 
gallons per 24 hours when full, or 5 feet above centre of invert. The maximum 
flow takes place when the depth of 
water is 7' 2", the delivery then being 
109,000,000 gallons. 

Fig. 1077 represents a section of 





Fig. 1076. 



Fig. 1077. 



the old Croton Aqueduct, in an open rock-cut. The width at spring of arch, 
7' ; versed sine of invert, 6" ; height of conduit, 8' 6" ; fall or inclination of 
bottom, about 1 in 5,000. 

Fig. 1078 is a two half section of the new Croton Aqueduct, of which one 
is in earth and rock, and the other entirely in rock. The foundation is in con- 
crete, the lining and arches in brick. At the junction of the invert and side 
linings there is a special angle block in brick ; exterior of brickwork is plastered. 

Before the construction of High Bridge water was conveyed for the supply 
of the city through siphon pipes beneath the Harlem Kiver, afterward through 
two 3' cast-iron pipes in the masonry of the bridge. As the demand for water 
increased in the city, the obstruction caused by lack of capacity in these pipes 
made the introduction of a larger pipe necessary (Fig. 1079), which has been 



ENGINEERING DRAWING. 



459 



made of wrouglit-iron, J-" thick and 7' 6J" in diameter, supported by cast- 
iron columns which admit of a rocking movement, and slip-joints in the 
pipe to compensate for any ex- 
pansion or contraction. The 
pipes are inclosed in a long cham- 
ber, extending the whole length 
of the bridge, covered by a brick 
arch, laid in cement with a cover 
of asphalt, and a brick pavement 
over all. A A are the arch-stones 
of the bridge. 

In large works, where there 
is considerable length of conduit, 
receiving reservoirs, within or 
near the limits of the city, are 
necessary as a precaution to guard 
against accidents which might 
happen to conduit or dam, and cut off the supply, and also as a sort of balance 
against unequal or intermittent draught among the consumers. The size of 
these reservoirs must depend on the necessities of the case, and on the facilities 




Fig. 1078. 




Fig. 107 



for construction. At Ridgewood, Brooklyn, there are three reservoirs in con- 
nection, of total capacity of about 325,000,000 gallons. The capacity of the 
upper Croton reservoir in Central Park, New York, in two compartments, is 
about 1,000,000,000 gallons. 

Fig. 1080 is a section of the division-bank of the Croton reservoir, made of 
earth, with a puddled ditch in the centre. 



460 ENGINEERING DRAWING. 

Extracts from the specification : 

"All the banks will have the inner and outer slopes of 1^ base to 1 perpendicular. 
All the inner or water-slopes will be covered with 8" of broken stone, on which will be 
placed the stone pavement, 1| foot thick. The outer slopes will be covered with soil 1 




Fig. 1080. 

foot thick. The banks, when finished, to be 15 feet on top, exclusive of the soil on the 
outer slope. The top of the outer bank to be 4 feet above water-line ; the top of the 
division-bank to be 3 feet below water-line. In the centre of all the banks a puddle- 
bank will be built, extending from the rock to within 2 feet of the top of the outer bank. 
It will be 6' 2" wide at top in division -bank, and 14' wide at top in exterior bank, and 
16' wide at a plane 38' feet below top of exterior bank. In the middle of the division- 
bank there will be built a concrete wall 4' high, 20" wide ; 8" thickness of concrete to be 
laid on the top of the bank, on each side of, and connected with, this wall. On the 
pavement 18" thick will be laid in concrete. The slope-wall on each side of the division- 
bank, 10' in width, to be laid in cement. 

"Puddle-ditches are to be excavated to the rock under the centre of all embank- 
ments. The earth within the working-lines of interior slopes to be excavated to the 
depth of 40' below top of exterior bank, rock 36'. The puddle-ditch to be formed of 
clay, gravel, sand, or earth, or such admixture of these materials, or any of them, as the 
engineer may direct, to be laid in layers of not more than 6", well mixed with water, 
and worked with spades by cutting through vertically, in two courses at right angles 
with each other; the courses to be 1" apart, and each spading to extend 2" into the 
lower course or bed. The puddle to extend to all the masonry and pipes, as the engineer 
may direct. 

"The embankments to be formed in layers of not more than 6", well packed by cart- 
ing and rolling, and, where rollers can not be effectually used, by ramming. The em 
bankments to be worked to their full width as they rise in height, and not more than 2' 
in advance of the puddle. The interior slopes of all the banks to be covered with 8" 
thickness of stone, broken to pass through a 2" ring. On this to be laid the paving, 18" 
in thickness, of a single course of stones set on edge at right angles with the slope, laid 
dry, and well wedged with pinners. " 

Fig. 1081 is a drawing of a sheet-iron water pipe as used in the States of the 
Pacific slope. The bottom joint is a slip-joint of the stove-pipe iron order, 
which Mr. Hamilton Smith considers good for pressures not exceeding 380 
feet. For pressures greater than this, the lead joint, as shown in Fig. 1082 
in section, should be used ; it consists of an inner sleeve riveted to the inside 



ENGINEERING DRAWING. 



461 



of one pipe and an outer sleeve covering the joint with a |" space, into which 
lead is run and calked as for cast-iron pipes (see page 463). 




Fig. 1081 



The pipe as drawn is on an incline and is anchored by a wire cable. Un- 
der heavy heads and on inclines the pipes should be wired together, and at 
angles lead joints should be used. 

The pipes are invariably coated with asphalt, inside and out, by immersing 
them for some minutes in the hot liquid. The pipes are double riveted, and 
the thickness of the iron very much less than used here ; the Cherokee pipe, 30 
inches diameter up to 203 feet head, is No. 14, or -083" thick ; head 900 feet, 
I" thick. 

At first slip-joints were made for expansion, but were found unnecessary. 
Time has shown no practical depreciation in the pipes. 

For conduits of large size, and under extreme pressure, wrought-iron or 
steel may be considered the rule in the United States ; they are more econom- 
ical in cost and safer than masonry, less disturbance from settlement, practi- 
cally without leak, and admitting of prompt and easy connections and repairs. 

In construction pipes are made up at shops and riveted like boilers, and are 
put together in such lengths as can be readily transported and laid. Welded 
longitudinal joints on the separate lengths can be obtained without much in- 
crease in cost, and flanges may be turned on them for bolting or riveting. 

For water supplies to locomotives on our railroads, the usual tanks are 
wooden cisterns strongly hooped and resting on timber frames. Fig. 1083 is a 
tank of wrought-iron on the Orleans Eailway, containing 22,000 gallons, and 
applicable to small services of towns and villages. The inverted-dome bottom 
has no supports except at the circumferenct^, where there is a strong iron plate 
with extra angle irons, as shown in detail. The pipes pass through the bottom, 
but give it no support. This form has been applied at the Liverpool water- 
works in the Xorton Tower, where the tank is 82 feet in diameter and contains 
651,000 gallons. 



462 



ENGINEERING DRAWING. 



Water-works for small towns often draw their supply from driven wells, 
and for this service stand-pipes or tanks of iron are preferable to reservoirs in 
earth ; but waters from these sources are usu^ly deficient in oxygen, and con- 
fervas develop rapidly in open reservoirs exposed to the light and air. They 
must therefore be of small dimensions, so that there be no stagnation ; the 
water must circulate and be changed often. These inconveniences, together 




Fig. 1083. 

with warmth in such metallic tanks in summer weather, has led to the making 
of tight tanks as in the elevator service, under a pressure of about 100 pounds 
to the square inch and earth covered. 

Distribution. — Figs. 1084 to 1088 are sections of the spigot and faucet ends 
of cast-iron water-mains as used in Brooklyn and Philadelphia. 

Below is given a table of dimensions, thickness, etc., of pipes, which may 
be considered fair averages for water-mains ; 4" pipe is the smallest diameter 
to be used in distribution, and if a hydrant is placed at the extremity of 500 
feet of such pipe, the head will be very much reduced in case of fire service. 



ENGINEERING DRAWING. 



46a 



In cities the minimum diameter is usually 6", except in the 4" connection of 
dead ends for circulation. The thicknesses given in the table are as low as ad- 




Fig. 1084. 





Fig. 1086. 



Fig. 1087. 



missible for tapping, and if the pipe is not of uniform thickness, is to be put 
the thickest side up for this purpose. 

The diameters given in the table are such as can 
-2H H be found in stock, but other sizes will be made to 




Fig. 1088. 



Diameter. 


Thick- 
ness. 


Weight per 
foot laid. 


Lead-joint 
weight. 


Safe, feet 
head. 


4 


0-42 


19-7 


4 


1,609 


6 


0-47 


32-6 


7 


1,200 


8 


0-47 


42-4 


10 


900 


12 


0-61 


82-2 


16 


800 


16 


0-67 


119-7 


23 


680 


20 


0-75 


164-7 . 


31 


600 


24 


0-80 


210-3 


40 


520 


30 


0-98 


320-0 


57 


520 


36 


1-15 


450-0 


75 


500 


48 


1-44 


757-0 


120 


480 



order ; if ordered of extra thickness the bore is preserved uniformly, and the 
extra metal is put on the outside. 

After laying, a hemp gasket is forced down to the lower end of the bell to 
prevent the molten lead from escaping into the pipe ; the end of the pipe is 
then stopped by a clay roll, or a rope covered with clay, or clay alone, or with 
a metal clamp containing clay, and the molten lead is then poured in through 
an aperture or gate at the top ; after cooling, the joint is made secure and tight 
by compacting the lead with calking tools made for this purpose. 

Wrought-iron pipes have also been used for distribution, generally with 
cast-iron bells, riveted at one end and a smali ring on the other (Fig. 1089) or 
by flanges secured on both ends and bolted together when laid. 

Specials. — All parts of a main except the straight pipes are called special 
castings. 

Fig. 1090 is a 12" X 8" 4-way branch, shown full and in section, diagonally. 



464 



ENGINEERING DRAWING. 



The horns on the branch are for straps to hold in a plug, cap, or a connected 
short or curved pipe. The 4-way branches are often called crosses, and the 




Fig. 1089. 




Fig. 1091. 




Fig. 1092. 




Ftg. 1090. 

3-way T's, or single branches. The branches may be 
of any appropriate size. In ordering, designate diam- 
eter of main pipe first, and then that of the branches. 
It is very common in these pipes to make all of the 
ends bell ends — it saves sleeves when pipes are cut, as 
they usually are at street intersections. 

Fig. 1091 is a section of a sleeve for uniting cut 
pipes or uncut spigot-ends ; a kind of double hub is 
often used for the former. Sometimes sleeves are 
made in halves, and bolted together. 

Fig. 1092 is the section of a reducer for the con- 
nection of pipes of unequal diameters. 

Fig. 1093 is the section of a hend ; the horns on 
the outer circle are for straps between the pipes, as 
the pressure is unbalanced. 




Fig. 1093. 



ENGINEERING DRAWING. 



465 



House-services are mostly lead pipes ; the taps on the mains for house-con- 
nections in New York city are usually 1". 

Fig. 1094 is a clamp sleeve. 
Figs. 1095 and 1096 are globe specials 
of the Builders' Iron Foundry, Providence, 





Fig. 1094. 



Fig. 1095. 



Fig. 1096. 



a T and a cross branch, which serve the purpose of Fig. 1090 and are much 
lighter, and Figs. 1097 to 1102 are specials of the same makers. 



Fig. 1097. 



C^ 



Fig. 1100. 




Fig. 1098. 



Fig. 1099. 




Fig. 1101. 




Fig. 1102. 



According to the specifications of " Cast-iron Distribution-Pipes and Pipe- 
Mains, with their Branches," etc., Brooklyn, L. I. : 

Every pipe-braach and casting to pass a careful hammer-inspection, to be subject 
thereafter to a proof by water-pressure, and while under the required pressure to be 
rapped with a hand-hammer from end to end, to discover whether any defects have been 
overlooked. The pipes were to be carefully coated inside and outside with coal-pitch 
and oil, according to Dr. R. A. Smith's process, as follows : 
31 



4:QQ ENGINEERINa DRAWING. 

' ' Every pipe must be thoroughly dressed and made clean from sand and free from 
rust. If the pipe can not be dipped promptly, the surface must be oiled with linseed-oil 
to preserve it until it is ready to be dipped ; no pipe to be dipped after rust has set in. 
The coal-tar pitch is made from coal-tar, distilled until the naphtha is entirely removed 
and the material deodorized. The mixture of 5 or 6 per cent of linseed-oil is recom- 
mended by Dr. Smith. Pitch, M^hich becomes hard and brittle when cold, will not an- 
swer. The pitch must be heated to 300° Fahr., and maintained at this temperature 
during the time of dipping. Every pipe to attain this temperature before being removed 
from the vessel of hot pitch. It may then be slowly removed and laid upon skids to 
drip." 

Setuers. — For the removal of waste water from houses and rainfall, sewers 
are very convenient in towns and cities, even before the construction of water- 
works ; but, after the introduction of a liberal and regular supply of water, 
sewers are indispensable. The ruling principle in the establishment of sewer- 
age-works is, that each day's sewage of each street and of each dwelling should 
be removed from the limits of city and town promptly before decomposition 
begins, and that it should not be allowed to stagnate in the sewers, producing 
noxious gases prejudicial to health. To attain this end, the refuse fluids must 
be sufficient in quantity to float and carry off the heavier matters of sewage. 

There has been considerable discussion of late whether sewage and rainfall 
should be carried off by a single system of pipes. This must depend largely on 
the location, economy of construction, and the financial ability to carry out 
the design. If the rainfall can be provided for by street gutters, the sewers may 
be for the conveyance of house-waste only and very small. If the sewage is to 
be discharged into a river of so large a flow that practically it will not pollute 
it, or into large bodies of water not used for domestic purposes, it is cheaper 
and better to discharge rainfall and sewage by one channel. The dimensions 
of the sewer will depend on the quantity to be discharged and the grade for 
which graphic sheets will be found in the Appendix. The rainfall is here 
estimated at 1" in depth per hour for the whole area drained, but this is in 
many places exceeded for excessive rainfalls, and it is well at such times to 
have a partial relief by the street gutters. For the sewage flow it is usual to 
calculate it from the water that is or may be furnished on any length, and 
that the maximum that may be delivered at any one time is 50 per cent greater 
than the average flow, and further that at that time the sewer should be on6 
half full. 

The value of sewers depends on the correctness of their lines, uniformity of 
descent, and smoothness of interior surface. 

For Washington, Brooklyn, and 'New York, and many other large cities 
discharging into large rivers, there is but one system of sewers for rainfall and 
sewage, and for the great areas drained very large sewers are necessarily con- 
structed. Fig. 1103 is a section of a Washington sewer, the largest in the 
United States. The bottom course of the sewer, which is exposed to a strong 
current, is of stone ; the ring courses are of brick — three for the 13-foot sewers 
and two for the 7-foot. 

Fig. 1104 is a section of the largest Brooklyn sewer. In general there is no 
base or side supports of concrete or wall, except where the bottom is of quick- 
sand. The sewer at the upper end is of circular section 10' diameter, brick- 



ENGINEERING DRAWING. 



467 



work 12" ; next size 12', then 14', and 15' — all brickwork 16". At the dis- 
charge into Gowanus Creek the section is nearly rectangular with top of iron 
beams and brick arches, brick side-walls, and inverts. 

The smaller sewers in all cities and towns are of vitri- 
fied ware or cement of circular section, or of cement of 





Fig. 1103. ^ 

egg-shaped form, but beyond the diameter of 24 inches or its equivalent section 
brick is generally used. The vitrified pipe is laid either with (Fig. 1105) or 

without concrete base and side sup- 
ports, depending somewhat on the 
kind of earth through which it is 




Fig. 1104. 




Fig. 1105. 



468 



ENGINEERING DRAWING. 



laid and the desirability of uniformity or security of construction, but the 
joints are laid full in cement with a re-enforce outside and wiped clean on the 
inside. Up to 15" the pipes are usually bell and spigot, larger they are laid 
with collars. The egg-shaped cement pipe is usually constructed with a sole 
plate, which rests on a base of plank double thickness at the joints. The joints 
of the pipe are struck with cement mortar inside and out, made very strong 





Fig. 1106. 



Fig. 1107. 



outside and very smooth inside, but usually without concrete backing, but 
packed solidly in earth. Fig. 1106 is a section of an English form of sewer 
cheap and strong. The bricks are laid with close joints inside and an exterior 
coating of cement plaster. 

This form of construction is not uncommon here with a central pipe of 
vitrified stoneware. The concrete backing is very desirable to withstand the 
shock of heavy moving loads, especially for pipes of large diameter. 

Fig. 1107 is the usual form of 
EGG-SHAPED SEWERS. egg-shaped pipe, of which the pro- 

portions are given in the table. 

Thickness of brickwork, 8"; 
boards shown at bottom only used 
in cases of soft earth for convenience 
of construction. For area of egg- 
shaped sewer of above section, multi- 
ply E' by 4-6, 

In general, brick sewers are only 
well packed in earth, but when the 
soil is loose and it is desirable to secure an extended base and side supports, 
the form Fig. 1108 is adopted, which may be in rubble masonry or concrete, 
and if the earth cover is light and the structure exposed to heavy moving loads 
the masonry should be carried above the arch. At the bottom, where the arch 
is of small radius and it is difficult to get good joints in the brickwork, it is 
very common to place inverts of vitrified ware which are sold for this purpose. 
Fig. 1109 is a section of a sewer constructed in situ at Mount Vernon, N. Y., 
through a long rock-cut. Concrete was rammed in around an inverted centre, 
and after it was withdrawn the face was plastered with a very thin coat of 



Equal to a 
circular 


D inches. 


I) and R' 
inches 


R" inches. 


sewer of 


' 






Diamster. 








24 in. 


19-8 


29-8 


5-0 


30 " 


24-8 


37-2 


6-2 


36 " 


29-8 


44-7 


7-4 


42 " 


34-8 


52-1 


8-7 


48 " 


39-7 


59-5 


9-9 


54 " 


44-6 


67-0 


11-2 


60 " 


49-6 


74-4 


12-4 



ENGINEERING DRAWING. 



469 




Fig. 1108. 



Portland cement ; the invert is of vitrified ware. A plumb i is inserted across 
the sewer (Fig. 1110) with points for centres at different heights, the radius 
is uniform, and the arch turned as high as convenient for the rock sides and 




a 



& 



Fig. 1111. 












Fig. 1109. 



Fig. 1110. 



470 



ENGINEBRINa DRAWING. 



street grades, either on levels and offsets or by inclines, the object being to se- 
cure space in the sewer, and save the rock excavated for other city purposes. 
Fig. 1111 represents the first joint from the sewer on house branches curved 

and with a cover by means of which any 
obstruction in sewer or branch could 
be better reached and removed. 

Man-holes are built along the line 
of sewers, usually from 200 to 400 feet 
apart, and at every junction and change 
of direction, to give access to the sewers 
for purposes of inspection and removal 
of deposit. 





Fig. 1112. 



Scale : J ' = 1 foot. 
Fig. 1113. 



In the large Washington sewer the man-hole is constructed on the side of 
the sewer ; in the Brooklyn one the aperture of the man-hole comes within the 
exterior wall. In most sewers it is directly over them. 

Figs. 1112 and 1113 are section and 
plan of the man-hole at present used by 
the Croton Sewer Department. It consists 
of a funnel-shaped brick wall, oval at the 
bottom 4', circular at top 2' diameter. 





Fig. 1114. 



Fig. 1115. 



Side-walls, 8" thick, through which the pipe-sewers pass at the bottom of the 
well. Across the open space the sewer is formed in brick, whose bottom section 
corresponds to that of pipe, side-walls carried up perpendicular to top of sewer ; 



ENGINEERING DRAWING. 



471 



the flat spaces at the sides of sewer are flagged. The top of the sewer is a 
heavy cast-iron frame, fitted with a strong cover, which may or may not be per- 
forated, for ventilation. In the figure the main sewer is 12" pipe, with a 12" 
branch entering at an acute angle, as all branches and connections with a 
sewer should. The short lines on the left vertical wall represent sections of jj 
staples, built in to serve for a ladder. 

When the T is at right angles to the through pipe it is very convenient to 
form the base, as in Fig.* 1114, in concrete to a wooden mould, with the inside 
plastered. This form enables the sewer to be seen in all directions by a light 

from man-hole to man-hole. Curved pipes 
are now seldom laid ; angles are made at the 





Fig. 11 



Fig. hi; 



man-holes, with straight pipe between. When necessary, catch-basins (of 
which Fig. 1115 is a vertical section. Fig. 1116 a half plan and a half sectional 
plan) are placed at the corner of the street or at depressions of the street gut- 
ters, to catch any heavy matter that might clog the sewer or fill the dock slips, 
and is removed by hand. The cast-iron hood makes a seal, preventing the es- 
cape of sewer gas through the sewer branch. Fig. 1117 is a perspective draw- 
ing of the basin head at the corner of the street. 

Where, by the difference of grades between the main line of sewer and the 
branches, the latter are at a considerable height above the base of the man-hole, 
it is best to lead the branch down by a vertical cast-iron pipe having a cros& at 
the top for access to the branch, and an elbow at the bottom to protect the ma- 
sonry from the effects of the discharge. 

Gas- Supply. — Next in importance to the necessities of a city or town for 
water-supply and sewerage is the luxury of gas-supply. The gas-works should 
always be placed remote from the thickly populated part of the city, for under 
the best regulations some gas (offensive and deleterious) will escape in the manu- 
facture. They should be placed at the lowest level, for gas, being light, readi- 
ly rises, and the portions of the city below the works are supplied at less pres- 
sure than those above. Gas-mains, like those for water, are of cast-iron, and put 
together in the same way ; but, as they have to resist no pressure beyond that of 
the earth in which they are buried, they are never made of as great thickness as 
those of water-pipes, but drips must be provided, and the pipe laid with such in- 
clination to them that the condensed tar may be received in them and pumped out. 

Owing to the reduction in price complete systems of wrought-iron gas-pipe 
are now laid, with the usual screw-coupling and tested to a pressure much in 
excess of that of the gas. 



472 



ENGINEERING DRAWING. 



WEIGHT OP GAS-PIPES PER RUNNING FOOT. 



3' 12 lbs. 

4" 16 '• 

6" 27 " 

8".. 40 " 



10". 
12" 
16". 
20". 



50 lbs. 

62 " 
103 " 
150 " 



The holes for access to the valves on gas-pipes usually consist of two pipes, 
the lower one with a saddle base resting on the pipe, the upper with a cap at 
the top which is adjustable to the height of the pavement by screws cast on 
both pipes, the upper one being the extension. 

Roads and highways are terms applied distinctively to routes of land travel 
in the country, though in general they may include city streets and avenues. 
Lines of canal, river, lake, and ocean transit are often designated as highways. 

The first requirements in the opening up of a country are good roads, which 
must naturally be of the cheapest kind, but with the increase of population 
they must be made more and more permanent, and the reflex action extends to 
farming and mechanical facilities and increase in population. 

For constant and continued use there can be no good road without drain- 
age ; there may be seasons when hauling is practicable, but no road will stay 
good unless the surplus water is got rid of, and if the road is well drained it 
will pay the farmer to extend the drainage to the fields adjacent. 

Fig. 1118 is a section of a dirt road in whichr there is a central drain, and 
above it a 4" layer of coarse straw, hay, or stubble, the bed for which has been 
excavated on slopes toward the drain of 1" to 2" to the foot. The earth should 
then be filled above in layers and rolled, with slopes to the sides sufficient to 




Fig. 1118. 




Fig. 1119. 



carry off all the water from the centre. The width of a common road should 
be 16 feet, slopes of about 8 inches to each side, grade not to exceed 9' to the 
hundred, or about 5°, and this not continuous, but broken by changes of grade. 
Fig. 1119 is a section of a gravel road similar to the dirt road, but, as illus- 
trative of a road with a steep grade, the cut across the turf borders are diagonal 
to turn the water more readily into the ditches, while in the level road the cuts 
are at right angles. If not convenient to construct the drains in the centre of 
the road, they may be placed at the sides with the sub-slopes discharging into 
them. Throughout our country there is at .the present time a strong move- 



ENGINEERING DRAWING. 



473 



inent in favour of good roads, and machinery has been designed and constructed 
by which the cost of construction has been very much reduced, with great im- 
provement in the character of the roads. 

Across marsh lands it is important that the surface of sods and roots should 
not be broken, but that the weight of the roadway should be further distrib- 
uted by a layer of brush, fagots, or poles, on which the layers of earth should 
be sods from the marsh taken distant from the roadway, compacted in layers 
and finished like the dirt road, but without gutters, or at such distance and 
depth as not to weaken the road float. 

For country roads, wagons subject to heavy loads should have wide tires, 
say 4" tires for the front wheels and 6" for the rear ones, and the paths of the 
wheels should lap but not track, the axles of the rear wheels being longer than 
those of the fore. 

Near the sea, where the soil is sand or gravel and stone is not to be had 
readily, oyster shells make an admirable road ; they are arranged in layers like 
Macadam, and grinding together beneath rolling and travel, they make a com- 
pact and solid cover. 

Macadam was the first to reduce the construction of broken-stone roads to 
a science, and has given the name, in his own and this country, to all this class 
of roads. He says that " the whole science of artificial road- making consists in 
making a dry, solid path on the natural soil, and then keeping it dry by a dura- 
ble water-proof covering." The road-bed, having been thoroughly drained, 
must be properly shaped, and sloped each way from the centre, to discharge any 
water that may penetrate it. Upon this bed a coating of 3" of clean broken 
stone, free from earth, is to be spread on a dry day. This is then to be rolled, 
or worked by travel till it becomes almost consolidated ; a second 3"-layer is 
then added, wet down so as to unite more readily with the first; this is then 
rolled, or worked, and a third and fourth layer, if necessary, added. Macadam's 
standard for stone was 6 ounces for the maximum weight, corresponding to a 
cube of 1|", or such as would pass in any direction through a 2^" ring. The 
Telford road is of broken stone, supported on a bottom course or layer of stone 
set by hand in the form of a close, firm pavement. 

Early in the construction of the New York Central Park, after trials of the 
Macadam and Telford roads, gravel was adopted and still maintains its position 
for these roads. The gravel road, of which a cross-section of one half is shown 
(Fig. 1120), consists of a layer of rubble-stones, about 7" thick, on a well-rolled 
or packed bed, with a covering of 5' of clean gravel. C is the catch- basin for 




Fig. 1120. 



474 



ENGINEERING DRAWING. 



i 5 X 10 



the reception of water and deposit of silt from the gutters ; S is the main 
sewer or drain, and s a sewer-pipe leading to a catch-basin on opposite side of 
the road. In wider roads each side has its own main drain, and there is no 
cross-pipe s. The road-bed was drained by drain-tiles of from 1J-" to 4" bore, 
at a depth of 3' to 3^' below the surface. The maximum grade of the Park 
roads is 1 in 20. 

In New York the streets above Fourteenth Street running north and south 
are called avenues, and those at right angles, streets, and boulevard is applied 
to very wide avenues in which there are rows of trees. The terms street and 
avenue, as laid out, are the established bounds within which no buildings 
may be erected. The street, therefore, technically includes the street or trav- 
elled way for carriages, and the side- 
walks and front areas. New York 
^ 1 streets above Fourteenth Street are 60 

and 100 feet wide, avenues 100 feet, 
of which the carriage-way occupies 
one half (Fig. 1121), and the sidewalks 
and area one quarter on each side. 
The space occupied by areas is from 
5 to 8 feet, which may be inclosed by iron fence ; the space beneath it and the 
sidewalk to the curb and used for vaults can be, leased from the city. The 
stoop-line extends into the sidewalk beyond the area-line some 1' to 18", fixing 
the limit for the first step and newel to a high stoop or platform. The boule- 
vard in the old line of upper Broadway and the Bloomingdale Eoad is 150 
feet wide, of which 100 feet are to be carriage-way, and 25 feet on each side for 
sidewalk and area, the latter not to exceed 7 feet ; one row of trees to be set 
within the sidewalk, about 2 feet from the curb. 

The best grade is from 1 in 50 to 1 in 100; this gives ample descent for the 
flow of water in the gutters. Many of our street-gutters have a pitch not ex- 
ceeding 1 foot in the width of a block, or 200 feet. 

The grade of a road is described as 1 in so many ; so many feet to the mile, 
or such an angle with the horizon : 



<i 




Fig. 1121. 



Inclination. 


Feet 


per mile. 


1 in 10 
1 " 11 
1 " 14 
1 " 20 
1 " 29 




528 
462 
369 
264 

184 



Angle. 



43' 



52' 



Inclination. 



1 in 
1 " 
1 " 
1 " 
1 •' 



30 
40 
50 
57 
100 



Feet per mile. 



Angle. 



176 


I'' 55' 


132 


r 26' 


106 


r 9' 


92 


1° 


53 


35" 



The foot-walks in this city and vicinity are generally formed of flags, or 
what is here termed blue-stone, laid on a bed of sand or cement-mortar. The 
flags are from 2" to 4" thick. Stone thicker, select in quality, upper surface 
hush hammered or planed, close jointed, and covering the whole width of the 
sidewalk in one stone, add much to the exterior finish of large houses. Bricks 
are often used in towns, or places where good flagging can not be readily ob- 
tained, usually laid flatways on a sand-bed. Granite is often employed for side- 
ivalks in lengths equal to the width of the sidewalk, and making a cover for the 



ENGINEERING DRAWING. 



475 



vault beneath ; the objection to it is that by wear and under certain atmospheric 
conditions it becomes slippery. 

Cement face, with a base of concrete and laid in squares to admit of expan- 
sion, makes a good and permanent walk. For the country a composition of 
coal tar, or asphalt and gravel, is economical and satisfactory. 

In Paris there is no area (Fig. 1122) ; the sidewalk comes up to the house 
or street-line, and there is a space for trees between sidewalk and street-curb. 




Fig. 1122. 



This space is available for pedestrians, a part being a gravel, asphalt, or flagged 
walk. The following are the dimensions according to the law of June 5, 1856 : 



Entire width of 
boulevard and 


Width of 
carriage-way. 


Width of 
sidewalk. 


Width for 
trees. 


Rows of 
trees. 


, DISTANCE OF ROW FROM 


avenues. 


Street-line. 


Street-curb. 


Metre*. 

26 to 28 


Metres. 

12 

14 

12 to 13 

14 


Metres. 

3-5 
3-5 


Metres. 


1 

1 
2 
2 


Metres. 

5-5 to 6-5 

6-5 " 8-5 

50 " 5-5 

6-5 


Metres. 

1-5 


30 " 34 




1-5 


36 " 38 
40 


8-0 to 8-5 
9-5 


1-5 
1-5 



1 metre = 3-281 feet. 

GKAN^ITE BLOCK PAVEMENT WITH FOUNDATION AGREEABLY TO NEW YORK 
CITY SPECIFICATIONS (Fig. 1123). 

Stone blocks of granite, measuring on the upper surface not less than 8" nor 
more than 12" in length, not less than 3^" nor more than 4|-" in width, not 




Fig. 1123. 



less than 7" nor more than 8" in depth, blocks to be dressed to form when laid, 
close-end joints, and side joints not exceeding 1" in width. 

Bridge or Crossing Stones. — Each stone to be not less than 4' nor more than 
8' long and 2' wide ; thickness, from 6" to 8" ; dressed to an even face on top, 
bottom bedded, sides square and full, ends cut to a bevel of 6" in 2' not paral- 
lel with the line of vehicle travel. 



476 ENGINEERING DRAWING. 

Curlstones shall not be less than 3' in length, 5" thick, 20" deep, matched 
width, the top cut to a bevel of 1", front cut to a fair line to a depth of 14", 
ends from top to bottom squared. 

The subsoil to be excavated and removed to a depth of 16" below the top 
line of the proposed pavement; roadbed shall be truly shaped and trimmed to 
the required grade, and rolled to ultimate resistance with a roller weighing not 
less than ten tons. When the roller can not reach any portion of the roadbed 
it shall be tamped or rolled with a small roller. Upon the foundation a 6" bed 
of concrete, except in the space between the rails known as the horse- ways, 
where no concrete shall be laid. Concrete of Portland cement — one part of 
cement, three parts of sharp sand, seven parts of broken stone by measure ; or 
one part of cement, three parts of sand, four of broken stone, and three of gravel. 
Of Rosendale cement — one part of cement, two of sand, and four of broken 
stone ; or one of cement, two of sand, two of broken stone, and two of gravel. 

On this concrete foundation, and on the foundations of the horse-ways of 
street railways (where no concrete shall be laid) shall be laid a bed of clean, sharp 
sand, perfectly free from moisture, not less than 1|-" thick, to the depth neces- 
sary to bring the pavement to the proper grade when properly rammed. Upon 
this bed of sand cross-walks to be laid, stone blocks in courses at right angles 
with the line of street, except in intersections of streets, when the courses shall 
be laid diagonally. Each course of blocks shall be of uniform depth and width, 
so laid that all end joints shall be broken by a lap of at least 3" ; joints be- 
tween courses not more than 1" in width. As the blocks are laid they shall be 
covered immediately with clean, hard, hot, dry gravel, of proper size, which 
shall be brushed into the joints until all the joints become filled ; gravel shall 
be free from sand. Blocks shall be thoroughly rammed to an unyielding bear- 
ing, with uniform surface, true to the roadway grade. Before pouring the 
paving cement, the joints and gravel filling must be made dry and free from 
dirt. Paving cement shall be poured into the joints while the gravel is still 
hot (paving cement to be heated to 300° Fahr.) until the joints are filled flush 
with the top of the blocks. 

Paving cement to be composed of twenty parts refined Trinidad asphalt 
and three parts of residuum oil, mixed with a hundred parts of coal tar. 

Gutter stones are not now used, the paving extending to the curbstone. 

Granite Pavement without Concrete Bed — Similar to the above, excepting 
that the subsoil shall be excavated and removed to the depth of 10" below 
the top line of the proposed pavement when rolled or rammed. Upon this 
foundation shall be laid a bed of clean sharp sand, or clean fine gravel, to the 
depth necessary to bring the pavement and cross-walks to the proper grade. 
No ramming shall be done within 25 feet of the face of the work being laid. 
Whenever the pavement shall have been constructed it shall be covered with a 
good and sufficient second coat of clean sharp sand, and immediately thoroughly 
rammed until the work is made solid and secure ; no paving cement in the 
joints of the blocks. 

Asphalt Pavement with Concrete Foundation (Fig. 1124). — The subsoil or 
other matter shall be excavated and removed to the depth of 9 inches below the 
top line of the proposed Trinidad asphalt pavement, which shall have a crown 
not to exceed the rate of 5 inches on a roadway of 30 feet, 9|- inches below the 



ENGINEERING DRAWING. 



477 



top of the proposed asphalt pavement, and 13^ inches below the top of the 
stone block pavement adjoining the rails, man-hole heads, and stop-cock boxes. 




^ BINDER 
6"C0N CRETE 



Fig. 1124. 



the entire road-bed to be thoroughly rolled with a heavy roller. Upon the 
foundation thus prepared shall be laid a bed of hydraulic cement concrete, 6 
inches in thickness, which, if necessary, must be protected from the action of 
the sun and wind until set. Upon this foundation must be laid a fine bitumi- 
nous concrete or binder of clean, broken stone not exceeding 1^ inch in their 
largest dimensions, thoroughly screened, and coal-tar residuum, commonly 
known as No. 4 paving composition. The stone to be heated by passing 
through revolving heaters, and thoroughly mixed by machinery with the pav- 
ing composition in the proportion of 1 gallon of paving composition to 1 cubic 
foot of stone. The binder to be spread with hot iron rakes to true grade of 
the pavement and to such thickness that, after being thoroughly compacted 
by tamping and hand rolling, the surface shall have a uniform grade and cross- 
section, and the thickness of the binder at any point shall be not less than three 
fourths of an inch, the upper surface to be parallel with the surface of the 
pavement to be laid. Upon this foundation must be laid the wearing surface, 
the basis of which, and of paving cement, must be pure asphaltum, unmixed 
with any of the products of coal tar. The wearing surface to be composed of 
refined asphaltum, heavy petroleum oil, fine sand containing not more than 
one per cent of hydrosilicate of alumina and fine powder of carbonate of lime ; 
asphalt from the Pitch Lake, on the Island of Trinidad ; petroleum oil to be 
freed from all impurities and brought to a specific gravity of from 18 to 22° 
Beaume, and a fire test of 250° Fahr. The cement from these two hydro- 
carbons shall have a fire test of 250° Fahr., to be composed of 100 parts of pure 
asphalt and from 15 to 20 parts of petroleum oil. 
The pavement mixture to be composed of : 

Asphaltic cement 12 to 15 parts. 

Sand 83 to 70 " 

Pulverized carbonate of lime 5 to 15 " 

Sand and asphaltic cement to be heated separately to about 300° Fahr., the 
carbonate of lime while cold to be mixed with the hot sand and then with the 
asphaltic cement. The pavement mixture, at a temperature of about 250°, shall 
then be carefully spread by means of hot iron rakes in such manner as to give 
a uniform and regular grade. The surface shall then be compressed by hand 
rollers, after which a small amount of hydraulic cement shall be swept over it, 
and it shall then be thoroughly compressed by a steam roller weighing not less 
than 250 pounds to the inch run, the rolling to be not less than five hours for 



478 



ENGINEERINa DRAWING. 



every 1,000 yards of surface. After its ultimate compression the pavement 
must have a thickness of not less than 2 inches. 

Of the powdered carbonate of lime, 5 to 15 per cent shall be of an impalpa- 
ble powder, the whole of it to pass a No. 26 screen ; of the sand, none to pass 
a No. 80 screen ; and the whole of it, a No. 10 screen. 

Pavements^ Salt Lake City^ Utah. — The streets are 92 feet from curb to 
curb. The pavement is practically in two portions — an asphalted central por- 
tion and two stone-block surfaces — arranged as shown in Fig. 1125. The 
foundation of the block pavement is 10 feet wide on each side, is composed of 



' V>/y/W///^//%y///y/////% 



yS^one 




/lsp/70/t 



3^o/7e 



/isp/70rr Cirone , 



Co/7crefe 6 



3^^^ 



Fig. 1125. 



coarse sand laid on a foundation compacted by a 10- 
ton steam roller ; the sand stratum is 6" thick. The 
blocks are of very hard sandstone, and vary from 
4J" X 7" ; they form a pavement 7" thick, with 
filled with fine-screened gravel and grouted pitch. 



7" X 3i" X 7" to 10" X 

joints not over f" wide, 

Before the joints are poured the blocks are rammed with hammers weighing 

from 75 to 80 pounds until brought to a firm bed at the proper level. The 

asphalted portion of the street is laid on a concrete foundation 6" thick. 

Methods of laying Brick Pavements (Fig. 1126). — After excavation the 
ground is compacted with rollers weighing about 2 tons. A foundation course 




of sand or broken stone is thoroughly compressed with the roller to the exact 
form and crown of the finished pavement. On this foundation a layer of 
brick is laid flatwise, with the longest dimension longitudinal with the road- 
way; on this layer sufficient sand is spread to fill all joints and then rolled or 
rammed ; then a cushion of 1" or 2" of sand, and on this a layer of brick is set 
on edge, with the longest dimension across the roadway, which layer is either 
rolled or rammed. After rolling is completed, any broken bricks are replaced 
with whole ones ; this is also done in the first layer. By some a foundation is 
preferred composed of 8" to 15" of broken stone, made compact with rollers 
weighing from 12 to 15 tons, and upon this is spread a 3" cushion of sand. A 
crown of 4" is allowed in a roadway 50 feet wide, and 3" in a roadway 40 feet 
wide. 

^lodulus of rupture in compression : First-quality brick, 1,700 pounds per 
square inch ; absorption, 1*6 per cent; abrasion under test to be equal to granite. 



ENGINEERING DRAWING. 



4Y9 



Modulus of rupture in compression: Second-quality, 1,500 pounds per square 
inch ; absorption, 5 per cent ; abrasion not to exceed twice that of granite. 
Of wooden pavements, cedar block is the most general (Fig. 1127). The 




6 CEDAR BLOCKS 

2"x 12" PLANK 
l"x 12"STRINGER 
S'SAND 



curbstone is set to the true grade, and the ground between is graded to the 
true cross-section of the street. After this the surface is rolled by a heavy 
steam roller ; next, 3" of coarse sand is spread over the entire surface. String- 
ers 1" X 12" are then laid across the street from curb to curb, usually 8" apart 
and bedded in the sand to the true section of the roadway ; after the stringers 
are in place and well tamped, sand is levelled between flush to the top of the 
stringers. On the stringers and sand the foundation planks, 1" to 2" thick, 
well seasoned and dry, are laid close together lengthwise of the street, the ends 
abutting on the stringers. Sometimes the foundation boards are dipped in hot 
coal tar before laying. The paving blocks are sawed from peeled cedar fence 
posts, and run from 4' to 8" diameter. The standard length is 6", but some 
cities use blocks 7* or 8" long. 

The cedar blocks are packed on end close together upon the plank founda- 
tion, and with the spaces between adjoining blocks three-sided rather than 
more sides. Against the curb, or any other straight vertical surface, each 
alternate block should be split in halves and the straight side placed against 
the curb. After the blocks are in place the spaces between them are filled with 
gravel rammed down by iron rods. Some require that a paving cement, com- 
posed of coal tar and asphalt, be poured over the whole surface of the pave- 
ment, and run into the spaces between the blocks. The entire surface of the 
pavement is then covered with about 1" of fine roofing gravel. 



RAILROADS. 

The necessity of a well-drained road-bed is as important beneath rails as on 
a highway. The cuts should be excavated to a dej^th of at least 2 feet below 
grade, with ditches at the sides still deeper, for the discharge of water. The 
embankments should not be brought within 2 feet of grade; this depth to be 
left in cut and on embankment for the reception of ballast. The best ballast 
is Macadam stone, in which the cross-ties are to be bedded, and finer broken 
stone packed between them. Good coarse gravel makes very good ballast ; but 
sand, although affording filtration for the water, is easily disturbed by the pas- 
sage of the trains, raising a dust, an annoyance to travellers, and an injury to 
the rolling-stock by getting into boxes and bearings. The average length of 
sleepers on the 4' 8-J-" gauge railways is about 8 feet ; bearing surface, 7" ; dis- 
tance between centres, 2' to 2' G", except at joints, where they are as close to 



480 



ENGINEERING DRAWING. 



each other as the necessity of tamping beneath them will admit. Average 
width of New York railways of same gauge as above, for single lines, in cuts 
18', banks 13' ; for double lines, cuts 31', banks 26^. 

Figs. 1128 and 1129 are two standard sections of the permanent way of the 




cross section gravel ballast. 
Fig. 1129. 



Pennsylvania Eailroad, in which the width of cuts and top of embankments are 
the same, 31' 4", and other dimensions equally ample. 

Eail sections are of infinite variety and weights, adapted to the class of 
railroads on which they are to be used, and the loads and speed of trains to 
which they are to be sabjected. Eor roads of the^common gauge, the weight of 
rails is from 56 to 100 pounds per yard. The joints are made with a fish-plate. 

Figs. 1130, 1131, and 1132 are the elevation, section, and plan of the 
standard rail- joint of the West Shore Eailroad. 




With the increase of speed on railways, the tracks on the larger roads are 
being laid with rails of 100 pounds to the yard, and wrought-iron ties are being 
tested, but experiments on them with very heavy trains and high speeds have 
not yet been conclusive as to their adoption. 



ENGINEERING DRAWING. 
DIMENSIONS OF STANDARD RAILS. 



481 



Pounds per Yard. 



40. 
45. 
50. 
55. 
60. 
65. 
70. 
75. 
80. 
85. 
90. 
95. 
100. 



A. 


B. 


c. 


D. 


E. 


F. 


H 


3i 


n 


1 


m 


Ilf4 


3H 


m 


2 


cf7 


m 


i-iV 


H 


H 


2i 


"Tfl" 


2-^, 


H 


4-/, 


4tV 


2i 


If 


2a 


3U 


4i 


H 


n 


n 


2-^1 


hV 


4fd 


4i\' 


2ii 


M 


21- 


1:^? 


4t 


4f 


2-1^ 


iil 


2:^f 


IM 


411 


4-ii 


2M 


M 


2if 


111 


.) 


5 


2i 


■R 


21 


li 


•5A 


5A 


2A 


H 


^t. 


Iff 


5| 


51 


2f 


^f 


2H 


5A 


5i% 


2}-^ 


if 


2H 


Ih 


5i 


51 


2f 


fi 


8-ef4 


. m 



G. 



T5 



* Dimensions not giv^en in table are constant, and are to be taken from the standard sec- 
tion of a 70-pound rail. 



Fig. 1132 is a drawing of a standard 70-pound rail. 



tfli u 




Figs. 1133, 1134, and 1135 are the front elevation, plan, and side elevation 
of a New York city cable conduit adapted to Love's electric traction, one half 
of each, showing the construction of the hand holes h on each side at every 
third yoke about 15 feet centres, the other half showing the intermediate con- 
struction. Details of hand hole are shown in Figs. 113G, 1137, and 1138. 
32 



482 



ENGINEERING DRAWING. 



There are two copper-wire conductors supported and well insulated beneath 
each hand hole, which affords access to the insulator and wire. The support 
for the conductor is formed by two iron rods made fast inside the yoke, carry- 
ing the mica block into which the hook-shaped conductor is inserted. 




Fig. 1134. 



Fig. 1133. 



Under the main body of the car is a thin, broad plough (Figs. 1139 and 
1140), side and front elevation, that passes through the slot between the rails 
with wires (as shown in figures) leading to the trolley, which is brought in 
contact with the conductor by making connections with both wires as it is 

h 




Fig. 1138. 



Fig. 1137. 



ENGINEERING DRAWING. 



483 



pressed against them. The 
current forms a complete cir- 
cuit, passing up through one 
wire and one blade of the 
plough to the motor; thence it 
returns through the other blade 
and wire to the power house. 
None of the current returns 
through the rails or escapes 
through the ground. 

The pulleys shown (Fig. 
1133) are those belonging to 
the cable traction, see Appen- 
dix. Manholes into the con- 
duit are placed at intervals for 
inserting the lower bar of the 
plow, the tongue of which is 
raised through the slot, and 
fastened by the pin 'p to the 
head attached to the car. 




Nfia 



Fig. 1139. 



ROOFS AND BRIDGES. 

At pages 490 and 1:91 will be found illustrations of the trussing of wooden 
beams. These are simple forms, which may be used in roofs or bridges, and 
rules are given for the proportion of parts. Eolled I-beams or plate-girders 
will serve also for floor-beams and moderate spans, but with modern necessities 
much more complicated structures are required. 

On the General Principles of Bracing. — Let Fig. 1141 be the elevation of 
a common roof-truss, and let a weight, W, be placed at the foot of one of the 
suspension-rods. Now, if the construction consisted merely of the rafter C B, 
and the collar-beam C 0, resting against some fixed point, then the point B 
would support the whole downward pressure of the weight ; but in consequence 
of the connection of the parts of the frame, the pressure must be resolved into 
components in the direction C A and C B ; Q' h will represent the pressure in 

the direction C B, C 2V the portion 
of the weight supported at B, C a 




Fig. 1141. 



Fig. 11^2. 



the pressure in the direction C A, and lu W the portion of the weight sup- 
ported on A. The same resolution obtains to determine the direction and 
amount of force exerted on a bridge-truss of any number of panels, by a weight 
placed at any pointy of its length (Fig. 1142). In either case, the effect of the 
oblique form C A upon the angle C is evidently to force it upward ; that is, a 
weight placed at one side of the frame has, as in case of the arch, a tendency 



484 



ENGINEERINa DRAWING. 



to raise the other side. The effect of this upward force is a tension on a por- 
tion of the braces, according to the position of the weight ; but as braces, from 
the manner in which they are usually connected with the frame, are not capa- 
ble of opposing any force of extension, it follows that the only resistance is 
that which is due to the weight of a part of the structure. 

Figs. 1143 and 1144 illustrate the effects of overloading at single points such 
forms of construction. Such an unequal loading on trusses requires that a 




Fig. 1143 



Fig. 1144. 



Fig. 1145. 



portion of the load W be transferred to each "point of support inversely propor- 
tionate to the distances of the weight from each support. The above trusses 
are not prepared to transfer this weight to but one support. To remedy the 
difficulty, it will be necessary to add braces running in the opposite direction 

as shown by dotted lines (Fig. 1145), at every point 

subject to the above distortion. These are called 

counter -braces. 

To prevent the braces from becoming loose 

when the counter-braces are in action, it is always 
customary to give the braces and counter- braces an initial compression, by put-' 
ting a moderate tension on the suspension-rods. In this case, therefore, the 
passage of a load produces no additional strain upon any of the timbers, but 
tends to relieve the counters. The counter-braces do not assist in sustaining 
the weight of the structure ; on the contrary, the greater the weight of the 
structure itself, the more will the counter-braces be relieved. 

If, instead of the counter-braces, the braces themselves are made to act 
both as ties and struts, as in some iron bridges and trusses, then the upward 
force will be counteracted by the tension of the brace. 

If a systeui be composed of a series of suspension-trusses (Fig. 1146) in which 



4-1 i 




the load is uniformly distributed, represent the load at each of the points, 4, 3, 
2, 1, 2', etc., by 1, then the load at 4 will be supported ^ upon a and J- upon 
3 ; hence the strut 3 will have to support a load of 1 + '5 = 1*5 ; of this f 
will be supported by 2 and i by <2 ; f of 1-5 = 1, 1 -[- 1 = ^^ load on strut 2 ; 
f of this load, or 1'5, will be supported at 1, and since from the opposite side 



ENGINEERING DRAWING. 



485 



there is an equal force exerted at 1, therefore the strut 1 supports 1 -j- 1-5 + 
1-5 = 4. 



The tension on the rod c-2 — 2 —z. 



c a 



" " 2-3 = 2-|- " 

u tt 3_4 _ 3 u 

" " 4-6f = 3^ " 

If this construction be reversed as in a roof-truss, the parts which now act 
as ties become braces, and the braces ties. The force exerted on the several 
parts may be estimated in a similar way as for the suspension-truss. Neither 
of these constructions would serve for a bridge-truss, subject to the passage of 
heavy loads, but are only fit to support uniform and equally distributed loads. 

To frame a construction so that it may be completely braced — that is, under 
the action of any arrangement of forces — the angles must not admit of altera- 
tion, and consequently the shape can not. The form 




Fig. 1147. 



Fig. 1148. 



Fig. 1149. 



should be resolvable into either of the following elements (Figs. 1147, 1148, 
and 1149) : 

In these figures, lines - represent parts required to resist compres- 
sion ; lines parts to resist tension only ; lines = parts to re- 
sist both tension and compression. 

In a triangle (Fig. 1147), an angle can not increase or diminish without 
the opposite angles also increasing or diminishing. In the form Fig. 1148 a 
diagonal must diminish; in Fig. 1149 a diagonal must extend, in order that 
any change of form may take place. Consequently, all these forms are com- 
pletely braced, as each does not permit of an effect taking place, which would 
necessarily result from a change of figure. Hence, also, any system composed 
of these forms, properly connected, breaking joint as it were into each other, 
must be braced to resist the action of forces in any direction ; but as in general 
all bridge-trusses are formed merely to resist a downward pressure, the action 
on the top chord being always compression, it is not necessary that these chords 
should act in both capacities. 

Most city roofs are flat; the timbers are placed like those of the floor be- 
neath, but at greater distances between centres, as they have less load to sustain. 
The roof covering is inclined to discharge the rain water ; and the timbers be- 
neath are arranged to admit of this inclination, which may be quite small, J 
of an inch to the foot ; but it should be positive and uniform, to prevent the re- 
tention of the water in puddles. It is an advantage to hold the snowfall, as it 
relieves the street of a great encumbrance. 

Figs. 1150, 1151, and 1152 represent ele^fations or portions of elevations of 
the usual form of framed roofs. The same letters refer to the same parts in 
all the figures. T T are the tie-heams, R R the mai% rafters, r r the jack-raf- 
ters, P P the plates, p p the pmrlins, K K the king-posts, k k king-bolts, q q 
queen-holts — both are called suspension-lolts — C the collar or straining learn, 
B B braces or struts, b b ridge-boards, e corbels. 



486 



ENGINEERING DRAWING. 



The pitch of the roof is in the inclination of the rafters, and is usually des- 
ignated in reference to the span, as ^ i, f , etc., pitch ; that is, the height of 




Fig. 1150. 



the ridge above the plate is ^, J, f , etc., of the span of the roof at the level of 
the plate. The steeper the pitch of the roof, the less the thrust against the 




Fig. 1151 



side- walls, the less likely the snow or water to lodge, and consequently the 
tighter the roof. For roofs covered with shingles or slate, in this portion of 
the country, it is not advisable to use less than ^ pitch ; above that, the pitch 
should be adapted to the style of architecture adopted. The pitch in most 
common use is ^ the span. 

Fig. 1150 represents a simple form of framed roof ; it consists of rafters, 
resting upon a plate framed into the tie- or ceiling-beam ; this beam is sup- 
ported by a suspension-rod, Jc, from the ridge, if supported from below, the rod 
is omitted. If neither ceiling nor attic floor are necessary, an iron tie-rod con- 
necting the plates is sufficient. The rafters are to be spaced from 1 to 2 feet 
centres, and the tie-beams at intervals of from 6 to 8 feet ; the roof cover to be 
of boards nailed to the rafters. This form of construction is sufficient for any 
roof of less than 25 feet span, and of the usual pitch, and may be used for a 
40-foot span by increasing the depth of the rafters; deep rafters should always 
be bridged. By the introduction of a purlin extending beneath the centre 



ENGINEERING DRAWING. 



487 



of the rafter, supported by a brace to the foot of the suspension-rod, as shown 
in dotted line, the depth of the rafters may be reduced. If the tie-beam. 




Fig. 1152. 



which is also a ceiling and floor beam, be below the plate some 2 to 4 feet the 
thrust of the roof is resisted (Fig. 1153) by bolts, h ^, passing through the plate 
and the beam, and by a collar-plank, 0, spiked on the sides of the rafters, high 
enough above the beam for head-room. For roofs f pitch and under 20 feet 
span the bolts are unnecessary, the collar alone being sufficient. 

Fig. 1151 represents a roof, a larger span than Fig. 1150 ; the frame may 
be made very strong and safe for roofs of 60 feet span, 
sion-rods are now oftener used than posts, with a small 
triangular block of hard wood or iron, at the foot of 
the bolts, for the support of the braces. The objec- 
tion to this form of roof is that the framing occupies 
all the space in the attic ; on this account the form, 
Fig. 1152, is preferred for roofs of the same span, and 
is also applicable to roofs of at least 75 feet span, by 

the addition of a brace to the rafter from the foot of the queen-bolt. The col- 
lar-beam (Fig. 1155) is also trussed by the framing similar to Fig. 1151. 

In many church and barn roofs 
the tie-beam is cut off (Fig. 1154), 



King- bolts or suspen- 




T 

Fig. 1153. 






Fig. 1154. 



Fig. 1155. 



488 



ENGINEERING DRAWING. 



the queen-post being supported on a post, or itself extending to the base, with 
a short tie-rod framed into it from the plate. 

Figs. 1156 and 1157 are representations of the feet of rafters on an enlarged 
scale. In Fig. 1156 the end of the rafter does not project beyond the face of 
the plate ; the cove is formed by a small tri- 
angular, or any desirable form of plank, se- 

21 





Fig. 1156. 



Fig. 1157. 



Fig. 1158. 



cured to the plate. The form given to the foot of the rafter is called a crow- 
foot. In Fig. 1157 the rafter itself projects beyond the plate to form the cov- 
ing. Fig. 1158 represents a front and side elevation and plan of the foot of 
a main rafter, showing the form of tenon, in this case double ; a bolt", passing 
through the rafter and beam, retains the foot of the 
former in its place. Fig. 1159 represents the foot of a 
main rafter, with a wooden-shoe too short at «, outside 
of the rafter ; it should be framed as in Fig. 1158. 



Fig. 11.59. 







n 

I 



o I n o 
— 1 I — ' — ■ 



Fig. 11(30. 



Fig. 1161. 



Fig. 1162. 



Roofs may be very neatly and strongly framed by the introduction of cast- 
iron shoes and abutting plates for the ends of the braces and rafters. Fig. 1160 



1 






! 


o o 
m 


A 








<■ 




1 


y^ 




m 


\ 




£1 




Fig. 116.3. 



Fig. 1164. 



represents the elevation and plan of a cast-iron king-head for a roof similar to 
Fig. 1151 ; Fig. 1161, that of the brace-shoe ; Fig. 1162, that of the rafter-shoe 



ENGINEERING DRAWING. 



489 




Fig. 1165. 



for the same roof; Fig. 11G3, the front and side elevation of the queen-head 
of roof similar to Fig. 1152 ; and Fig. 1104, elevation and plan of queen brace- 
shoe. Fig. 1165 represents the section of a rafter-shoe 
for a tie-rod ; the side flanges are shown in dotted line. 

On the size and the proportions of the different 
members of a roof : Tie-beams, usually serving a double 
purpose, are affected by two strains : one in the direc- 
tion of their length, from the thrust of the rafters ; the 
other a cross-strain, from the weight of the floor and 

ceiling. In estimating the size necessary for the beam the thrust need not be 
considered, because it is always abundantly strong to resist this strain, and the 
dimensions are to be determined as for a floor-beam merely, each point of sus- 
pension being a support. When tie-rods are used, the strain is in the direction 
of their length only, and their dimensions can be calculated, knowing the pitch, 
span, and weight of the roof per square foot, and the distance apart of the ties, 
or the amount of surface retained by each tie. 

The weight of the wood-work of the roof may be estimated at 40 pounds 
per cubic foot ; slate at 7 to 9 pounds, shingles at 1^ to 2 pounds per square 
foot. The force of the wind may be assumed at 15 pounds per square foot. 
The excess of strength in the timbers of the roof, as allowed in all calculations, 
will be sufficient for any accidental and transient force beyond this. Knowing 
the weights, pressures, and their directions on parts of a roof, their stresses may 
be determined by the parallelogram of forces and dimensions proportioned to 
the strength of the materials of which the roof is composed. It will generally 
be sufficient for the draughtsman to have practical examples of construction to 
draw from. Dimensions are therefore given of the parts of wooden roofs already 
illustrated. Beams are usually proportioned to the weight that they are to sus- 
tain in floors and load, but where tie-rods are used, the stress uj^on them may 
be determined by the following rule : 

Rule. — Multiply one half the weight of the roof and load by one half 
the span, and divide the product by the rise or height of ridge above 
eaves. 

Gwilt, in his "Architecture," recommends the following dimensions for por- 
tions of a roof : 



Span. 


Form of Roof. 


Rafters. 


Braces. 


Posts. 


Collar-beams. 


Feet. 




Inches. 


Inches. 


Inches. 


Inches. 


25 


Fig. 1151, 


5x4 


5x3 


5x5 




30 


a 


6x4 


6x3 


6x6 




35 


Fig. 1152, 


5x4 


4x2 


4x4 


7x4 


45 




6x5 


5x3 


6x6 


7x6 


50 


2 sets of queen-posts. 


8x6 


5x3 


( 8x8 ) 
] 8x4f 


9x6 


60 


U (( 


8x8 


6x3 


jlOxS^ 
] 10x4f 


11x6 



These dimensions, for rafters, are somewhat less than the usual practice in 
this country ; no calculations seem to have been made for using the attic. An 
average of framed roofs here would give the following dimensions nearly : 30 
feet span, 8x5 inches ; 40 feet, 9x6; 50 feet, 10 x 7 ; 60 feet, 11x8; col- 



490 



ENGINEERING DRAWING. 



lar-beams the same size as main rafters. Roof -frames from 8 to 12 feet from 
centre to centre. 

Dimensions for jack-rafters, 15 to 18 inches apart : 

For a bearing of 12 feet. ... 6x3 inches. I For a bearing of 8 feet. . . 4x3 inches. 



10 



. 9x3 



20 



...10 



Purlins 



Length of bearing. 


Distances apart in Feet. 


Feet. 

8 

10 
12 


6 

7x5 

9x5 

10x6 


8 

8x5 

10x5 

11x6 


10 

9x5 
10x6 
12x7 


12 

9x6 
11x6 
13x8 



The pressure on the plates is transverse from the thrust of the rafters, but 
in all forms except Fig. 1150, owing to the notching of the rafters on the pur- 
lins, this pressure is inconsiderable. The usual size of plates for Figs. 1150 
and 1151 is 6 X 6 inches. The dimensions of rafters depend on the distances 
between their supports and between centres. The depth in all such cases to be 
greater than the width ; 2 to 6 inches may be taken as the width, 8 to 12 for 
the depth. 

In the framing of roofs it is now customary, for roofs of mills, to omit pur- 
lins, jack-rafters, and plates, and make the roof-boards of plank stiff enough to 
supply their places, from 2" to 3" thick (according to the space between the 
frames), tongued and grooved, and strongly spiked to the main rafters. There 
is no need of plates ; the plank forms a deep beam, and, if the ends of the 
frame are secured, there is no need of intermediate ties. 

Joinings. — As timber can not always be obtained of sufficient lengths for 
the different portions of a frame, or to tie the walls of a building, it is often 
necessary to- unite two or more pieces together by the ends, called scarfing or 
lapping. Fig. 1166 is a most common means of lapping or halving employed 
when there is not much longitudinal stress, and when a post is to be placed 
beneath the lower joint. 

For beams with a butt joint under the last condition joint bolts (Fig. 1167) 
are often used in which the ends of the timber are squared and held together 
by bolts inserted in holes central of the beams with the nuts in side-pockets, in 
which one is screwed up by turning the bolt and the other by a cold chisel. 

Fig. 1168 is a long scarf, in which the parts are bolted through and strapped, 
suitable for tie-beams. Joints (Figs. 1169, 1170, and 1171) are also often made 



?^ 




Fig. 1166. 



Fig. 1167. 



Fig. 1168. 



by abutting the pieces together and bolting splicing-pieces on each side ; still 
further security is given by cutting grooves in both timbers and pieces and 
driving in keys, h Ic. 

Iron Roofs. — Eoofs of less than 30 feet span are often made of corrugated 
iron alone, curved into a suitable arc, and tied by bolts passing through the 
iron about 2 to 4 feet above the eaves. 



ENGINEERING DRAWING. 



491 



Fig. 1172 represents the half elevation of an iron roof of a forge at Paris ; 
Figs. 1173, 1174, and 1175, details on a larger scale. This is a common type of 



T r — rr y 1 

I, '• 'i i! 

j1 '^ Ih A 1 



r-T 


■, 


D 7 


.: „ -h ;. 1 


i i: 


" i; 

n ' 


. I 




lii 


° 1 


^ ,'i 





Fig. 1169. 




O O « • O O 



Fig. liro. 



Fig. 11 71. 



iron roof, consisting of main rafters, E, of the I-section (Fig. 1175), trussed by 
a snspension-rod, and tied by another rod. The purlins are also of I-iron, se- 
cured to -the rafters by pieces of angle-iron on each side ; and the roof is cov- 
ered with either sheet-iron resting on jack-rafters, or corrugated iron extending 




from purlin to purlin. Tlie rafter-shoe. A, and the strut, S, are of cast- 
iron ; all the other portions of the roof , are of wrought-iron. In Ameri- 
can practice it is usual to make the strut of wrought-iron, with a single 
pin connection at its foot, instead of as in the figure. 
The surface covered by this particular roof is 53 metres (164 feet) long and 

30 metres (98|- feet) w^ide. There are eleven frames, including the two at the 

ends, which form the gables. 



492 



ENGINEERINa DRAWING. 



The following are tlie details of the dimensions and weights of the different 
parts : 

Pounds. 

2 rafters, 0*72 feet deep ; length together, 99-1 feet 1,751 

5 rods, 0-13 feet diameter ; length together, 131-4 feet 882 

16 bolts, 0-13 feet diameter 79 

8 bridle-straps, 0-24 x 0-05 123 

2 pieces, 0*46 thick, connecting the rafters at the ridge, ) ^^^ 

4 pieces, 0-46 thick, at the foot of the strut ) 

4 pieces, 0-36 thick, uniting the rafters at the junction in the strut — together 

with their bolts and nuts 176 

2 cast-iron struts 308 

2 rafter-shoes 287 

Total of one frame 3,694 

16 purlins, 1 ridge-iron, each 0-46 deep, 17*2 long 2,985 

Bolts for the same , 64 

16 jack-rafters, I-iron, 0-16 deep 2,489 

Weight of iron covering, including laps, per square foot 2*88 



Roofs are sometimes made with deep corrugated main rafters with flat iron 
between, or purlins and corrugated iron for the covering. The great objec- 
tion to iron roofs lies in the con- 
densation of the interior air by the -_i^ -p 

outer cold, or, as it is termed, 
sweating ; on this account, they 
are seldom used for other buildings 




Fig. 1174. 



than boiler-houses or depots, except a ceil- 
ing be made below to prevent the contact 
of the air inside with the iron. 

Fig. 1176 is an elevation of one of the 
j^ three panels of one of 

p^=J]^p=pzzi the cast-iron girders for connecting the columns, and carry- 
/^biiflf ^Qi ^ ing the transverse main gutters, which supported the roof 
of the Crystal Palace of the English Exposition of 1851. 
Figs. 1177 to 1181 are sections of various parts on an en- 
larged scale. The depth of the girder was 3 feet, and its 
length was 23 feet 3f inches. The sectional area of the 
bottom rail and flange in the centre (Fig. 1178) was 6 J 
Fig. 1175. square inches ; the width of both bottom and top rail (Fig. 




ENGINEERING DRAWING. 



493 



1177) was reduced to 3 inches at their extremities. The weight of these girders 
was about 1,000 pounds, and they were proved by a pressure of 9 tons, dis- 
tributed on the centre panel. 




Fig. 1170. 



A second series of girders were made of similar form, but of increased di- 
mensions in the section of their parts. Their weight averaged about 1,350 




'/ //////////A >^ 



Fig. 1181. 



pounds, and were proved to 15 tons. A third series weighed about 2,000 
pounds, and were proved to 22^ tons. 

Figs. 1182 and 1183 are sections and details of the trusses for su&taining the 
roof and floor of the English High and Latin School Gymnasium, Boston, 
Massachusetts. The object of sustaining the gymnasium-floor by rods was to 
secure a drill-hall for the military exercises of the school, and trusses were de- 
signed to have sufficient strength to resist the vibration of the floor. As the 
trusses were to be in sight, a central cloumn of cast-iron was introduced to sus- 
tain the centre of the top chord, with lattice between the main diagonals to 
enable them to act as counters, and a 3|-inch gas-pipe for horizontal bracing- 
struts. The floor-sustaining rods all have upset ends, and their tops pass 
through ornamental foliated castings, but their connection with the trusses is 
wholly of wrought-iron. 

The top chords consist of two 9-inch channel-irons weighing 50 pounds per 




49^ 



ENGINEERING DRAWING. 



yard, and one plate 12 X f in.ches. The end-posts have the same section. 
The bottom chord consists of four bars 2|- X 1 inch at the shallow end of the 




Fig. 1183. 



truss, and four bars 2|- X f of an inch at the deep end of the truss. The diago- 
nals are two bars 3x1 inch at deep end of truss, and two bars 3 X |- inch at 
shallow end of truss. The pins are all 2^ inches diameter. The trusses were de- 
signed and constructed by D. H. Andrews, 0. E., of the Boston Bridge Works. 

In order to secure free space in the room beneath the roof, a roof or bridge 
truss may be constructed above, and the roof framed as a floor sus23ended from 
it, with such pitch as is requisite to shed rainfall. 

Figs. 1184 to 1189 are the elevation and details for an iron roof-truss, for 
wood, slate, or corrugated iron covers, built by the Missouri Valley Bridge and 
Iron Works, A. S. Tulloch, engineer. 

Fig. 1190 is a half cross-section of a two-story freight-shed for the N.ew 
York, Lake Erie and Western Kailroad, a simple and cheap construction of 
wood, readily framed and put together. The shed rests upon a pile-dock. 
The platform for the reception of freight is 4 feet above the dock-planking 
and about 26 feet wide, with occasional inclined runs for the transfer of freight 
to or from vessels. 



ENGINEERING DRAWING. 



495 






i" 


oj 




oj 


11 


(^ 


s^ 


°i 


# 



496 



ENGINEERmG DRAWING. 



CEOSS-SECTION OF ONE HALF OF A FREIGHT-SHED, NEW YORK, LAKE ERIE 
AND WESTERN RAILROAD. 




II y II 



Fig. 1190. 



ENGINEERING DRAWING. 



497 



Fig. 1191 is a section of the Baltimore and Ohio coaling bins for loco- 
motives. 

Piers. — Fig. 1192 is an elevation of a pile-pier for a bridge. Tenons are 
cut on the top of the piles, and a cap {a) mortised on. The two outer piles 




Fig. 1191. 



driven in an inclined position, and the heads bolted to the piles adjacent. The 
piles are made into a strong frame laterally by the planks h and c, and plank- 
braces d d on each side of the piles, bolted through. The string-pieces of the 




Fio. 1192. 

bridge rest on the cap. Longitudinal braces are often used, their lower ends 
resting on the plank h — which should be, then, notched on to the piles — and 
their upper ends coming together, or with a straining-piece between, beneath 
33 



498 



ENGINEERING DRAWING. 



the string-pieces, acting not only as supports to the load, but also as braces to 
prevent a movement forward of the frames. As the tendency of a moving 
train is to push forward the structure on which it is supported, in railway- 
bridges especially, great care is taken to brace the structure in every way — ver- 
tically and horizontally, laterally and longitudinally. If the plank c be a tim- 
ber-sill, and the piles beneath be replaced by a masonry-pier, the structure will 
represent a common form of trestle. 

Fig. 1193 is an illustration of a trestle-bent supporting a span of the Brook- 
lyn Elevated Kailroad over its coal-yard. The timber is of yellow pine of the 




Fig. 1193. 

dimensions shown ; the ties are extended beyond the guard-rail on one side to 
support a plank walk. The bent is about 15 feet high. 

Bridge-Trusses. — Whatever maybe the form of truss or arrangement of 
the framing, provided its weight is supported only at the ends, the tension of 
the lower chord, or the compression of the upper chord at centre, may be de- 
termined by this common rule : 

Rule. — The sum of the total weight of the truss, and the maximum dis- 
tributed load which it will be called on to bear, multiplied by the length of the 
span, and divided by 8 times the depth of the truss in the middle, the quo- 



ENGINEERING DRAWING. 



499 



tient will be the tension of lower chord and compression of upper at the mid- 
dle. In nearly all the forms of diagonal bracing, if the uniform load be con- 
sidered as acting from the centre toward each abutment, each tie or brace 
sustains the whole weight between it and the centre, and the strain is this 
weight multiplied by the length of tie or brace, divided by its height. Anv 
diagonals, equally distant from the centre, sustain all the intermediate load : if 
rods, as in Fig. 1195, by tension ; if braces, as in Fig. 1194, by compression. 
It follows, therefore, that in all these trusses the upper and lower chords 




Fig. 1194. 



Fig. 1195. 



should be stronger at the centre than at the ends, while diagonals should be 
largest at the abutments. Unless the weight of the bridge is great compared 
with the moving loads, counter-braces become necessary. 

The general rule adopted in the construction of the Howe truss is, to make 
the height of the truss one eighth of the length up to 60 feet span ; above this 
span the trusses are 21 feet high, to admit of a system of lateral bracing, with 
head clearance for a person standing on the top of a freight-car. From 175 
feet to 250 feet span, height of truss gradually increased up to 25 feet. Moving 
load for single-track railroad-bridge calculated at 2 tons per running foot. 

Wooden Truss- Bridges. — Fig. 1194 is the elevation of a few panels of a 
Howe truss, and Fig. 1195 of a Pratt truss. The Howe truss is by far the most 
popular of all wooden trusses, being readily framed and put together, uniting 
great strength with simplicity of construction. 

Fig. 1196 is the side elevation of three of the five panels of a Howe truss 
highway-bridge of the New York, Lake Erie and Western Eailroad. Fig. 1197 
is a cross-section. There is a section of 3" plank laid close, and another beneath, 
laid with spaces ; these planks are laid diagonally across the floor-beams, and 
at right angles to each other, to act as lateral bracing. Fig. 1198 is the details 
of the abutment end of bridge ; the foot of the brace rests on a cast-iron shoe. 
The length over all — that is, including the portions on the abutment — is 81' 2", 
or 75 feet between abutments, usually designated as the span. 

Figs. 1199, 1200, and 1201 are the side elevation, floor cross-section, and 
plan of floor and bottom chord of three of the twelve panels of a single-track 
railway Howe truss. Their length is each 10' lO^y. The centre braces are 
two, 7" X 10" ; the centre rods three, 1|-" diameter. The counters, each one 
6" X 8"; lateral brace, top and bottom, 6" X 6"; rods 1^^" ; top chord, four 
pieces, 7" X 12" ; bottom chord, four pieces, 7" X 15" ; floor-beams, 7" X 16". 
The shoes, splices, and blocks between chord-timbers are of cast-iron. In the 
earlier practice the angle-blocks were of oak, and the splices made as in Fig.. 
1202. Both were satisfactory. 



500 



ENGINEERING DRAWING. 



N-0«y/SV>f»V 



FS^^^ 




ENGINEERING DRAWING. 



501 



V/)tei-/o/i- 




^%.\Vs^ 



Fig. 1199. 




J*^ v'-S'^ 



8'M — * 



^ ". g O/ll^ TIC C^l/>£0 QfJ 1 



zLL 



7'fG 



W 




-^6'. O"' 

Fig. 1200. 




Fig. 1201. 



502 



ENGINEERING DRAWING. 




ENGINEERING DRAWING. 



503 



Comhijiation Truss. — Fig. 1203 is the elevation and details of a combina- 
tion or composite truss, which owes its name to the use of the two materials, 
wood and wrought-iron, the 
tension members being of 
iron and the compression of 
wood. This class is entirely 







T- 


f 


C ' ' ' ' 


\ 


\ ' 


__j 






^r^ 


_. \ 



American in practice, and 
embodies an essentially Amer- fig. 1202. 

ican feature, pin connections. 

The bridge illustrated. is a double intersection combination through bridge, de- 
signed by L. L. Buck, C. E., for the Northern Pacific Eailroad crossing the 
Yakima Eiver in the State of Washington. The span is 300 feet between cen- 
tres of end pins, and is divided into 15 panels of 20 feet each. The height from 
centre to centre of chords is 40 feet, and width 20 feet from centre to centre. 

The cheapness of timber and the distance from which iron had to be 
secured made it advisable to construct this form of bridge. The timbers 
are heavy and framed, so that no two pieces are in direct contact, and provision 
has been made by which iron can at any time be substituted for the wood. 

Iron Bridges. — When the span is of moderate extent, the load can be safely 
carried by beams put together at the works and transferred to the road in 
complete form. Plate or lattice girders are used, put together with rivets. 

Fig. 1204 is a plan side and end elevation of a plate-girder bridge on the 
New York, New Haven and Hartford Railroad. The bridge is for a single line 
of rails, crossing a highway on a skew. The following is the bill of material : 



LIST OF MATERIAL FOR PLATE-GIRDER BRIDGE, WOODMONT, CONN. 



Number. 


Section. 


Length. 


Weight, pounds. 


32 


6''x6" xf^"Ls. 


47' 1" 


40,530 




8 


5" X 3^x1" Ls. 


15' 10" 


2,140 




4 


5" X 3" X fg-" Ls. 


19' 9" 


884 




8 


4''x3'' xf Ls. 


15' 10" 


1.068 




68 


8"x3'' xf" Ls. 


15' 10" 


7,538 




14 


it t( .. u 


28' 10" 


2,826 




4 


ii (( u (( 


23' 0" 


644 




4 


a it a a 


27 0" 


756 




4 


S^'x-Li" bars^ 


24' 6" 


786 




38 


8'- x-^r " 

Totfil Tj^ and bar^ 


24' 6" 


6,405 






63,572 
17,590 




16 


48" X i?^" plate. 


15' 8^" 




8 


48" xf" 


15' 5r 


7,419 




16 


2orxr " 


2' 0" 


1,880 




1 


15" xf" " 


25' 6" 


478 




1 


U U (( 


10' 3" 


192 




6 


14" xf" » 


18' 3" 


1,916 




1 




23' 0" 


402 




16 


(t u u 


21' 7" 


6.043 




16 


U (( u 


4' 1" 


1.143 




16 


(( u u 


1' 5" 


396 




16 


14" x-iV " 


' 26' 10" 


8,766 




32 




23' 5f" 


15,342 




2 


(( a u 


29' 0" 


1,184 




4 


12*" X -1^^" ^' 


24' 6" 


1,786 




2 


12" xf" " 
. of bridge, exclusive of rivet he 


22' 6" 

g^(Jg 


675 




Total weight 


128,784 










504 



ENGINEERING DRAWING. 



xna±s atra 




ENGINEERING DRAWING. 



505 



Figs. 1205, 120G, and 1207 are plans, elevations, and details of a plate-girder 
river bridge built for the New York, New Haven and Hartford Railroad by the 
Berlin Iron Bridge Company within the liipiits of the builders' yards. It is a 
single-track bridge 102' 9" from end to end of girders fixed at one end and sup- 
ported on rollers at the other. 

Figs. 1208, 1209, and 1210 are respectively the outside elevation, top lateral 
bracing, and cross-frame of a single-track lattice-deck span designed by the 
Phoenix Bridge Company. The bridge is 70 feet long over all, and divided 
into four panels, two of which are shown in the figure ; there are five cross- 
frames attached to the vertical posts. Each truss is built in two sections, 
spliced as shown, the blackened circles indicating holes through which the 
connecting rivets will be driven in the field. The girders are 7' 11" deep, and 
placed 6' 6" apart. The ties of the railroad rest immediately on the top chord. 

BILL OF MATERIAL. 
Two lattice girders and bracing (Figs. 1208, 1209, 1210). 



Description. 



Top chords. . . . 
Bottom chords 
Diagonals 



Verticals 

Top laterals. 



Connecting angles for 
end bottom laterals. 

Struts 

Bottom laterals 



Cross bracing,. . . 
Top and bottom struts. 
Web for top chord 

• (( a .. (( 

Web for bottom chord. 
Splice plates .... 



Diagonals.. 
Wall plates 
Gussets 



Fillers . 



1,482 pairs rivet heads at 4 
Total 



Sections. 


Sizes. 


Length. 


Weight 
per foot. 


No. of 
pieces. 


Angles. 


6x4 


.32 


4" 


16-3 


4 


'' 


6x4 


37' 


7" 


16-3 


4 


" 


6x4 


32' 


4" 


15-0 


4 


a 


6x4 


37' 


t 


15-0 


4 


u 


6x4 


11' 


1 


16-7 


8 


u 


5x3i 


11' 


3" 


9-0 


8 


" 


5x3A 


11' 


3" 


9-0 


8 


" 


4x3 


7' 


10" 


6-7 


20 


" 


5x3i 


9' 


4" 


14-0 


2 


(' 


5x3^ 


9' 


4" 


11-3 


6 


u 


5 x 3 .V 


0' 


9" 


10-0 


2 


" 


3x3 


5' 


5" 


60 


4 


"• 


3x3 


9' 


7" 


6-0 


2 


u 


3x3 


9' 


3" 


6-0 


6 


" 


3x3 


8' 


9' 


6-0 


10 


(( 


3x3 


6' 


2" 


6-0 


10 


Plates. 


12x f 


32' 


5" 


30-0 


2 


a 


12x f 


37' 


8" 


30-0 


2 


" 


12 X f 


15' 


9" 


30-0 


2 


u 


12x f 


21' 


0" 


30-0 


2 


a 


12 X f 


2' 


0" 


30-0 


4 


" 


12 X ,V 


2' 


2" 


17-5 


4 


(( 


11 X f 


2' 


2" 


13-8 


8 


" 


8x * 


2' 


2" 


13-3 


8 


" 


6x H 


11' 


6" 


13-8 


8 


" 


12x f 


1' 


8" 


30-0 


4 


u 


10 X t 


1' 


4" 


12-5 


2 


(( 


10 X 1 


1' 


2" 


12-5 


2 


" 


10 X -a\ 


1' 


0" 


10-4 


20 


" 


9x f 


1' 


4" 


11-3 


4 


u 


9x 1 


0' 


6" 


11-3 


4 


" 


9x -h 


1' 


0" 


9-4 


6 


u 


7x A 


0' 


8" 


7-3 


5 


(( 


10 X t 


2' 


1" 


12-5 


2 


u 


9x 1 


2' 


1" 


11-3 


2 


(( 


9x -i&fi 


1' 


9" 


0-4 


4 


ii 


6x U- 


0' 


9" 


13-8 


8 


n 


6x i 


1' 


0' 


10-0 


8 


(( 


3x ^ 


0' 


9' 


1-9 


8 



Remarks. 



Cut. 



Cut. 



Top lateral. 



Cut. 

Sway frame. 

Cut. 

Top lateral cut. 

Bottom lateral cut, 

Sway frame. 

Top lateral. 

Top lateral cut. 

Bottom lateral. 



Weight, 
pounds. 



2.106 

2,452 

1,938 

2,256 

1,547 

792 

792 

1,049 

261 

633 

14 

129 

115 

333 

525 

372 

1,945 

2,262 

945 

1,260 

240 

152 

242 

234 

1,270 

204 

25 

23 

208 

38 

16 

40 

24 

52 

39 

66 

83 

80 

13 

593 

25,368 



506 



ENGINEERING DRAWING. 




ENGINEERING DRAWING. 



507 






I \ 



508 



ENGINEERING DRAWING. 




ENGINEERING DRAWING. 



509 




510 



ENGINEERING DRAWING. 



Fig. 1211 is a partial plan and elevation of a highway bridge built by the 
King Bridge Company. It is pin connected, with floor-beams riveted to the 
posts above the pin. Fig. 1212 is a section, and Fig. 1213 the end post, with 
part of the portal bracing. The lateral bracing of both top and bottom chords 
is designed to take the stresses arising from wind pressure. Each system forms 
with the respective chords of both trusses an independent truss, for which the 
stresses are calculated and the members proportioned. The wind stresses of 
the upper system are carried through the portal bracing and end posts to the 
abutments, and those of the lower lateral bracing immediately to the end shoes 
and abutments ; the floor-beams are compression members. 

Fig. 1214 contains drawings in detail of a railroad bridge through span on 
the Lima and Oroya Railroad, and is a good example of the usual American 
practice. It is a single-intersection Pratt truss through span, built of iron and 
steel. The length from centre to centre of end pins is 180 feet, with eight 
panels, each 22 feet 6 inches ; depth of truss 26 feet and distance between 
trusses 16 feet. The bridge is of the pin-connected type, the tension members 
being steel eye-bars, and the compression members built sections of plates and 
angles. The floor- beams are riveted to the posts above the pins. 

Fig. 1215 is a side elevation of an angle connection of end brace and top chord. 

Conventional signs of riveting will be found in the Appendix. 

Fig. 1216 is a standard pin-nut, on sale in sizes from 1||" to *7^-q" diameter 





Fig. 1216. 



of pin; Fig. 1215 is an example of its use. Fig. 1217 is a side and top eleva- 
tion of a standard clevis, in sizes, changing by eighths from J" to 3" diam- 
eter of bar. 

Figs. 1218, 1219, and 1220 are elevation, plan, and detail of a turn-table as 

made by the Passaic Rolling Mill Company. 
The table is entirely centre-bearing, and 
rests on a hard steel base. The girders are 
strongly built of plates and angles and cover- 
plates, and connected to each other by 
frames and lateral angle bracing. The sizes 
vary from 40 to 60 feet in length. 

Figs. 1221, 1222, and 1223 are section 
and details of a turn-table as made by the 
Creenleaf Manufacturing Company. The 
conspicuous feature of this centre is the 
nest of rollers, shown on a larger scale in Fig. 1222. The rolls and bearings 
are made of good quality tool steel and are 2^ inches in length and of the 




Fig. 1217. 



ENGINEERING DRAWING. 



511 




Fig. 1219. 



same diameter on the large end and lyV inch in diameter on the small end, 
and run free in the annular groove. Fig. 1223 is the end carriage of the same 
table. 




Fig. 1220. 



Fig. 1223. 



512 



ENGINEERINa DRAWING. 



li 



Jilll 



imL 



'm 





ENGINEERING DRAWING. 



513 



Figs. 1224 to 1228 are illustrations of a landing-bridge common at New 
York city ferries. Fig. 1224 is a longitudinal section, showing a section of the 

float,/, with its lever shown at one 
side of the float and stone coun- 
terpoise to balance the weight of the 
bridge. Fig. 1225 is the front ele- 
vation, and Fig. 1226 the plan, one 
half in planking and one half in 
framing. There are two chain- 
barrels, on each side of the bridge, 




Fig. 1229. 



Fig. 1230. 



worked by hand-wheels ; on the outer ones are the chains by which the boat is 
drawn up to the bridge ; on the inner ones the chains by which the bridge is 
adjusted to the load on the boat, and by which a part of the weight of the 
bridge is held, the upper ends of the chains being attached to the frame over- 
34 



514 



ENGINEERING DRAWING. 



head. The details (Figs. 1227 and 1228) in section and plan explain the con- 
struction of the land-hinge ; a cushion of rubber is introduced into the joint 
to modify the shock caused by the boat striking the bridge, and a flap of 
wrought-iron to cover the joint, for protection to travel, and security from dirt. 




Fig. 1231. 



For motives of economy in cost or space, it has become very common among 
engineers to construct bridges with frequent wrought-iron piers or trestles of 
great height rather than extended truss spans ; one of the most remarkable of 
these is the Kinzua Viaduct, of which Fig. 1229 represents a single pier in per- 
spective, with details. Fig. 1230. 

Fig. 1231 is a section of the roadway of the Eivermont Bridge, Lynchburg, 
Va., supported by similar piers. 

Fig. 1232 is the elevation of a bridge over the Rio Galisteo, Apache Canon, 
on the line of the N. M. & S. P. R. R. The ends of the bridge rest on abut- 
ments on opposite sides of the canon. The centre line of the track is on a ten- 
degree curve, and is 14J inches off the centre line of .the plate girders at the 
centre and at both ends of the span. 

Fig. 1233 is an elevation of one bent of the Third Avenue Elevated Road, 
and Fig. 1234 of post and foundation on a line of cross-section. 

The foundations for the columns supporting the iron structure are simply 
blocks of concrete, capped with a block of granite, to which the bases of the 
wrought-iron columns are bolted. In soft material nine piles were driven, 
capped with 12-inch timbers, and concrete filled in around them. On sandy 
bottom concrete was placed about 6 feet below the surface. On a portion of 
the line a right of way 50 feet wide was secured ; the tracks were supported on 
plate girders resting upon piers of brick masonry, with foundations of concrete 
below the surface of the ground. The brick piers were capped with granite. 



ENGINEERING DRAWING. 



515 



Fig. 1235 is an elevation and half plan of the foundations of a post on the 
Brooklyn Elevated Railroad, with a base of cast-iron, and Fig. 1236 a similar 




Fig. 1232. 



one, with a wrought-iron base. In neither is there any cap except that con- 
nected with the post base, and the anchorage is to cast-iron plates wholly with- 
in the masonry, which is of concrete. 

Fig. 1237 is a plan of one of the stone piers of the railway bridge across 
the Susquehanna at Havre de Grace. To lessen as much as possible the ob- 



^7 



n 



^7 



£3 



£^1 



< 15- >\* ^13.5- 



-80 

Fig. 1233. 



struction to the flow of the stream, it is usual to make both extremities of the 
piers pointed or rounded. Sometimes the points are right angles ; sometimes 
angles of 60°; often a semicircle, the width of the pier being the diameter; 
occasionally pointed arches, of which the radii are the width of the pier, the 
centres being alternately in one side, and their arcs tangent to the opposite 
side. None of the stones break joint at the angle ; this is important in oppos- 
ing resistance to drift-wood and ice. It is not unusual, in very exposed places, 
to make distinct ice-breakers above each pier usually of strong crib-work, with 
a plank-slope upstream of 45°, and with a width somewhat greater than that 
of the pier. 

Fig. 1238 is the plan and Fig. 1239 the side elevation of a pier of a bridge 
across the Missouri, on the Northern Pacific Railroad at Bismarck, designed and 



516 



ENaiNEERING DRAWINa. 



constructed by George S. Morison, 0. E. In this design both ends of the pier 
are rounded, but the upper extremity is extended beyond the main body of the 
pier, and is inclined and plated with iron between low- and high- water mark. 




^nsn/ie 




^fti-.::7::zzl8k. 



Fig. 1235. 




A:::.r"r:^ 



Fig. 1336. 




Fig. 1234. 



Fig. 1237. 



ENGINEERING DRAWING. 



517 




Fig. 1238. 







n-r-n-i i 1 



Fig. 1239. 



518 



ENGINEERING DRAWING. 



This is intended not only to turn aside drift, but as an ice-breaker ; the ice, 
moving up the incline, is broken by its own weight. 

Fig. 1240 is a section of the foundation of the Bismarck bridge, showing 
the construction of the inverted caisson, similar to that used for the Brooklyn 




Fig. 1240. 

Bridge piers. The caissons are 74' long, 26' wide, and 17' high outside ; the 
working-chamber 7 feet high. The caissons are built of pine, sheathed with 
two thicknesses of 3" oak-plank. Above is crib-work filled in with Portland 
cement concrete ; a a are the air-locks. The sand was removed from the 
caissons by water-ejectors. 

Arch bridges are of stone, brick, concrete, or metal ; the parts of the arch 
exert a direct thrust upon the abutments, resisted by the inherent weight of 
the latter, or its absolute fixed mass, as in the case of natural-rock abutments. 

Arch bridges, in masonry, are arcs of circle, semicircular (Fig. 1241), seg- 
mental (Fig. 1242), elliptical, or described from three or five centres (page 32). 





Fig. 1241. 

The stones forming the arch are called votissoirs, or arch-stones ; those form- 
ing the exterior face are called ring-stones, the inner line of arch the intrados, 
exterior line the extrados. The stones at the top, which are those set last and 
complete the arch, are keystones. The courses from which the arches spring 
are called shew-hachs^ and the first course the springing -course. The masonry 
on the shoulders of the arch is called the spandrel-courses^ or spandrel-hacking. 
The weight at the crown of a semicircular arch tends to raise the haunches. 



ENGINEERING DRAWING. 519 

This is counteracted by the spandrel-backing, and by the earth-load, which 
should be carefully distributed on each side of the arch. 

To determine the depth of the key-stone, Rankine gives the following em- 
pirical rule, which applies very well to most of the above examples : 

Depth at key, for an arch of a series, in feet, = -^/'l? X radius at crown. 

For a single arch, = /v/*12 X radius at crown. 
To find the radius at crown of a segmental arch, add together the square of 
half the span and the square of the rise, and divide their sum by twice the rise — 

jS' + r' 
^= 2r 
Thus, the Blackwall Railway bridge has a span of 87 feet, and a rise of 16 — 
43-5' + 16^ _ 1892-25 + 256 _ 
2 X 16 ~ 32 ~ 

To find the radius of an elliptical arch, on the hypothesis that it is an arch 
of five centres (Fig. 103, page 32), the half-span is a mean proportional be- 
tween the rise and the radius. Thus, for example, the Great Western Railway 
bridge is 128' span, and 24*25' rise — 

64^ = 24-25 X R 

-P 4096 -, .o 4- ^ 
^ = 24^ = ^'^ ^'''' 

To find the depth of key-stone, by rule above, as in one of a series — 
d = ^'Yl X 169 = v'^8^ = 5-33. 

The depth of the voussoir is increased. in most bridges from the key-stone 
to the springing-course, but not always ; it is safer to increase the depth. 

If an arch be loaded too heavily at the crown, the lines of pressure pass 
above the extrados of the crown and below the line of intrados at the haunches, 
depressing the crown and raising the haunches, separating the arch into four 
pieces, and vice versa if the arches are overloaded at the haunches. To pre- 
vent such effects, especially from moving loads, in construction the arches are 
loaded with masonry and earth, and this constant load in such excess that there 
will be no dangerous loss of equilibrium by accidental changes of load. 

The horizontal thrust may be determined, according to Rankine, by the 
following approximate rule, which seldom errs more than 5 per cent : 

The horizontal thrust is nearly equal to the iceight supported hetiueen the 
crown and that part of the soffit whose inclination is Jf5°. This thrust is to be 
resisted by the masonry of the abutment and the earth-load behind it. 

Thus, if Fig. 1243 be a section of an abutment of an arch, the horizontal 
thrust exerted at T is resisted by the mass of masonry of the abutment ; the 
tendency is to slide back the abutment on its base A C, or turn it over on the 
point A. The sliding motion is resisted by friction, being a percentage, say 
from i to f of the weight of the abutment.and of half the arch which is sup- 
ported by this base ; but, in turning over the abutment on the point A, the ac- 
tion may be considered that of a lever, the force T acting with a lever T C to 
raise the weight of the abutment on a lever A B (G being the centre of gravity, 
and G B the perpendicular let fall on the base), and the weight of half the 
arch on the lever A C. That is, to be in equilibrium, the horizontal thrust 



520 



ENaiNEERING DRAWING. 



T X T C must be less than the sum of the weights of the abutment multiplied 
by A B, and the weight of the arch multiplied by A C. 

Skew bridges are those in which the abutments are 

-c^^^^-"*^ parallel, but not at right angles to the centre line, 

^"^y and the arches oblique. To construct these in cut 

stone requires intelligence and education both in the 
designer and stone-cutter; but, when the work is 
laid full in cement, so that the joints are as strong as 
the material itself, this refinement of stone-cutting is 
not necessary. The arch may safely be constructed 
as a regular cylinder of a diameter equal to the rec- 
tangular distance between the abutments, with its 
extremity cut off parallel to the upper line of road. 
For such an arch hard-burned brick is the best material, the outer voussoirs 
being cut stone. 

In the rules above given no consideration is paid to the strength of the 
cement in which the stones are bedded. When the cement is thoroughly set, 
the structure is in a measure monolithic, and the thrust is inconsiderable. 

Fig. 1244 is the elevation of one of the stone arches of the Minneapolis 
II niou Railway Viaduct, with the timber centres on which the arch was turned. 
The arch is nearly semicircular, 97*82 feet span, 50 feet rise ; width, 28 feet ; 





Fig. 1244. 



depth of arch at spring, 40" ; at key, 36". The piers are 10 feet thick at 
springing line ; their up-stream ends are at angles to the main body of the 
piers, and parallel to the thread of the stream. The whole length is 2,100 feet, 
of which there are 3 arches of 40 feet span, 16 of 80 feet, and 4 of 100 feet. 
Height above water, 65 feet ; total height, 82 feet. 

The centres were very light frames, five to each arch ; the chords, timber 
arches, and ties were each 12" X 12", the central braces 10" X 10", and the 
shorter side-braces 8" X 8" ; the bolts, single, 1^" diameter. 



ENGINEERING DRAWING. 



521 



The bridge was constructed after the designs and under the direction of 
Charles C. Smith, C. E., Chief Engineer of the St. Paul, Minneapolis and 
Manitoba Railway, and is an example of a very economical and stable con- 
struction. The piers are of Minnesota granite, but above springing line the 
masonry is of magnesian limestone. It was commenced in February, 1882, and 
completed in November, 1883. 




Fig. 1245. 



Fig. 1245 is a half-elevation and half -section of the Cabin John Bridge used 
for supporting the Potomac conduit on the line of supply to the city of Wash- 
ington. 



Location. 



Manchester and Birmingham Railroad. 

(( (( u n 

London and Brighton Railroad 

" " Blackwall " 

Great Western Railroad 

Chestnut Street (Philadelphia) Railroad 

High Bridge, Harlem River, New York 

St. Paul, Minneapolis & Manitoba Rail- 
road (largest arch), at Minneapolis. . 

Cabin John Washington Aqneduct 

Licking Aqueduct and Ohio Canal. . . . 

Monocacy " 

Hutcheson " 

Chemin du Fer du Nord, sur I'Oise 

D'Enghien Railroad du Nord 

Du Crochet Railroad 

Experimental arch, designed and built 
by M. Vaudray, Paris 



Material. 



Brick. 



Stone. 



Form of arch. 



Semicircular. 

a 

Segmental. 

Elliptical. 

Segmental. 

Semicircular. 

Segmental. 

Elliptical. 

Segmental. 

Semicircular. 

Segmental. 







Depth 


Span. 


Rise. 


at 
crown. 


18 


9 


1-6 


63 


31-6 


3 


30 


15 


1-6 


87 


16 


4-H 


128 


24-3 


5 


60 


18 


2-6 


80 


40 


2-8 


97-8 


50 


3 


220 


57-3 


4-2 


90 


15 


2-10 


54 


9 


2-6 


79 


13-6 


3-6 


82-5 


13-5 


4-6 


24-4 


12-2 


1-4 


13-2 


6-6 


l-7i 


124 


6-11 


2-8 



Depth 

at 
spring. 



Uniform. 

2-3 

Uniform. 

7-li 



3-4 



4-6 



3-7 



The arch last in the list was a very bold specimen of engineering, built as 
an experiment, preliminary to the construction of a bridge over the Seine. It 
was made of cut stone, laid in Portland cement, with joints of f", and left to 
set four months ; the arch was 12' wide ; the centres rested on posts in wrought- 
iron boxes filled with sand, and, as the centring was eased by the running out 
of the sand, the crown came down ^'';'the joints of one of the skew-backs 
opening j^jVo-" during the first day, it came down j^". It was then loaded 
with a distributed weight of 360 tons ; under this load the crown settled yV 
more. Since then nothing has stirred, although it was afterward tested by 
allowing five tons to fall vertically 1' 6" on the roadway over the key-stone. 
This bridge will not come within any of the rules laid down for other construe- 



522 



ENGINEERING DRAWING. 



tions. The rise is about ^ the span, although the usual practice for segmental 
and elliptical arches is more than i or within the limits of J and -J. 

Melan concrete arch, Stockbridge, Mass. (Figs. 1246 and 1247), is a seg- 
mental arch of 100 feet span and y^ rise. 



Concrete, /Cc/r7.i-a^/i/lp'fr^y^e 




jijri^ef 



Fig. 1246. 



The iron in the arch consisted of bent ribs of 7-inch, 15-lb. I-beams, spaced 
28 inches apart and raised about 1^ to 2 inches from the soffit. The concrete 

in the abutments (1 cement, 3 sand, and 6 
stone) was put in first with the adjoining 
wing walls to such a height as to inclose 
the ends of the iron ribs, which abutted 
against an iron cross-angle previously 
bolted to them. 

The concrete in the arch is 9 inches 
thick at the crown and 30 inches at the 
haunches. The concreting of the arch 
was done in one day. Then the concrete 
filling, the face and wing walls, and finally 
the coping were built. 

The bridge is a concrete monolith, the 
coping forming one piece with the arch. 
The iron railing is embedded in the con- 
crete. 
After striking the centres the arch settled about \ inch at the abutments 
and f inch at the centre. 

The bridge was built for 11,475. 

In suspension-bridges the platform of the bridge is suspended from cables, 
or chains, the ends of which are securely anchored within the natural or arti- 
ficial abutments. 

The curve of a suspended chain is that known as the catenary, and, if the 
whole weight of the structure were in the chain itself, this would be the curve 
of the chains of a suspension-bridge ; but, as a large part of the weight and the 
whole of the loading lies in the platform, the curve approaches that of the 
parabola, and in all calculations it is so regarded. 




Fig. 1247. 



ENGINEERING DRAWING. 



523 



Let Fig. 1248 represent a suspension-bridge, in which A, B, 0, are points in 
a parabolic curve. 

Rule. — Add together four times the square of the deflection (E B)" and the 
square of half-span (A E)'', and take the square root of this sum ; multiply this 





C 












E 








A 






.-"^T" 


V 




KI _ E 


^ 










[.^ 


_ 






^y^ 


/ 1 




■n> 


«,^_^^ 




1 ^^^ 








^N,„^ 


^^^ 


/ 1 






■^N^ 


^ 


■ 


~YX^ 








1 


^\ 


N 


/ 1 1 








^. 




1 ! 








M 


M 




/ -^ 1 










^^ 


h; 




r 




F 





Fig. 1248. 

result by the total weight of one chain and all that is suspended from it, in- 
cluding the distributed load, and divide this product by four times the deflec- 
tion (E B) of the cable at the centre, and the result will be the tension on one 
chain, at each point of support, A and 0. The angles made by the chain at 
the point of support — viz., angle POL and the angle of the back-stays, or con- 
tinuation of the chain (angle L N) — should be equal to each other, in order 
that there be no tendency to overturn the tower L and A F. 



Bridges. 



Menai 

Chelsea 

Pesth 

Bamberg 

Freyburg' . . . . 
Niagara Falls. 
Cincinnati.. . . 
Brooklyn 





Deflection 


No. of 


Main 


of chain or 


chains and 


spans. 


cable. 


cables. 


570 


43 


16 


348 


29 


4 


666 


47-6 


4 


211 


14-1 


4 


870 


63 


4 


821 


54 and 64 


4 


1,057 


89 


2 


1,595-5 


128-5 


4 



Total effective 

section of 

cable in 

square inches. 



260 
230 
507 

40-2 

49 
241-6 
172-6 
188 



Mean weight 

of cable per 

foot of span 

(pounds). 



767 
1,690 
137 
167 
820 
516 
501-3 



Fixed load 
per ft. of 
span (lbs.). 



9,892 
1,581 
760 
2,032 
2,580 
5,865 



Breadthof 

platform 

in feet. 



28 

47 

46 

30-5 

21-25 

24 

36 

85 



BOILER-SETTING. 

Eig. 1249 is a longitudinal section, Fig. 1250 a plan with section of wall, 
and Fig. 1251 an elevation half -front and half -sectional of a boiler and setting 
as recommended by the Hartford branch of the Hartford Steam-Boiler and In- 
spection Company, showing the interior bracing, steam and water connections, 
and brickwork. There are ten braces in each head, secured to pieces of T-iron, 
placed radially, as shown in dotted lines (Eig. 1251). The feed-pipe is through 
the front-head, just above the line of tubes, extending to the back of the boiler, 
with a perforated branch across it, that the water may be warmed in its passage 
and distributed. The front is 2i projecting cut-away front, the boiler-head being 
nearly on a line with the front. below, different from that given in Fig. 918, 
where the lower part of the shell projects beyond the head of the boiler, and 
the cast-iron front covers the end. The doors giving access to the tubes are 
usually semicircular, and hung on the top diameter, but it will be found more 
convenient to form them in two quadrants, and hung so as to move horizontally. 
The boilers are to be protected against radiation by a covering of ashes, or a 
brick arch, resting on the side-walls. 



524 



ENGINEERING DRAWING. 




In the figure the man-hole frame is 
riveted to the inside of the boiler ; fre- 
quently it is on the outside. In many 
positions the man - hole should be 
placed in the back-head, as easier of 
access. With the blow-off in the flue 
(Fig. 1249) it is well to make it a circu- 
lating pipe by connecting an inch-pipe 
inside the valve with the upper water- 
space of the boiler. 

Figs. 1252, 1253, and 1254 are draw- 
ings of boiler as made by the Fishkill 
Landing Machine Company. The 
boilers are suspended between vertical 
side - walls. The side-walls here are 
composed of bearing walls, air spaces, 
and an inside 4" wall, which is exposed 




Fig. 1251. 



ENGINEERING DRAWING. 



525 




Fig. 1253. 



Fig. 1254. 





r 



^ 



Fig. 1252. 



526 ENGINEERING DRAWING. 

to the heat of the gases from combustion. The fire-box is lined with fire-brick 
to the height of the centre of the boiler, and also the exposed surface of the 
bridge wall. A covering of thin corrugated iron extends from wall to wall over 
the boiler, and supports a thick cover of ashes. 

The boiler is built without dome, but of full diameter to give steam capa- 
city; the dry pipe of light iron (gutter or y shape) extends the whole length 
of the upper part of the boiler, to which it is riveted, but with a washer be- 
tween it so as to leave open joints of about -J* for the admission of steam. The 
pipes are laid out in fan lines to offer as much surface as possible to the flame 
and to admit of ready cleaning. There are two man-holes, one above the tubes 
where easiest of access, and one beneath in the front-head with a hand-hole in 
the back-head. The breeching is of cast-iron, attached to the boiler, with doors 
opening laterally ; the smoke-pipe leads out from the top with a damper at 
the bottom ; the size of the smoke-pipe is proportioned to the number and size 
of tubes, according to the tables given in the Appendix. 

The furnace doors are hung to the sides of the frames to expose the full 
width of opening for cleaning, and smaller doors are hung on the main doors 
for firing. 

CHIMITETS. 

Figs. 1255 and 1256 are sections of a small circular chimney, about 100 feet 
high, in which the buttresses are within the outer -shell, supporting but not at- 
tached to a central flue ; these flues may be made of brick glazed ware or con- 
crete. This chimney is without outside buttresses, panels, or ornaments, and 
offers the least possible resistance to wind. 

For chimneys of small diameter it is difficult to obtain circular brick, 
but the chimney may be made octagonal of any face, with a strong bond, 
by corner brick, from brickyards and terra-cotta works. Chimneys of the 
above section, 100 feet high, with bottom corners rounded, will give ample 
draft with an area of chimney-flue of two square inches for every pound of 
anthracite per hour burned upon the grate. 

If the chimney is of less height it is well to increase the section in propor- 
tion to the reduction, but the top should be always above buildings, trees, etc., 
and remote from obstructions that would check the draft. Chimneys should 
have flues at least 16" diameter, and there is no objection to flues of larger area 
than given by rule above ; but it is indispensable for a sure draft that all flues 
should have corners rounded without abrupt changes in area or direction. 

Fig. 1257 is a sectional elevation of a chimney 160 feet high, from John T. 
Henthorne, M. E., with a cross-section (Fig. 1258) midway of the height. 

Figs. 1259, 1260, and 1261 are sectional elevation, front elevation, and cross- 
sections of a chimney of large dimensions, built by Mr. Henthorne for the 
Narragansett Electric Light Works, Providence, R. I. 

Fig. 1262 is a vertical section of a chimney at the Ridgewood Pumping- 
engine House, Brooklyn, 1^. Y., and Fig. 1263 an elevation at the point where 
the square base is changed into an octagonal. 

Fig. 1264 is the cross-section of a buttressed chimney at 100 feet above base, 
built for the Calumet & Hecla Mining Company, and designed by E. D. 
Leavitt, Jr., M. E. The whole height of the chimney is 150 feet. The but- 
tress walls are 16" and 12" thick, that of the body 12" and 8", and of the cen- 



ENGINEERINa DRAWING. 



527 




:i;i 



Fig. 1258. 



Fig. 1255. 



-\r"\ 



■1— i 



^:i 



/I .y sq' 
'3'. sa' 
/2'.7'sa' 

Jt'.i'SKf 



■'f-' 



.-11/3 jgr 
../7/rjf 
--ii'v-'iq' 






./^'|JV/-'^. 



Fig. 1257. 



528 



ENGINEERINO DRAWING. 




3~ 




--b 



C- 






FiG. 1259. 



Fig. 1260. 



Fig. 1261. 



ENGINEERING DRAWING. 



529 



I 



C3 




iT\ 



Fia. 1265. 




Fio. 1264. 



530 



ENGINEERING DRAWING. 



M^M 



i 




Fig. 1267. 



tral flue 8" and 4", offsetting into 
each other by 1" offsets ; the taper 
is 4 inches to 10 feet on each side. 
Fig. 1265 is a half elevation and 
half section of the cap and the 
cover of the interior flue by which 
its expansion is permitted. 

Figs. 1266 and 1267 are eleva- 
tion and section of a wrought-iron 
chimney stack, such as are now in 
common use ; they are brick-lined, 
with a spread base well anchored 
and without other stays. 

In most chimneys an interior 
and independent flue is used, 
which may expand without dis- 
turbing and cracking the exterior 
shell. Chimneys are built of va- 
rious sections, uniform throughout, 
with flues tapering to the top, or 
inci^asing in section, bell-mouthed, 
some, like a lamp chimney, con- 
tracted at the entrance ; all draw 
well if without abrupt changes in 
section and direction, and adapted 
to the position. Chimneys are 
less likely to be overturned by the 
wind, the nearer the section to the 
circular and the smoother in out- 
line, and the fewer the projections. 

ON THE LOCATION OF MACHINES. 

The construction of buildings 
for mills and manufactories (if 
any aesthetic effect is intended) is 
usually left to the architect, but 
the necessities of the construction, 
the weights to be supported, and 
the space to be occupied, must be 
supplied by the mechanical en- 
gineer or millwright. 

In the arrangement of a manu- 
factory or workshop it is of the 
utmost importance to know how 
to place the machinery, both as to 
economy of space and also of work- 
ing. Where a new building is to 
be constructed for a specific pur- 



EXGIXEERIXG DRA^yIXG. 



531 



pose of manufacture, it will be found best to arrange the necessary machines 
as they should be, and then build the edifice to suit them. For defining the 
position of a machine, the space it occupies in plan and elevation, the position 
of the driven pulley or gear, of the operative, and the spaces for the working 
and access to parts, are required. To illustrate this subject, take a two-story 
weaving-room, of which Fig. 1268 is an elevation and Fig. 1269 a plan. 




Lay down the outlines of an interior angle of the building, and dot in, or 
draw in red or blue, the position and width of beams. This last is of impor- 
tance, as no driving-pulley can come beneath the beam, and this is also the posi- 



532 



ENGmEEKING DEAWING. 





s^ 




t^ 







-— 1(- 




r r 



V>a 



>^ 










/2"__L _, 36" 



\z 



J£ 



B 





I .. I 



n 



Fig. 1269. 



ENGINEERING DRAWING. 533 

tion for the hanger. Lay off the width of the alleys and of the machines. The 
first alley, or nearest the side- wall, is a back alley ; that is, where the operative 
does not stand, and so on alternate alleys. Draw the lines of shafting central 
to the alleys, as in this position the belts are least in the way. One operative 
usually tends four looms ; they are therefore generally arranged in sets of four, 
two on each side of the main alley, where the operative stands ; the twos are 
placed as close to each other as possible, say one inch between the lays, a small 
cross-alley being left between them and the next set. Lay off next the alley 
necessary at the end of the room, and space off the length of two rows of looms 
wdth alleys at the end of alternate looms, and mark the position of the pulleys. 
Looms are generally rights and lefts, so that the pulleys of both looms come in 
the space where there is no alley. Should the puile}'; come beneath a beam, 
the loom must be either moved to avoid it, or the pulley may be shifted to the 
opposite end of the loom. Parallel with the pulleys on the looms draw the 
driving-pulleys on the shafts, that is, h parallel with ^, ^ with Z>, / with /, and 
so on. Draw the third and fourth rows of looms ; since the second and third 
rows are driven from the same shaft ; if they are placed on the same line, it will 
be impossible to drive both from the same end, and, as this is important, move 
the third row the width of the pulley J, and, for the sake of uniformity, the 
fourth row also. Lay off the length of looms and position of pulleys as before, 
and parallel with the pulleys the driving-pulleys on the shaft, that is, c against 
c, g against ^, and so on. Having in this way plotted in all the looms, every 
alternate set being on a line with the third and fourth row, if there are to be 
looms on the story above, proceed to lay down the position of the looms on this 
floor; and since for economy of shafting it is usual to drive from the lines in 
the lower rooms, to avoid errors, interference of belts and pulleys, plot the 
upper room on the same paper or board as the lower room, in two different 
colored inks, or drawing the machines in one room in deep and in the other 
in light line, as shown in Fig. 1269. If the width of the rooms is the same, 
the lateral lines of looms and alleys are the same, and it is only necessary, 
therefore, to fix the end lines. As the first loom in the outer row of looms, 
in the lower room, occupies for its belt the position Ic on the shaft, the loom 
in the upper room must be moved either one way or the other to avoid 
this ; thus the position i of the pulley on the loom must be made parallel 
to the pulley i on the shaft, so in the other looms a io a^ e to e, d to d^ 
and U to li. 

Besides the plan, it is often necessary, and always convenient, to draw a 
sectional elevation (Fig. 1268) of the rooms, with the relative positions of the 
driving-pulleys and those on the machines, to determine the length of the belts, 
and also to see that their position is in every way the most convenient possi- 
ble. In the figure, one of the lower belts should have been a cross-belt, and 
one of the upper ones straight : had the belts to the second row of looms in the 
upper story been drawn (as they should have been) straight, the belt would 
have interfered a little with the alley, and it would have been better to have 
moved the driving-shaft a trifle toward the wall. 

From this illustration of the location of machines, knowing all the require- 
ments, in a similar way any machinery may be arranged with economy of space, 
materials, power, and attendance. These last two items are of the more im- 



534 



ENGINEERING DRAWING. 




ENGINEERING DRAWING. 



535 



portance as they involve a daily expense, where the others are almost entirely 
in the first outlay. 

Macliine Foundations. — Figs. 1270, 1271, and 1272 are side, end elevations, 
and plan of the foundation of the stationary steam-engine. F is the cast-iron 
frame or bed-plate of the engine; B the granite bed of the engine, or coping of 
foundation ; P the stone or brick pier, laid full in cement. The sides and sur- 
faces of granite exposed are usually fine-hammered, the upper bed or build to 
receive the engine-frame, hammer-dressed and set level. Strong wrought iron 
bolts pass through frame, bed, and pier, with nuts at each end, and the whole 
is strongly bolted together. Pockets are left in the pier near the bottom for 
access to nuts, and these pockets are covered by granite caps or iron plates. 

Few stationary steam engines are now built with bed-plates extending the 
whole length of the engines, but the illustration is applicable to the partial 
plates supporting the cylinder and pillow-block, and to engines and machines 
for which heavy foundations are necessary. It is not an uncommon practice, 
instead of granite caps, to use timber, to cushion the shocks and blows incident 
to most machinery. 

Tunnels. — Figs. 1273 to 1282 are illustrations, with description, taken from 
" Tunneling," a standard work on this subject by H. S. Drinker, C. E. 





Fin. 1273. 



Fig. 1274. 



Figs. 1273 to 1278 illustrate the principles of timbering applied to driving a 
gallery through running material. Figs. 1273 and 1274 are parts of the con- 
struction on a large scale, with the technical names of the parts. Each frame is 
called a timber-set. Suppose a leading set (Figs. 1275 and 1276) is in place, 
close to the face, and that the leading ends of the poling-boards resting above 
this leading set are held up from the collar by wedges sufficiently high to allow 
the insertion of the new poling-boards. In- Fig. 1276 the sets e e, standing mid- 
way between the front and the hind ends of the poling-boards, serve as middle 
sets between the main sets d d. By referring to the plan (Fig. 1278) of a gal- 
lery thus timbered it will be seen that the s\de-poli?ig has to be wedged out at 
its leading end, just as the roof-poling is wedged up, and the space to be filled 
across the top by the roof-poling is wider over a front main-set than over a back 



536 



ENGINEERING DRAWING. 



one. The two outer top poling-boards (Fig. 1273) are therefore made wider at 
their leading ends than at their back ends. The miners begin by inserting the 
roof -poling at either corner of the face, removing the extreme end-wedges be- 
tween the collars and the poling, and driving into this space the new poling- 
boards (i. e., the ones shown in Fig. 1273). Though the wedges between the 
collar and the poling-boards serve well enough to keep back the material, it 
would be dangerous thus to take any of them out were there no other guard 
for the poling, as the board just above the wedge removed would be pressed 
down ; a run might also be started, and all the other wedges forced out, when 
the poling-boards would snap down on the leading collar, and perhaps break 




Fig. 1275. 



Fig. 127 



off; in any event, it would be a matter of great trouble to get them wedged up 
again. In order to guard against this trouble, a cross-board or plank a (Fig. 
1274) is placed just under the poling-boards, and over the wedges. Then, when 
one wedge is removed, this cross-connection holds in place the poling-board 

that is immediately above the wedge 
removed, until the new board can be 




Fig. 1277. 




put in ; it also stays the tendency to any general movement. The new poling- 
board being inserted, it is driven ahead six or twelve inches, and then tem- 



ENGINEERIXG DRAWING. 



537 




Fig. 127 

(Section of Fig. 1281, through A B, looking west.) 

HOOSAC TUNNEL. 

Timbering and arching through soft ground at the West End. Scale, 10' = 1". 




Fig. 1280. 



538 



ENGINEERINa DRAWING. 




Fig. 1281. 

HOOSAC TUNNEL. 

West End. Scale, in' =z 1' 




Fia. 1282. 



ENGINEERING DRAWING. 539 

porarily stayed by wedges, h (Fig. 1277). The corner roof-polings being thus 
in place, the middle ones (Fig. 1273) are similarly inserted. Then the top 
retaining-board in the face is cut out, and the material allowed to flow into the 
heading through the space. As room is thus given ahead, the poling-boards 
are gradually driven forward, say 24 or 30 inches, or about half the length of 
a board. Whenever they are thus tapped, the wedges b (Fig. 1274) must be 
loosened, and then tightened again after the driving. The side-poling is simi- 
larly advanced ; as space is gained ahead, it must be protected by new face- 
boarding, stayed by stretchers. Thus the work can be gradually carried down 
to the floor of the heading by successively taking out the face-boards. Often 
the floor of the gallery also has to be planked, and, in very extreme cases, to 
be poled similarly to the roof and sides. 

While inserting the new poling-board for half its length the boards have 
been held in place by the double support offered by a and h. The face retain- 
ing-boards are kept back by a vertical plank laid across them, and stayed by 
stretchers. On this newly excavated chamber the outside pressure will be 
great, acting, as it does, on the front half length of the poling-board c a, and, if 
the remaining work is not rapidly executed, the front ends of the boards may 
be snapped beyond a ; then, if it were attempted to drive the remaining portion 
of the board on, as soon as its back end left b it would snap between a and b. 
A middle set is therefore required at once. The middle set being in position, 
the work of excavating the face can be proceeded with as before. The face- 
boards are removed, one by one, from top to bottom, and the polings are driven 
in to their full length ; then in the new length ahead the next main set is 
erected. Such are the general principles of heading-driving through running 
ground, or sheet-2nling in tunnelling. 

Figs. 1279 to 1282 show the English system of bar-timbering, as used at 
the Hoosac Tunnel for the soft ground at the west end. The material was of 
the worst character, and was exceedingly difficult to drive through. Figs. 1279 
and 1280 are cross-sections, the one looking west from A B, the other east. 
Fig. 1281 is a longitudinal section. Fig. 1282 is a cross-section of the tunnel 
as completed with an invert, and the bars not drawn but bricked in. 

Railway Stock. — Figs. 1283 and 1284 are the elevation and plan of a stand- 
ard box-car of the New York Central and Hudson Eiver Railroad. 

Figs. 1285 to 1288 are the plan and elevations of the truck for the 
same car. 

Figs. 1289, 1290, and 1291 are end-elevations and cross-sections. Figs. 1292 
and 1293 longitudinal sections, and Fig. 1294 plan of a standard passenger-car 
of the Pennsylvania Railroad. 

Fig. 1295 is a plan and section of a pair of wrought-iron plates which sup- 
port a car body in the centre of the truck. There are two — the body centre- 
plate and the truck centre-plate. The centre-pin or king-bolt, not shown, carries 
none of the strain except in emergencies. 

Figs. 1296 to 1299 are elevations, in full and parts, and Fig. 1300 a plan of 
the trucks of the above car. 

In the figures, both of standard box and passenger cars, the elevations and 
plans are usually broken, to show the construction. When the two sides or 
two ends of a car or truck are similar, it has not been considered necessary to 



540 



ENGINEERING DRAWING. 




ENGINEERING DRAWING. 



541 




centers or side Door- - 

C(:nterS vf Svfing Hangers 4-5 "- 




•^ Centers of Sw;,-ig i HAiirier Bearing 4'-3 

-Spring PlanK 2'-IO'/a" >i 

• —Swing Bolster. 2- lO/j" i ->i 

Centerof 5pr<'iig 2-4'' ■ — -*i 
Between Centers oF Journal Bearing 6-3 ■ 



— Transom 3-3" -x 

I 



J^: 



w 




^ 



1 . ^-^ .(/ I 



Fig. 1288. ;^ Axle 5- 5 V3 - -3 

EiAd EJevation. 
Tro.cK Gfliuge ^'-o'/i' 




542 



ENGINEERING DRAWING. 




Fig. 1295. 



ENGINEERING DRAWING. 



543 



g 



f~^y1 ^ — - — ^ g 




Fig. 1300. 



544 



ENGINEERING DRAWING. 




ENGINEERING DRAWING. 



545 



show both, but the figure is completed with a section of the other part, through 
a different plane. 

The following letters of reference and technical names of similar parts 
apply equally to all the figures : 

a, Sill. 

a', End-sill. 

&, Intermediate floor-timbers. 

&', Centre floor-timbers. 

c, Sill knee-iron or strap. 

d, Body bolster. 

e, Body bolster truss-rod. 
/, Truck side-bearing. 
g, Centre plate, body or truck. 
h. Check-chain on the truck, hooking into 
h', Check-chain eye on the car. 
i, Body truss-rod. 
i', Body truss-rod queen-post, 
y, Cross-frame tie-timber. 

Fig. 1301 is a plan and elevation of the frame of a locomotive as designed 
by Mr. Robert Buchanan of the New York Central and Hudson River Railroad. 
The distinguishing feature is the American " bar " frame, while the plate frame 
may be called the English practice. The latter admits of a wider fire-box be- 
tween the frames, but in the American example the fire-box is entirely above 
the frames. 

TheWave-line Princi/ple of Ship- Co?istruction, from B^usselVs "Naval Archi- 



k. 


Draw- bar. 


I, 


Journal-box. 


m, 


Pedestal. 


n, 


Pedestal tie-bar. 


0, 


Pedestal stay-rod. 


P, 


Pedestal arch-bar. 


P\ 


Pedestal inverted arch-bar. 


9^ 


Transom. 


r, 


Truck bolster. 


«j 


Spring-plank. 


t, 


Swing-hanger. 


u, 


Safety-beam. 


V, 


Equalizing-bar. 




Fig. 1302. 



tecture." — The general doctrines arrived at by J. Scott Russell, F. R. S., from 
numerous and long-continued experiments and practical tests, is " that the 
form of least resistance for the water-line of the bow is horizontally the curve 
of versed sines, and that the form of least resistance for the stern of the vessel 
is the cycloid ; and you can either adopt the said cycloid vertically or horizon- 
tally, or you can adopt it partly vertically and partly horizontally, according to 
the use of the vessel or the depth of water." 

" That the length of entrance, or fore body, should be |, and that of the 
run, or after body, f ." 
36 



646 



ENGINEERING DRAWING. 

" When it is required to construct the tcater-lmes of the 
boiv of a ship of which the hreadth and the length of the how 
are given^ so as to give the vessel the form of least resistance 
to passage through the water, or to obtain the highest velocity 
with a given power : Take the greatest breadth, M M (Fig. 
1302), on the main section of construction at mid ship- breadth, 
and halve this breadth, MO; at right angles to M M at 
draw the centre line of the length of the bow, X ; on each 
half-breadth describe a half-circle, dividing its circumference 
into, say, eight equal parts. Divide the length X into the 
same number of equal parts. The divisions of the circle, 
reckoned successively from the extreme breadth, indicate the 
breadths of the water-line at the successive corresponding 
points of the line of length. Through the divisions of the 




Fig. ia03. 



circles draw lines parallel to X, and through the divisions 
of X lines parallel to M M. These, intersecting one an-- 
other, show the successive points in the required water-line. 
The line traced through all these points is the tvave luater- 
line of least resistance for a given length of bow and breadth 
of body." 

To construct the water-lines of the after body or run of a 
ship (Fig. 1304), the mid-section (Fig. 1303) being given : 
The bow is constructed as in Fig. 1302, but with 12 divisions 
on the centre line ; for the run lay off 8 divisions, each equal 
to those of the bow ; divide the half circle into 8 equal parts, 
and draw chords to these divisions from to 1, 2, 3, 4. From 
the point 1 on the centre line lay off an inclined line equal 
and parallel to the chord 1 ; the point 1' will be in the water- 
line. In the same way from the point 2 draw an inclined line 
parallel and equal to the chord 2, for 2', and determine in 
the same way the points 3', 4', 5', 6', 7'. The other circles 
drawn in the figure are described on semi-diameters of the 
mid-section at different levels, and the points of their wave- 
lines are determined on the same inclined lines 1 1', 2 2', but 
the lengths are those of the chords of the different circles. 
In Fig. 1303, the elevations of the mid body, the curved lines 
of sections are projected from the plan. 

Fig. 1305 is a body plan of a vessel adapted to speed ; 
Fig. 1306 of one adapted to freight. 

" To determine the after body it is expedient to construct 



ENGINEERING DRAWING. 



547 



a vertical wave-line on the run as well as a horizontal one, and in designing 
shallow vessels to give more weight to the vertical wave-line." 

" The wave system destroys all idea of any proportion of breadth to length 
being required for speed. An absolute length is required for entrance and run, 
but, these being formed in accordance with the wave principle for any given 
speed, the breadth may have any proportion to that which the uses of the ship 
and the intentions of the constructor require." 

" The wave system allows us to give the vessel as much length as we please. 
It is by this means that we can give to a vessel of the wave form the capacity 
we may require, but which the ends may not admit. Thus, the Great Eastern, 





Fig. 1305. 



Fig. 1306. 



which is a pure example of the wave form, has an entrance or fore body of 
330', a run or after body of 220', and a middle body of 120', which was made 
of this length merely to obtain the capacity required. The lengths of the fore 
and after body are indicated by the required speed, and if the beam is fixed, 
it is only by means of a due length of middle body that the required capacity, 
stability, and such other qualities are to be given as will make a ship, as a whole, 
suit its use." 

Length of entrance of a vessel for a 10-mile speed should be 42 feet, of run 
30 feet ; for a 20-mile speed, 168 and 120 feet ; that is, the lengths increase as 
the squares of the speed. 

Under Isometrical Drawing is given an illustration of a vessel constructed 
on wave-lines. 



ARCHITECTURAL CONSTRUCTION. 

It is the duty of an architect to design a building to be suitable and con- 
venient for the purposes for which it is intended ; to select and dispose of the 
materials of which it is composed to withstand securely and permanently the 
stresses and wear to which they may be subjected ; to arrange the parts to pro- 
duce the artistic effects consistent with the use of the building and its location, 
and to apply such appropriate ornament as may express the purpose and har- 
monize with the construction. 

In domestic architecture, by far the most extensive branch of the profession, 
most persons can give some idea of the kind of building which they wish to 
have constructed, and perhaps express by line the general arrangement of 
rooms ; but it is left to the architect to settle the^style of building appropriate 
to the position, to adapt the dimensions and positions of rooms and passages to 
the requirements, to determine the thickness of walls and partitions, and arrange 
for drainage, heating, and ventilating. The graphical representation is left to' 
the draughtsman, and his assistance is the more valuable if he is not only con- 
versant with practical details, but understands the best proportions of parts, the 
necessities of construction, and the requirements of building laws. 

The draughtsman usually commences his education with the copying of 
drawings. For this purpose, in Figs. 1307 to 1310, inclusive, are given plans 
and elevations of a simple house, showing the drawings necessary to get a clear 
comprehension of plans and elevation ; but for an estimate and for constructive 
purposes it is necessary in addition to draw elevations of the remaining sides 
and one or more longitudinal and transverse sections showing the framing and 
general construction; details drawn to a large scale are also required, from which 
and the specifications the building may be erected. 

The size of the page has compelled the titles to be put within the body of 
the drawings ; after copying, place them outside, and give ample margin. In 
all scale drawings the scale should form a part of the title. On Fig. 1311 the 
section and end-elevation are given together. This is also for economy of space, 
but should be copied by the draughtsman in two distinct drawings, each of the 
full width of the building. 

Instead of hatching the walls and partitions, as in the examples given, these 
are often indicated in solid black, or in colour, brick walls by carmine, wooden 
walls and partitions by burnt sienna, other materials by colours as nearly repre- 
senting them as possible, which may be purchased in pans under the name of 
technical water colours. 

Plate XIII is an illustration in colour of a plan and ceiling from a design 
of Arthur Gilman, architect. 

548 



ARCHITECTURAL DRAWING. 



549 




550 



AROHITEOTURAL DRAWING. 




ARCHITECTURAL DRAWING. 



551 




552 



AEOHITEOTUEAL DRAWING. 



I I 



o 



ARCHITECTURAL DRAWING. 



553 



END ELEVATION. 



Scale : 4' = 1 inch. 



SECTION. 




Fig 1311. k .. \ x J 



554 



ARCHITECTURAL CONSTRUCTION, 



Details of Construction. — Foundations in variety and requirements are 
treated fully under " Engineering Drawing," but for common structures the 
draughtsman, if there are examples in the vicinity of the proposed structure, will 
conform to the teachings of practice, or to the building laws, if there are any in 
force. In general, for small buildings, cellar- walls, if of stone laid in mortar, 
should not be less than 18" thick ; if of brick, 16'', and the base 6" to 12" wider. 






rrri: 




N 







□ aDDDODD : 





"^ 






Fig. 1312. 



Fig. 1313 



Wl 



m. 



Fig. 1314. 



Figs. 1312 to 1314 represent the side and end elevations and plan of a tim- 
ber frame building, of common construction, supported on brick or stone walls. 



ARCHITECTURAL CONSTRUCTION. 



555 



in which s s are the sides, b' V the floor-beams, 1 1 trimmer-beams, and li the 
header. The beams, l ^, framed into the header are called tail-beams; 2^]) are 
posts, which are distinguished by their position, as corners, intermediate and. 
window posts ; p' 2^' studs, g g girts, c c plates, d d braces, and r r rafters. 

Usual dimensions of timber for frame of common dwelling-houses : sills 
6" X 8", posts 4" X 8", studs 2" X 4" or 3" X 4", girts 6" X the depth of floor- 
joists, plates 4" X G" ; the floor- joists (J, Fig. 1315) are notched into the girts. 
The posts and studs are tenoned into the sills and girts. Fig. 1316 represents a 



Fig. 1315. 



I c 



Fig. 1316. 









/ ■ 





a 


i 


G 



Fig. 1318. 




teno?i, h c, in side and end elevation, and mortise; a ; the portions of the end of 
the stud resting on the beam are called the shoulders of the tenon. 

The frame is covered with boards usually 1" thick, laid either horizontally 
or diagonally, and nailed strongly to the posts or studs. Fig, 1317 is the ele- 
vation of the end frame of a house, showing by breaks the diagonal cover of 
boards and the inner lathing. The lower story is sheathed or ceiled with nar- 
row boards, the upper shingled. 

In the balloon or spike frame the stiffness depends on the nailing, and mor- 



556 



ARCHITECTURAL CONSTRUCTION. 



CEIUNC LINE 




Fig. 1319. 



iv/^ 




Fig. 1320. 




tise and tenon are omitted, and the girts supplied by 
a board a 3" or ^" X 1" let into the studs (Fig. 1318) 
and firmly nailed to them. The studs are nailed to 
the plates and sills. 

The studs at all door-openings should be set at 
least 2" wider and 3* higher than the size of the fin- 
ished opening. It is not unusual to have double studs 
(2" X 4") to inclose these openings (Fig. 1319). This 
leaves the doorway more or less independent of the 
partition. Partition studs are of smaller dimensions 
than those of the frame, but are set like them and 
usually 12" and 16" centres, adapted to the length of 
the lath (48"). The sizes of the studs are generally 
2 X 4, 3 X 5, or 3 X 6 inches, according to the height 
of the partition ; for very high partitions, greater 
depth may be required for the studs, but three inches 
will be sufficient width. 

Partitions are usually cut in between sills placed 
on the floor-beams (Fig. 1320), and similar caps above, 
beneath the beams. Where partitions of the second 
story are directly above those on the first story it is 
better to foot the studs on the caps of the latter, and 
not on the beams (Fig. 1321). Where there are double 
floors, the sills are placed on the bottom floor, or on 
the floor without a sill. It may be important that the 
partitions should be self-sustaining. This is effected 
by simple bridging, well nailed to the studs, as shown 
in Fig. 1322, or by herring-bone bridge, as shown in 
plan of floor (Fig. 1330), or by a system of trussing, 
as in Fig. 1323. This method of trussing must vary 
with the position of opening. The foot of the braces 
should rest on a positive support. The bridging 
should be accurately cut and firmly nailed. Bridging 
distributes the weight of the partition, but trussing 
concentrates it at the ends of the braces. 

Walls in Masonry. — For walls above the cellar, it 
will be found difficult to lay stone walls in mortar, 



y 



Fig. 1322 



Fig. 1323. 




ARCHITECTURAL CONSTRUCTION. 



55Y 



with fair bond and face, less than 16" thick. Brick walls may be as thin as 8" 
for exteriors, and for partitions 4". Brick walls are usually bonded by head- 
ing-courses every fifth to seventh course. Where the outside 
course is pressed or face brick, these are laid on stretchers, and 
the bond with the backing may be thin strap-iron, laid in the 
joints, or, by cutting off the interior corners of the face-course, 
say every fifth course, and laying common brick diagonally of 
the wall resting in this clipped corner (Fig. 1324). The face of 
buildings is often built of thin ashlar, which is secured with 
iron anchors to the brick backing. 

In most cities there are building acts in force defining the 
kinds of material and thickness of walls and foundations, to 
which all constructions within their limits must conform. 

Openings in masonry-walls are covered by lintels or arches, 
or both. It is usual to place a stone or cast-iron lintel in the 
exterior face over openings for doors and windows, with a wooden lintel inside 
(Fig. 1325), and a relieving arch above. For larger openings, brick arches are 
turned on cast-iron skew-backs, 
of which the thrust is resisted 




Fig. 1324. 




Fig. 1325 



by a tie-bolt (Fig. 1326), or cast-iron lintels, box girders, j^- or rolled I-beams. 

But it is to be observed that, when the cement is set, there is little or no thrust 
from the arch. The whole dead work^ or masonry without 
an opening, forms a monolithic beam, and, if there is depth 
enough of this, the arch is of no account. It is the custom 
in the north of Italy to construct flat lintels of brick, of con- 
siderable span, depending entirely on the mortar for strength. 




Fig. 1327. 





Fig. 1329. 



To distribute the weight of piers over the foundation of walls with open- 
ings, it is very common to construct inverted arches beneath spans or open- 
ings. In old houses it was not unusual to make the exterior arches of an 



558 



ARCHITECTURAL CONSTRUCTION. 



opening flat or rectangular in outline, with the joints radial. This is now rele- 
gated to ornamental construction. 

Concrete Walls. — It is common in many places where brick and stone are 
expensive and gravel is abundant to make walls of concrete, in proportions of 



(as rp 



OS y 



Fig. 1330. 



one of cement to five to seven of gravel. The space requisite for the wall is 
inclosed with plank, and is filled in with concrete, well rammed. Figs. 1327 
and 1328 are plans of concrete walls with inclosing plank, and Fig. 1329 an 
elevation. The planks are held by bolts passing through wall and plank, all of 
which are removed after the wall is set, and the bolt-holes are then filled with 
cement. The thickness of walls should be a little in excess of those of brick. 

Flooring. — The timbers which support the flooring-boards and ceiling of a 
room are called the naked flooring. 

The simplest form of flooring, and the one usually adopted in the construc- 
tion of city houses and stores, is represented in plan and section (Fig. 1330). 
It consists of a single series of bea.ms or deep joists, reaching from wall to wall. 
As a lateral brace between each set of beams a system of Iridging is adopted, 
of which the best is the herring -hone bridging, formed of short pieces of joists 
about 2x3, crossing each other, and nailed securely to the tops and bottoms 
of the several beams, represented by a and h ; and wherever a flue occurs, or a 
stairway or well-hole prevents one or more joists from resting on the wall, a 
header^ H, is framed across the space into the outer beams or trimmer -heams 
T T, and the beams cut off or tail-heams are framed into the header. 

Whenever the distances between the walls exceed the length that can safely 
be given to floor-joists in one piece, an intermediate beam or girder, running lon- 
gitudinally, is introduced, on which the joist may be set (Fig. 1331), notched on 
(Fig. 1332), or boxed in (Fig. 1333), or both boxed and notched. They may 
also be framed in with tenon and mortise ; the best form is the tush-tQnon 



ARCHITECTURAL CONSTRUCTION. 



559 






Fig. 1331. 



Fjg. 1332. 



Fig. 1333. 



Fig. 1334. 



(Fig. 1334). Flooring is still further varied, by framing with girders longi- 
tudinally ; beams crosswise, and framed into or resting on the girders ; and 
joists framed into the beams, running the same direction as the girders. When 
the joists are not flush or level with the bottom of the 
beams or girders, either in the finish the beams will 
show, or ceiling- joists or furrings will have to be intro- 
duced. 

The width of beams as sold in the market is from 2" 
to 6" ; those for common houses and spans are 2", but 
for more important buildings and structures 3" to 4". 
The depth of beams and distances between centres may be determined from 
the weight to be supported (that is, load per square foot by the number of 
feet, including that of the floor), and from the table, page 239 ; but this table 
gives the central load, which is one half the distributed load. 

The following table gives the load per square foot for different characters of 
buildings ; for floors of — 

Dwellings 40 pounds per square foot. 

Churches and public halls 80 

Warehouses and general merchandise 250 

Factories 200 to 400 

Snow, 30 inches deep 16 

Maximum wind pressure 50 

Roofs for wind and snow 30 

For slate 45 

Plastering 8 

Timber on sale is seldom found sawed to fractional dimensions of an inch 
or in lengths to fractions of feet. 

Trimmer-beams and headers should be of greater width than the other 
beams, depending on the distance of the headers from the wall, and the num- 
ber of tail-beams framed into the trimmers ; by the New York Building Act all 
headers must be hung in stirrup-irons (Fig. 1335), and not framed. 

Beams must be anchored to the walls and to each other when there are 
two lengths meeting on girders. The straps to be not less than l^-" X f", 
spiked to sides, on top, or bottom of beam. The anchors and beams to make a 



U (\ 



Fig. 1336. 



Fig. 1335. 



Fig. 1337 



tie across the building about every 6 feet. Figs. 1336 and 1337 are common 
forms of ties between beams or between beams and walls. Fig. 1338 is an 



560 



ARCHITECTURAL CONSTRUCTION. 



anchor between beams and embracing a column. Fig. 1339 is a spear-anchor 
between beams and wall ; the angle is driven into the beam. In warehouses it 

is usual to carry anchors 
p"'"'^ ^ Mi through the wall with large 

l| '^ p washers, often ornamental, 

m . ^ and nut on the outside. 

wij. Wooden beams built into 

L S walls must have an air space 




Fig. 1338. 



Fig. 1339. 



round them with ends cut diagonally and anchored to the walls (Fig. 1340). 
The air spaces at the sides are for ventilation, and with the diagonal cuts at the 
ends permit the beams weakened by fire to fall without disturbing the walls. 
Cast-iron boxes and plates for ends of beams can be purchased, with flanges 
for anchors to walls and beams. 

Floors. — In New York it is usual to lay single floors of tongued and grooved 
boards directly on the beams, but in the Eastern States double floors are more 
common. The first floor consists of an inferior kind of boards, as hemlock, 
unmatched, laid during the progress of the work as a sort of staging for the 
carpenter and mason, and, in finishing, a second course is laid on them of better 
material, generally tongued and grooved, but sometimes only jointed. Ceilings- 
should always be furred.^ and the laths be nailed to the strips. Furring-strips 
usually are of inch board, 2" wide, and 12" from centre to centre, nailed cross- 
wise from joist to joist. 

In dwellings it is desirable to isolate the floors of each story, so that noise, 
vermin, smells, and fire may be cut off. The first is usually done by deafening, 
which consists (Fig. 1341) of a sub-floor, resting on cleats, nailed to the beams 

and about 4" below the floor. This space 
is filled with lime-mortar, weakened by a 
mixture of sand or gravel, but strong 





Fig. 1340. 



Fig. 1341. 



enough to set. If the timber is green, the contact of the mortar is apt to pro- 
duce dry rot. 

Deafening may be secured to great extent by double floors, with two or three 
thicknesses of carpet paper or sheathing quilt between. When small vermin, 
like cockroaches, can pass, stenches and fire can find their way. To prevent 
which, begin at the cellar and cut off all access to space between plastering and 
floor; if the ceiling is plastered, fill in between studs tightly with strips of 



ARCHITECTURAL CONSTRUCTION. 



561 



board, and above them a course of brick in cement. 
Fibrous hemlock boards prevent the gnawing of rats 
and mice. 

The fireproof of old builders consisted simply of 
plain cylindrical or groined arches (Fig. 1342) in 
stone or brick masonry or concrete. 

Figs. 1343 to 1347 are illustrations of Koman 
constructions in masonry, from " Dictionnaire Rai- 
sonne de I'Architecture," par M. Viollet Le Due. 

Fig. 1343 is a perspective view of a cylindrical arch in process of construc- 
tion. The centres A and lagging B are quite light, as the full load of the arch 




Fig. 1342. 




Fig. 1*4:3 



is never borne by them. On the lagging, B, a cover of flat tile, C, is laid in ce- 
ment, and above ribs, D D, and girts, E E, in brick masonry, shown on a larger 
scale in Fig. 1344, with the plank P used for the support of the girt bricks E, 
which is removed after the mortar is set. The panels are now filled with concrete. 
37 



562 



ARCHITECTURAL CONSTRUCTION. 



Fig. 1345 represents rib and portions of 
girts of a groin shown in plan, Fig. 1346, 
efg h being that of the rib ; K^ a timber of 
the centre. 

A similar construction also obtained for 
domes, the girts being of the same width as 
the ribs, and sunk panels formed by furr- 
ing up on the wooden lagging of the cen- 
tres. 

Fig. 1347 is a perspective of a dome, in 
which the brick skeleton, ribs, and girts 
are curved, with panels, B B, of concrete. 

In Italy ceilings are made in single 
courses of brick, groined, and laid without 
centres, the arcs being described on the 
side-walls, and the bricks laid in plaster to 
a line. The spandrels may be levelled up 
with concrete, when rooms above are to be 
occupied, but often there is only the 
brick arch forming the ceiling of the principal rooms, with a light wooden 
roof above. 




Fig. 1346. 



Fig. 1345. 




ARCHITECTURAL CONSTRUCTION. 553 

The sizes of Italian brick are 2" X 4" X 10" and If X 4" X 12" ; when 
there is no load above, these are laid flatwise in the arch. 

In one of the warehouses of the Appleton Manufacturing Company at 
Brooklyn the floor was constructed of groined arches in concrete, supported on 
brick side-walls and piers. Piers were 2' square and 13' centres ; the arches 
finished for a floor above were 21" deep at the spring and 9" at the key. Ceil- 
ing was plastered and the room beneath occupied as a warehouse. In the room 
above a wooden floor was laid and used as a printery, and has been occupied 
for many years. There has been found one objection to the concrete — that 
water in quantity spilt on the upper floor sipes through, to prevent which there 
should have been on the concrete floor a thin coat of Portland cement or of 
asphalt. 

The first fireproof buildings in use here were like the example above of the 
Appleton warehouse, with supports and arches entirely in masonry. The latter 
were usually cylindrical or segmental, plain or groined. The depth taken for 
the construction and the floor space occupied by the supports were objection- 
able, but as fireproof constructions they were the best. 

The erection of high buildings, the large and valuable stocks often carried 
in stores and warehouses, have involved the necessity of forms of fireproof con- 
structions \vhich will prevent the spreading of conflagrations and secure the 
contents of a building, but it must be understood that no construction has yet 
been invented that will prevent the destruction of a building by fire whose 
contents are large masses of combustibles ; the buildings should be called fire- 
resisting rather than fireproof. The first buildings designed for this purpose 
consisted of iron I-beams, brick arches, and concrete spandrels, with wooden 
floors above. This, aside from its weight, was satisfactory, but a skew-back tile 
and plaster were necessary to protect the bottom flange of the iron beam. The 
tie-rod, when necessary, was concealed in the arch. 

In another form of construction, instead of using a movable centre, a 
crimped sheet-iron arch was used, which was left in and made a part of the 
structure, above which there was a concrete filling to the level of the top of the 
beam. 

To reduce the weight of brick and increase their fire resistance, brick are 
now made hollow, with flat surfaces below for the reception of plastering, and 
above for the wooden floors (Fig. 1348). Such floorings weigh only about one 
half that of solid brick arches, and therefore admit of beams of less weight per 




Fig. 1348. 



square foot of floor, either by the reduction of the weight of the beam or an 
increase of span. A thin layer of concrete is put on the top of the brick, and 
wooden strips embedded to nail the floor to. 

By mixing sawdust with the clay, which is burned out in the firing, the 
product becomes a very light, porous, and firm substance, which can be cut 



564 



ARCHITECTURAL CONSTRUCTION. 



witli the saw and will hold a nail. Porous brick, hollow, with thicker ribs than 
the tiles, are sawed to voussoir joints and laid between I-beams as flat arches. 



^ 



m 



W////////////////////M 



Fig. 1349. 



M 



^ 



Fig. 1350. 



For ceilings, porous tiles about 2" thick rest on iron straps suspended from 

wooden beams (Fig. 1349), or on the flanges of _L-irons in a bed of mortar (Fig. 

1350), the thickness of the plaster finish beneath 

affording some protection to the iron straps and 

flanges from fire. 

Iron posts not protected are not as safe as wooden 
ones. Oast-iron posts may be cast with a surface of 
nails or projections for plaster of common mortar, or of 
cement, with a finish of Keene's cement, which admits 
of washing. Figs. 1351 and 1352 are elevation and 
section of a Phoenix column with a porous terra-cotta 
covering; Figs. 1353 and- 1354, a similar covering ap- 
plied to a square and round post. 

Fig. 1355 shows in perspective the applications of 
hollow brick to the lining of exterior walls bonding 
with the common-sized brick and equal in crushing 
strength ; they supply the place of a course, and the 
moisture will not strike through. 





Fig. 1351. 



Fig. 1352. 



Fig. 1353. 



Fig, 1354. 




Fig. 1355. 



Fig. 1356 is another form applied di- 
rectly to the face of a wall secured by 
flat-headed nails driven into the joints of 
the brickwork. 

Fig. 1357 shows the mode of setting 
hollow brick for a partition ; where it is 
necessary that nails should be driven, 
porous brick should be inserted. 

Improvements in material, especially 
the use of rolled steel instead of wrought- 



ARCHITECTURAL CONSTRUCTION. 



565 



irou, led to a skeleton construction which consists of rolled steel, wrought- or 
cast-iron columns supporting a frame of rolled steel, beams and girders, set 
and framed before any of the masonry except the foundation walls are laid. 

The next in order of construction are 
the side and end walls, of which the 
masonry may be wholly or partially self- 
sustaining or merely a screen or cur- 
tain extending from the top of any 
wall girder to the under side of the next 
girders above. The outside posts in 



/ / / -A 


///////A 


/ / / /y}//y 


1 


1 1 / a/V//\ 


1 1 


Ji 1 A/AA 


%'^\ 1 1 S 1 i i II 






1 'VxA^Vr 




1 ^A///// 




1 ///A/V/ 




w^Wm 




-W 




y 




Fig. 1357. 
Fig. 1356. 

the last case as well as the inside, therefore, sustain all the dead and live load. 
The dead loads include material nsed in actual construction, or fixtures and 
machinery which form a permanent part of the necessities of occupation. Live 
loads are the weight of occupants, furniture, goods, stores, and movables. 





J 




L 




—€■- 


fil^ 


hds__ 













L 










— 




r 




6/rc 


^prs 




Co/. 
















— 5" 




— 




















"I 


















r 




















1 , 






ir 




L 














. 






J 









Fig. 1358. 



Fig. 1358 is a floor plan of girders and beams of the standard form; columns 
are preferably of rolled steel, but often of cast-iron. In all the walls, centrally 
between walls and columns, and between columns, girders are framed on which 
the beams rest and to which they are usually fastened. 



566 



ARCHITECTURAL CONSTRUCTION. 



Under the head of " Engineering Drawing " foundations are shown with the 
bases of these columns and the iron grillage on which they are supported. All 
the parts are proportioned to the loads which they are to sustain. 

The iron surface of all columns, girders, and beams must be protected from 




Fig. 1359. 

fire, commonly by brick — common, hollow, or porous, and of thickness not less 
than 4''. The floors are usually flat arches of hollow brick (Fig. 1348) in which 
the skew-back extends below the flanges of beams and girders to sustain the 
plaster protection. 

Besides the flat arches of hollow brick and of porous brick, concrete has been 
used for beams and flooring, but, as the material has comparatively little tensile 
strength, the boitom tension of a concrete beam has been met by steel rods or 
wire anchored and embedded in the material. Twisted bars of wrought-iron 
from 1" to 2" square have been introduced by E. E. Eansome, of San Francisco, to 
strengthen flat floors of considerable span, and, as they can not slip, the anchor- 
age is well and uniformly distributed. Experiments by Kirkaldy for Mr. Hyatt 
demonstrated that the expansion and contraction of concrete and of iron is 
equal under changes of temperature. 

Metropolitan Fire Prooflng Company of this city make use of the I-beam 
frame and tension rods or wires of galvanized iron (Fig. 1359) which are em- 
bedded in a concrete composed very largely of plaster-of-Paris cement and a 
little sand, with crashed coke, cork, or sawdust. 

Figs. 1360, 1361, and 1362 are plan 
and elevations of one of the standard 
connections of I-beams and Z-bars 
from the hand-hook of the Carnegie 
Steel Company. 

Figs. 1363 and 1364 is a cross-pin- 
tle connection of girders and struts of 
the Phoenix Iron Company with their 
usual steel column. 

Figs. 1365 and 1S66 is a cast-iron 
pintle connection of the same company. 
Figs. 1367, 1368, and 1369 are 
drawings of a cast-iron joint detail. 

In the present form of framing 
steel skeletons, rivets are preferred to 
bolts, and much depends on their 
strength in shear. 

Fig. 1370 is a plate of the standard 
connection of angles for I-beams from 
Fig. 1360. the Carnegie Company. 




Fig. 1361, 



Fig. 1862, 




ARCHITECTURAL CONSTRUCTION. 



56Y 



3 O O 0| 




Faced Joinf 



Q Q jQ Q Q~0 



Qr3ct[d Ends 



Gjrder 



C OOjiO OOP 



C ""^faced Joint 



Fig. 1364. 



Hv 



^^^W 



^^^ 




Fig. 1363. 



Fig. 1365. 



Fig. 1368, 




Fio. 1367. 



v//y///////A 

Fig. 1371 



568 



ARCHITECTURAL CONSTRUCTION. 



Fig. 1371 is a section of the wall of the New Street front of the Manhattan 
Life Insurance Company of New York, showing the position of wall girders. 
The front is 176' X 254' high, with five posts, including the corner ones. 

The great objections made to the skeleton-frame construction are that the 



STANDARD CONNECTION ANGLES. 
FOR I BEAMS. 



ix 4x %"L-1-6'W. 




100 

for 24 I f^^- 

lbs. 



fors'ljeibs. 
for4"lf7lbs. 






TF 



6x 6x^/6 L -0-8 Jllg. 



for s'ljiolbs. 
, . ^ 4-1 jji > for e'l [13 lbs. 



.tt 



for 12 



.j4olbs. 



6x6x/,sL-0-4^1ff. 

for 7 I jislbs^ 



^ 



6x6xK6"L-0-6j^"lg. 



-f 



6x6x^^'L 



forro'li^sjbs. 
33 lbs. 






if^i^^^lfj^,' 






forSIjiSlbs. 
for 9' I j 21 lbs. 



4x4x%L— 0-10: 



CHANNELS. 



-i- W 






for 15 C —33 lbs-. 



4x a'x?|1— O^SMlg . 3Kx 3>^x ?/'l -04/lg, 

^^T^^TT^for 12" C 



for 8 CJ II lbs. 
for g'l: J 14 lbs. 

3>|x 3>|'x %L -O^Klg. 




20 lbs. 



. ~i47~Nii 



'i3|fe2?i.*l*2?4^j^/ 



iV?';^^^" 



forjc 
9.5 lbs. 



-*- -♦- 



for 10 C 
16.5 lbs. 



k^'^'^i^r 



Connections for 3, 4, 5, and 6 I-beams apply also to Channels. 
All holes for % Bolts or Rivets. 
Fig. 1370. 



iron is liable to rust in position where it can not be seen, but it is met by care in 
cleansing the iron, in boiling in oil and painting, or by the Smith process used 
in protecting cast-iron pipes, and, second, the want of protection against wind 
strains and a proper system of bracing without interfering with the occupancy 
of the building. The section of walls (Figs. 1372 and 1373) shows the dimen- 



ARCHITECTURAL CONSTRUCTION. 



569 




sions required by the Building Depart- 
ment of New York city for the skeleton 
construction and for plain walls with- 
out it. 

If the wall construction follows 
promptly that of the steel frame, and 
it is temporarily held by tie rods, a 
mortar set will be secured which will 
resist the usual wind stresses. For 
buildings entirely of brick masonry, it 
is usual to introduce wooden braces — 
as the work progresses — which are re- 
moved when fully closed in. 




Fig. 1372. 



Fig. 1373. 




In New England there has been introduced what are called fire-retarding 
constructions for mills, of which the beams, posts, and floors are of wood. The 




Fig. 1376. 



570 



ARCHITECTURAL CONSTRUCTION. 



principle of the construc- 
tion is to consolidate the 
material in such a way 
that a fire can be held long 
enough in any room in 
which it may originate till 
the water and appliances 
under the management of 
an established fire depart- 





ke s 



Fig. 1377. 



ment connected with the mills or public can get it 
under control. 

Figs. 1374 and 1375 are elevation and section of 
post, beams, and floors which show the details of con- 



FiG. 1379. 



struction, and Fig. 1376 of a mill showing a floor and 
a roof. The ceiling must be high posted and the 
windows wide, and -set well up to the ceiling to admit 
of light into a wide mill. When there is plenty of 
ground space, it is in most industries safer from fire 
and more economical in management to have a one- 
story mill (Fig. 1377), of which details are shown in 
Figs. 1378 and 1379. A one-story mill may be of any 
dimension required, as the central spaces are lighted 
by monitor decks. The principle of all this construc- 
tion is that there should be no spaces where dust may 
collect ; in the floors the material is close, but if the 



ARCHITECTURAL CONSTRUCTION. 



571 



timber be not seasoned or kiln-dried, as there is no circulation of air, it may dry- 
rot. The posts have a bore through the centre and holes connecting with it at 




Fig. 1380. 

top and bottom to provide air circulation, and it is better not to paint any of 
the exposed timber until all the moisture is dried out. 

In mills sheathing is preferable to plastering, as this last may break and pieces 
fall into the machinery ; but Fig. 1380 shows a form of construction that has 
served well for warehouses, and is safer and more ornamental than the usual 
timber constructions. The lathing consists of wire cloth fastened with staples, 
stapled through furring strips f " to |-", and then the usual three-coat plaster. 

Doors. — In stud-partitions, the openings for doors are framed as in Fig. 
1319, the door-frame being independent of the studs. 

Fig. 1381 represents the elevation and Fig. 1382 the horizontal section of a 
common inside-door. A A are the stiles, B, 0, H, D, the hottom, lock, parting, 
and toj) rail, E the panels, and F the 7nuntin ; the combination of mouldings 
and offsets around the door, G, is called the architrave ; in the section, a a are 
the partition-studs, h I? the door-jambs. 

Fig. 1383 represents the forms of the parts of a door, and the way in which 
they are put together. When the tenons are to be slipped into the mortises, 
they are covered with hot glue, and, after being closed up, keys are driven in. 

With regard to the proportions of internal doors, they should depend in 
some degree on the size of the apartments ; in a small room a large door always 
gives it a diminutive appearance, but doors leading from the same room or 
passage, which are brought into the same view, should be of uniform height. 
The smaller doors which are found on sale are 2 feet 4 inches X 6 feet ; for 
water-closets, or very small pantries, they are sometimes made as narrow as 15 
inches, but any less height than 6 feet will not afford requisite head-room ; 
2 feet 9 inches X 7 feet, 3 feet X 7 feet 6 inches, or 3 feet 6 inches X 8 feet, 
are well-proportioned, six-panelled doors. But the apparent proportions of a 
door may be varied by the omission of the parting-rail, making the door four- 
panelled, or narrowed still more by the omission of the lock-rail, making a two- 
panelled door. Sometimes the muntin is omitted, making but one panel ; but 
this, of course, will not add to the appearance of width, but the reverse. Wide 
panels are objectionable, as they are apt to shrink from the mouldings and 
crack. The mouldings are generally planted on, and nailed to the stiles and 
rails, but sometimes formed on the latter. 



572 



ARCHITECTURAL CONSTRUCTION. 



When the width of the door exceeds four feet, it is generally made in two 
parts, each part being hung to its side of the frame, or one part hung to the 

other, so as to fold back like a 
shutter; or the parts may be 
made to slide back into pockets 




12 



i 2 

Fig. 1382. 



^n 




Fig. 1383. 



or grooves in the partition. The doors may be supported on wheels, and run 
on tracks at the floor-level; or the tracks may be above the doors, and the 
doors suspended ; or they may be supported by levers, and be moved parallel 
without rollers ; all these appliances can be purchased. 

Figs. 1384, 1385, and 1386 are the elevation, vertical and horizontal sections 
of a pair of sliding-doors. There are no knobs, but countersunk pulls to the 
doors, that they may be slid entirely within the pockets, with a special handle 
in the locks at the edges of the doors for withdrawing them. 

Figs. 1387 and 1388 are vertical and horizontal sections of the same doors 
hung on butts or hinges. 

Figs. 1389 and 1390 are the elevation and horizontal section of an antae- 
finished outside-door, with the side-lights C, and a top, fan, or transom light 
B. The bar A is called a transom, and this term is applied generally to hori- 
zontal bars extending across openings, or even across rooms. 

Fig. 1391 is the elevation of an outside folding-door. The plan (Fig. 1392) 
shows a vestibule, V, and an interior door. The outer doors open, as shown by 
the arcs, and fold back into the pockets or recesses, 7? jt?, in the wall. This is a 
very common form of doors for first-class houses in this city. The fan-lights 
are made semicircular, and also the head of the upper panels of the door ; these 



ARCHITECTURAL CONSTRUCTION. 



573 



panels in the interior or vestibule door are of glass. Of late the outer doors are 
extensively used as storm doors, glazed with plate glass exposing the vestibule, 
and hung with spring butts and ornamental in finish. 




Fig. 1386. 



Windotcs are usually understood to be glazed apertures. The sashes may 
be stationary, but for most positions they are made to open either by sliding 



574 



ARCHITECTURAL CONSTRUCTION. 



vertically, or laterally, or like doors. The first is the common form of window, 
and the sashes are generally balanced by weights ; the second, except in a cheap 



(-■•'// 



Fig. 1387 




form in mechanics' shops, are seldom used ; the third, often used 
for access to balconies or between rooms, are called casements, or 
French windows. 

Figs. 1393 and 1394 are the outside elevation and horizontal 
section of one half of a common 




Fig. 1390. 



Fig. 1392. 



box-frame, and Fig. 1395 a vertical section of the same in a wooden 
frame house. S is the sill of- the sash-frame, W the frame-sill, 
with a wash to discharge the water, B the bottom rail of the sash, 
M the meeting rails, T the top rail, H the head of the sash-frame, 
and A the architrave similar to that around doors. Instead of 
two sills, S and W, one is often used, and inclined to form the wash. D is the 
common outside blind. In the sectional plan (Fig. 1400), C are the win- 
dow-stiles, F the pulley-stile, w id the sash-weights, p the parting strip, and D D 
double-fold shutters. 

Figs. 1396 and 1397 are the interior elevation and vertical section of a box- 
frame window in a masonry wall ; Fig. 1398 is an exterior view of the same 



ARCHITECTURAL CONSTRUCTION. 



575 







Fig. 1393. 



!■ ■■■■'■ 



J Feet 




H 



AV 



Fig. 1394. 



Fig. 1395. 



576 



ARCHITECTURAL CONSTRUCTION. 



window, and Fig. 1399 a horizontal section. In 
masonry walls the sills are usually of stone, as 
shown in Fig. 1397, with a lap of the window 
frame on it. In setting the sill, one course of brick 
is left out beneath the central portion to admit of 
settlement in the walls without stress to the sill. 




® 



Fig. 1396. 



Fig. 1397. 



.ARCHITECTURAL CONSTRUCTION. 



677 



In brickwork, the 
height of sill and 
cap corresponds 
to a determinate 
number of courses, 
so that it may not 
be necessary to 
split brick in set- 
ting them. 

Unless the win- 
dows begin from, 
or nearly from, 
the floor, the point 
a (Fig. 1395) may 
be fixed at a height 
of about 30 inches 
above the flooi-, 
and the top of the 
window sufficient- 
ly below the ceil- 
ing to allow space 
for the architrave 
or other finish 
above the window, 
and for the cornice 
of the room, if 
there be any ; a 
little space be- 
tween these adds 
to the effect. For 
common windows, 
the width of the 
sash is 4- inches 
more than that of 
the glass, and the 
height 6 inches 
more ; thus the 
sash of a window 

3 lights wide and 

4 lights high, of 
12" X 16" glass, is 
3 feet 4 inches 
wide and 5 feet 10 
inches high. In 
l)late - glass win- 
dows more width 
is taken for the 
stiles and rails. 

38 





578 



ARCHITECTURAL CONSTRUCTION. 



The usual sizes of cylinder glass are 7" X 9" up to 24" X 36", but 
glass may be had up to 40" X 60" ; double thick, 48" X 62". 
polished or rough, may be had of a size as large as 14 X 8 feet. 

In Fig. 1393 the 
blind D is hinged to 
the hanging stile, and 
is closed within the 
opening in the mason- 
ry. The slats are 



single 
Plate 



thick 
glass, 



s 




Fig. 1400. 



r 






























r~ 
















1 























tM 



7r}W 




Fig. 1401. 



Fig. 1402. 



movable on pin tenons, 

and those of each half, 

upper and lower, are 

connected by a central 

bar, so that they, are 

moved together, and 

adjusted at any angle to the light. In Fig. 1399 the blinds are inside, 4-fold, 

and folding back into pockets. It is more usual to make the pockets for the 

blinds inclined to , the window, as in Fig. 1400, giving to the interior more 

light, or ampler space for curtains. 

Fig. 1401 is the outside elevation of a French window or casement. 

Fig. 1402 represents the sectional elevation of the same window, in broken 
lines, and on a larger scale ; the same letters designate similar parts as in Fig. 
1395. A transom-bar is often framed between the meeting-rails, and in this 
case the upper sash may be movable ; in Fig. 1402 it is fixed. An upright, 
called a mullion^ is often introduced in the centre, against which the sash shuts. 

For use as doors, the lower sashes should not be less than 5 feet 6 inches 
high. In these forms of sash the rails and stiles are wide, and for equal aper- 
tures. French windows when closed admit light. The chief objection to this 
window lies in the difficulty of keeping out the rain at the bottom in a driving 
storm. To obviate this, the small moulding d^ with a drip or undercut, is nailed 
to the bottom rail ; but the more effectual means is the patent weather-strip, 
the same as used on outside doors. 

Dormer or attic windows are framed and set as in an upright stud-partition. 

Stairs consist of the tread or step on which to set the feet, and risers^ up- 



ARCHITECTURAL CONSTRUCTION. 



679 



right pieces supporting the treads — each tread and riser forms a stair. If the 
treads are parallel they are called fliei\9 ; if less at one end than the other, they 
are called tuinders, f and w (Fig. 1409). The top step, or any intermediate 
wide step, for the purpose of resting, is called a landing ; the height from the 
top of the nearest step to the ceiling above the lieaduuty ; the rounded edge of 
the step a nosing {a, Fig. 1403) ; and if a small hollow or cavetto (b) be glued 
in the angle of the nosing and riser, it is called a moulded nosing. The pieces 
which support the ends of the stairs are the strings (Fig. 1404) ; that against 
the wall the zuall-string, the other the 
outer string. Besides these strings, 
pieces of timber are framed and placed 
'beneath the fliers, when the stairs are 



i^' 



Fig. 1403. 




Fig. 1404- 



wide (Fig. 1405), called can'iages. Sometimes the strings, instead of being 
notched out to receive the steps, have the upper and lower edges parallel, with 

grooves cut in the inner faces to 
receive the ends of their steps and 




Fig. 1405. 




Fig. 1406. 



risers (Fig. 1406). These are called housed strings. Steps and risers are se- 
cured in the grooves by wedges covered with glue, and driven in. For the 
rough, strong strings of warehouses the carriages are made of plank, with 
grooves to receive plank-treads, and without risers. 

Figs. 1407 and 1408 are elevation and plan of a straight run of stairs, both 
partly in section. N is the 7iewel-post., n a baluster^ li the hand-rail, w the 
well. In the section of the floors, cleats are shown nailed to the beams ; on 
these short boards are nailed to form a box for the reception of mortar for the 
deafening. The opening represented in the plan (which must occur between 
the outer strings, if they are not perpendicular over each other) is called the 
well (W, Fig. 1409). 

The breadth of tread in general use is from 9 to 12 inches ; in the best 
staircases, it should never be less than 11 inches, nor more than 15. The 
height of the riser should be the more, the less the width of the tread ; for 
a 15-inch tread the riser should be 5 inches high; for 12 inches, 6.}; for 9 
inches, 8. In laying out the plan of stairs, having determined the starting- 



580 



ARCHITECTURAL CONSTRUCTION. 



point, either at bottom or top, as the case may be, find exactly the height of 
the story ; divide this by the height you suppose the riser should be. Thus 




Fig. 1408. 



(Fig. 1410), if the height of the story and 'thickness of floor be 9 feet, and we 
suppose the riser should be 7 inches high, then 108 inches, divided by 7 = 15f 

It is clear that there must be a full number of steps, either 16 or 15 ; to 
be near the supposed height of the riser, adopt 15, then — 
--if- = "^A inches, height of riser. 

For this particular case, assume the breadth of the step as 10 inches, and 
the length at 3 feet, a very usual length, seldom exceeding 4 feet in the stair- 
cases of private houses. For the plan— lay off the outside of the stairs, two 
parallel lines 3 feet apart, and space off from the point of beginning 14 treads 
of 10 inches each, and draw the cross-parallel lines. To construct the eleva- 



ARCHITECTURAL CONSTRUCTION. 



581 



tion, project tlie lines of the steps in plan, and divide the height, either on a 
perpendicular or by an inclined line, into the nnmber of risers (15), and draw 






Fig. 1409. 



Fig. 1410. 



horizontal lines through these points; or the same points may be determined by 
intersection of the projections of the plan with a single inclined line drawn 
along the nosing of top and bottom steps. The number of treads is always one 
less than the number of risers, the reason of which appears in the elevation. 

For the framing plan the drawing of the elevation of stairs is in general 
necessary, to determine the opening to be framed in the upper floor, to secure 
proper headway. Thus (Fig. 1410), the distance, a, between the nearest stair 
and the ceiling should not be less than 6 feet 6 inches ; a more ample space 
improves the look of the stairway ; but if confined in our limits, this deter- 
mines the position of one header ; the other will be of course at the top of the 
stairs. AYhen one flight is placed over another^ the space required for timber 
and plastering, under the steps, is about 6 inches for ordinary stairs. 

When the stairs are circular, or consist in part of winders and fliers, as in 
Fig. 1409, the width of the tread of the winders should be measured on the 
central line. The construction of the elevation is similar to that of the straight 
run (Fig. 1410), dividing the space between the stories by a number of parallel 
lines equal to the number of risers, and intersecting the parallels by projections 
from the plan. The objection to all circular stairs of this form, or with a small 
well-hole or a central shaft, is that there is too much difference between the 
width of the tread, but a small portion being of a suitable size. The hand- 
somest and easiest stairs are straight runs^ divided into landings, intermediate 
of the stories, and either continuing then in the same line, or making a full re- 
turn at right angles. It is at times fashionable to make the neivel a prominent 
feature in the hall, often occupying valuable space. It is sufficient that it 



682 



ARCHITECTURAL CONSTRUCTION. 



be large and stiff enough for a support to the hand-rail and may be equally 
ornamental. 

The top of the hand-rail should, in general, be about 2' 8" to 3' above the 
nosing, and should follow the general line of the steps. The angles of the hand- 
rail should always be eased off. A hand-rail, affording assistance in ascending 
or descending, should not be wider than the grasp of the hand (Fig. 1411) ; but 
where, for architectural effect, a more massive form may be necessary, it is very 
convenient to have a sort of double form, with the hand-rail at the top (Fig. 
1412), or as in Fig. 1413, with the groove outside. 

To a draughtsman conversant with the principles of projection already given, 
it will not be difficult to draw in the hand-rail of stairs, or to lay off the mould 






Fig. 1411. 



Fig. 1412. 



Fig. 1413. 



for its construction. It will follow the line of stair-nosing, and where there are 
changes of pitch they are made to connect by curves tangent to these pitches, 
except where the landings are square, and newels set at the head of the land- 




FtG. 1414. 



ings, le rail is framed into the newel. At the bottom the rail is curved to the 
horizontal, when it comes into or upon top of the newel. 

Balusters are of great variety— usually turned forms— attached to the treads 



ARCHITECTURAL COXSTRUCTION. 

by dovetails, covered with the returned nosing, or with pin-ends and 
treads and under side of caps. Sometimes (especially in iron-work) the 



583 

holes in 
baluster 



ELEVATION. 



PLAN. 




lailK-^:^^^^^^^ 



Fig. 141.5. 



Fig. 1416. 



is set in a bracket from the face of the string, as in Fig. 1415 ; or the balusters 
may be cast with the bracket. 

Fig. 1414 is the side elevation of a stairs with wronght-iron string and rail. 
The string is made of wrought-iron knees, wielded together continuously, with 




Fig. 1417. 



a flat bottom-bar riveted across the lower angle of the knees, usually snpported 
by an intermediate round bar-post. Where posts can not be put in, it is better 



584 



ARCHITECTURAL CONSTRUCTION. 



that the bottom bar should be a carriage or beam of I or channel-iron, with 
knees or cast-ij-on angle-blocks riveted on the top of the beam. It is not un- 
usual to make housed strings of ]3late-iron, with angle-irons riveted on to 
receive the treads and risers. If the plate-iron be wide- enough to serve in- 
stead of balusters, it makes a very strong and stiff carriage. 

Figs. 1415 and 1416 are the plan and elevation of a cast-iron stairs, with a 
central post or newel (this term is applied also to the first post of any stairs). 
The newel-ring, tread, and riser of each step are cast in one piece, and they are 
put together by placing one newel-ring upon that below and bolting the outer 
extremity of the riser to the tread below. 

Fig. 1417 is a form of cast-iron stairs with a well instead of a newel ; the 
step and riser are bolted together by the flanges. It will be seen that one tread 
is wider than the others ; this is a landing. 

Fireplaces. — Fireplaces for wood are made with flaring jambs of the form 
shown in plan (Fig. 1418) ; the depth from 1 foot to 15 inches, the width of 
opening in front from 2 feet 6 inches 
to 4 feet, according to the size of 
the room to be warmed ; height 2 





Fig. 1419. 



Fig. 1418. 

feet 3 inches to 2 feet 9 inches, tlie 
width of back about 8 inches less 
than in front ; but at present fire- 
places for wood are seldom used, 

stoves and grates having superseded the fireplace. The space requisite for the 
largest grate need not exceed 2 feet in width by 8 inches in depth. The requi- 
site depth is given by the projection of the grate, and the mantel-piece. Ranges 
require from 4 feet 4 inches to 6 feet 4 inches wide X 12 inches to 20 inches 
deep ; jambs 8 inches to 12 inches. 

Fig. 1419 represents the elevation of a mantel-piece of very usual propor- 
tions. The length of the mantel is 5 feet 5 inches, the width at base 4 feet 6 

inches, the height of opening 2 feet 7 inches, 
and width 2 feet 9 inches. A portion of this 
opening is covered by the iron sides or architrave 
of the grate, ajid the actual open space would 
not probably exceed 18 inches in width by 2 feet 
in height. In brick or stone houses the flues are 
formed in the thickness of the wall, but when 
distinct they have an outside shell of a half-brick or 4 inches, and sometimes 
8" (Fig. 1420) ; the tviths or division-walls always 4". 

The size of house flues is usually 8" X 8", but some are 4" X 8", 4" X 12", 
and 8" X 12". The flues of different fireplaces should be distinct. Those from 
the lower stories pass up through the jambs of the upper fireplaces, and, keep- 
ing side by side with but 4-inch brickwork between them, are topped out above 



*-c 








*^4'-^ 




**; 


-t-8'— * 


*i"^ 


^8'— 










J 



Fig. 1420. 



AKCHITECTURAL CONSTRUCTION, 



585 



the roof, sometimes in a double and often in a single line IG inches wide by a 
breadth required by the number of flues, as in Fig. 1420 or in Fig. 1421. The 

latter is an illustration of how far 
flues may be diverted from a vertical 
line, but it is to be observed that the 
construction must be stable, as any 
settling or cracks not only injures the 
draught of the chimuey, but impairs 




Fig. 1421. 



Fig. 1422. 



the securitv of the buildins^ as^ainst fire. Chans^es of direction of flues should 
never be abrupt. The back of the fireplace may be perpendicular through its 
whole height, but it is usual to incline the upper half inwardly toward the room, 
making the throat to the flue long and narrow. It is very common to form 
the upper 3" to 4" of the inclined back by an iron plate, which can be turned 
back or forward to increase or diminish the draught. Fig. 1422 represents the 
arrangement of frame and brick arch for the support of the hearth. The 
chimney is generally capped with stone, sometimes with tile or cement pots. 
As an architectural feature, the chimney is often made to add considerably to 
the effect of a design. 

Roofs. — Framed roofs have been illustrated (page 486). City roofs are 
usually flat, and timbered similarly to floors, but not so strongly, with a slight 
pitch to discharge rainfall. Roofs of country dwellings are usually framed like 
stud-partitions, with inclined studs somewhat deeper than if they were ver- 
tical, depending on the inclination from the vertical; if flat, depth like that 
of a floor. The theory of the 
construction of the gambrel or 
Mansard roof (Fig. 1423), a 





Fig. 1423. 



Fig. 1424. 



roof with two kinds of pitch, is that of the polygon of rods, and self-support- 
ing; but, in general, they have central support from partitions, and their 
outlines are much varied by curves in the lower rafters cut from plank. 



586 



ARCHITECTURAL CONSTRUCTION. 



Fig. 1424 is the plan of a roof as usually drawn, shaded strongly at the 
ridges. The transept roof is liippcd at A and B. 

Glitters are generally formed in the cornice (Fig. 1425) ; sometimes on the 
roof (Fig. 1426), and sometimes by raising a parapet (Fig. 142?) and forming 
a valley. The intersection of two roofs as at v forms a valley. 




Fig. 1426 



Fig. 1427. 



Fig. 1425 represents a form of gutter very common to city buildings, the 
roof boarding extending over the gutter ; but it is preferable to make the roof 
pitch from both rear and front to the centre of the building, and to carry the 
leader down in the interior, where it may serve as a soil- 
pipe for the water-closets, basins, and baths, affording 
ventilation in fair weather and a scour in rains. 





Fig. 1428. 



Fig. 1429. 



Fig. 1428 is a gutter of a cottage roof. 

Fig. 1429 is the section of a Mansard roof, showing the side elevation of a 
dormer-window, with the gutter below its sill. 

The sheet-metal forming the gutter must extend well up or back beneath 
the shingles or felt, or be soldered to the tin of the roof, to prevent water find- 



ARCHITECTURAL CONSTRUCTION. 



587 



ing its way into the interior; and at tlie 
sides flashings of tin must extend on the 
walls above the roof and into the joints of 
the brick. 

Sheet-metal cornices, at their first intro- 
duction, were put up on wood lookouts, cut 
to the form of the cornice,<^ut it is now the 
practice to use metal supports and fasten- 
ings to the entire exclusion of wood — in 
many cases cheaper and always safer against 
fire and rotting, but the iron used must be 
protected against rust by galvanizing or 
heavy coats of paint or by both. Fig. 1430 
shows a section of a galvanized cornice with 
bar-iron frames anchored to the wall and 
roof and riveted to the cornice ; the joints 

of the cornice should be both riveted and soldered. The pitch of the 
secured by variations in the bend of the roof braces. 

Plastering. — To prevent damp striking through the plastering 
walls, and cracks in ceilings, it is usual to fur walls and beams; that 




Fig. 1430. 



gutter is 

of outer 
is, to nail 




I 



Fig. 1431. 



Fig. 1432. 



Fig. 1433. 



vertical strips of wood to the walls, and across from beam to 
beam. Furring-strips are from 1^" to 2" wide, and about |-" 
thick, nailed at distances of 12" or 16" centres (usually the 
former), adapted to the length of the laths, which are 4 feet 
long, and about 1^" x \" — spaces between laths ^" to f". The 
first coat of mortar is the scratch-coat, which is forced through 
the interstices between the laths, to make a lock to retain it. 





Fig. 14.34. 



Fig. 1435. 




Fig. 1436. 



This coat is about ^^ thick. The next or brown coat is about 
■§-" thick, and if the last coat is a sand-finish, it will be less than 
■J" thick; while, if the last coat is a hard finish, its thickness 
will be almost imperceptible. Figs. 1431 and 1432 are sections 
of furring and plastering. 



588 ARCHITECTURAL CONSTRUCTION. 

The brovvm coat is usually carried down to the floor. Over this is nailed 
the base-board, A (Fig. 1433), for the finish around the bottom of the walls of 
the room. To guard against the crack formed between the floor by the shrink- 
ing of the base, a tenon is formed along the outer edge of the latter with a 
groove for its reception in the floor. This is termed dadoing. Above the base 
is a moulding forming a part of the base ; above this, there may be a moulded 
rail, B, called the chair-rail, or surbase, and between a panel, termed a dado. 
The walls of stores are generally ceiled up as high as the surbase. For the 
finish of the angle of the wall and ceiling, it is usual in the better rooms to 
form a cornice in plaster. The cornices are mouldings of varied forms, with 
or without enricliments — that is, plaster ornaments. Figs. 1434, 1435, and 
1436 are sections of cornices. If the rooms are low, the cornice should extend 
but little on the wall, but well out oii the ceiling. 

In all architectural finish mouldings are a necessity, the simpler forms of 
which are taken from Greek or Eoman examples. 

Greek and Roman Mouldings. — The regular Greek mouldings are eight in 
number : the Fillet or Band, Torus, Astragal or Bead, Ovolo, Oavetto, Cyma 
Kecta or Ogee, Cyma Re versa or Talon, and Scotia. 

The fillet {a, Fig. 1437) is a small rectangular member, on a flat surface, 
whose projection is usually made equal to its height. 

The torus and astragal are semicircles in form, projecting from vertical 
diameters, as in Fig. 1438. The astragal is distingaished from the torus in 
the same order by being made smaller. The torus is generally employed in the 
bases of columns ; the astragal, in both the base and capital. 



i-__.. 



c\ )(L 



r 

Fig. 1437. Fjg. 14JS. Fig. 1439. 

The ovolo is a member strong at the extremity, and intended to support. 
The Roman ovolo consists of a quadrant or a less portion of a circle (Fig. 1439). 
The Greek ovolo is elliptic. 

To describe the Greek ovolo (Fig. 1440): Draw cZ/ from the lower end of 
the proposed curve, at the required inclination ; draw the vertical g ef io define 
the projection, the point e being the extreme point of the curve. Draw e h 
parallel to df^ and draw the vertical d li k^ such that d li 
is equal to h k. Divide eli and e/into the same number 
of equal parts ; from d draw straight lines to the points of 
division in e/, and from k draw lines through the divi- 
sions in e li to meet those others successively. The inter- 
sections so found are points in the curve, which may be 
Fig. 1440. traced accordingly. 

The cavetto is described like the Roman ovolo — by 
circular arcs, as shown in Figs. 1441 and 1442. Sometimes it is composed of 
two circular arcs united (Fig. 1443) ; set off he, two thirds of the projection, 
draw the vertical h d equal to he, and on d describe the arc h i. Join e d and 
produce it tojt?; draw i n perpendicular to e d, set off no equal to ni^ and 




AriCHITECTURAL CONSTRUCTIOX. 



589 



draw the horizontal line o j^ meeting ej)^ on p describe the arc io to complete 
the curve. 

The ogee, or cyma recta (Fig. 1444), is compounded of a concave and a con- 
vex surface. Join a and h, the extremities of the curve, and bisect ab at c; on 
a and c, as centres, with the radius a c, describe arcs cutting 

! at d ; and on b and c, describe arcs cutting at e. On d and <?, 

f \ as centres, describe the arcs ac, ch, composing the moulding. 



Fig. 1441. 



Fig. 1442. 





Fig. 1443. 



Fig. 1444. 



e.1^- 


~fn 






r 



Fig. 1445. 



The cyma rcvcrsa, or talon (Fig. 1445), is a compound curve, distinguished 
from the ogee by baving the convex part uppermost. 

If the curve be required to be made quicker, a shorter radius than a c must 
be employed. The projection of the moulding n h (Fig. 1444) is usually equal 
to the height a n. 

To describe the Greek talon : Join the extreme points a, b (Fig. 144G) ; 
bisect a ^ at c, and on ac and c b, describe the semicircles b d c and c a. Draw 
perpendiculars d o, etc., from a number of j)oints in a c and 
c b, meeting the circumferences ; and from the same points set ,f, 

off horizontal lines equal to the respective perpendiculars : // j 

n equal to o d, for example. The / / i 

curve line b n «, traced through the 
ends of the lines, will be the contour 
of the moulding. 




Fig. 1446 



To describe a scotia : Divide the 
perpendicular a b (Fig. 1447) into three 
equal parts, and with the first, a e, for 
radius, on e as a centre, describe the arc 
afh, in the perpendicular c o set off cl equal a e, join e I, and bisect it by the 
perpendicular o c/, meeting c o at o, on the centre o, with o c for radius, complete 
the figure by the arc c h. 

These mouldings, and combinations of them, are stiiclc in wood, and are to 
be purchased in every variety. Fig. 1448 represents some of the common forms 
always to be had, and of suitable sizes. 

Pro2Jortions and Distribution of Rooms and Passages. — Rooms of dwell- 
ing-houses are to be proportioned and arranged according to the necessities of 
position and use, the space that can be occupied, the financial means available, 
and often to suit the peculiar wishes of owners or occupants. In cities, the 
limits of the lot restrict the arrangements to a small ground-space, and require 
an increase in the number of stories. Use has established certain forms often 
peculiar to different cities, beyond which there is little change ; but in the 
country, where there is plenty of ground-space, and where many stories are 
usually injurious to the aesthetic effect, and where there are few canons in archi' 



590 



ARCHITECTURAL CONSTRUCTION. 




Fig. 1448. 



ARCHITECTURAL CONSTRUCTION. 59I 

tecture to be observed, tliere is little limit to the variety of forms and arrange- 
ments of country-houses. 

In designing a country-house, where one is not restricted in space, it is often 
convenient to mark out the rooms of the desired size on slips of paper, accord- 
ing to some scale, then cut them out and arrange them in as convenient an 
order as possible, and modify the arrangement by the necessities of construction 
and economy. Thus, the greater the outside surface in proportion to the in- 
cluded area, and the greater the number of chimneys and space used for pas- 
sages, the greater the cost. The kitchen should be of convenient access to the 
dining-room, both should have large and commodious pantries, and all rooms 
should have an access from an entry, without being compelled to pass through 
other rooms ; this is particularly applicable to the communication of the kitchen 
with the front door. Outside doors for common and indiscriminate access 
should not open into important rooms. All rooms to be occupied as living or 
bedrooms should have flues opening directly or indirectly to the outer air for 
ventilation. 

As to the size of the different rooms, they must of course depend on the pur- 
poses to which they are to be applied, the class of house, and the number of 
occupants. The kitchen for the poorer class of houses is also used as an eat- 
ing-room, and should therefore be of considerable size to answer both purposes; 
for the richer houses, size is necessary for the convenience of the work. In the 
older Xew York private houses the average was about 16 X 20 feet ; for me- 
dium houses in the country generally less, say 12 X 16. A back kitchen, scul- 
lery, or laundry, should be attached to the kitchen, and may serve as a passage- 
way out. 

Tlie Dini7ig or Eating Rooms. — The common width of dining-tables varies 
from 4 to 5 feet 6 inches ; the space occupied by the chair and person sitting 
at the table is about 18 inches ; the table-space, for comfort, should be not less 
than 2 feet for each person at the sides of the table, and considerable more at 
the head and foot ; hence the space that will be necessary for the family and 
its visitors at the table may be calculated. Allow a further space of 2 feet at 
each side for passages, and some 3 to 5 at the head for the extra tables or chairs, 
for the minimum of space required ; but, if possible, do not confine the dining- 
room to meagre limits, unless for very small families ; let not the parties be lost 
in the extent of space, nor let them appear crowded. 

The parlours should be made according to the rules given below, not square, 
but the length about once and a half the width; if much longer than this, break 
up the walls by transoms or projections. As to the particular dimensions, no 
rules can be given; they must depend on every person's taste and means; 
20 X 16 is a very fair size for a regular living-room parlour, not a drawing- 
room. The same size is ample for a sleeping -room. The usual width of single 
beds is 2' 8" to 3' 6" ; of three-quarter, 4' to 4' 6" ; of whole, 5 to 6 feet ; the 
length, 6' 6" ; and as the other furniture may be made to consist of but very 
few pieces, if adequate means of ventilation are provided parties may live 
snugly in small quarters. The bed should not stand too near the fire, nor 
between two windows ; its most convenient position is head against an interior 
wall, with a space on each side of at least 2 feet. To the important bedrooms 
of first-class houses, dressing-rooms should be attached, and, if there is water 



592 



ARCHITECTURAL CONSTRUCTION. 




ARCHITECTURAL CONSTRUCTION. 593 

and sewer service, fitted with set bowls and baths and water-closets. If pos- 
sible, there should be windows opening to the outer air, but always with flue- 
ventilation. 

Pantries. — Closets for crockery should not be less than 14 inches in depth 
in the clear ; for the hanging up of clothes, not less than 18 inches, and should 
be attached to every bedroom. For medium houses, the closets of large sleep- 
ing-rooms should be at least 3 feet wide, with hanging-room, and drawers and 
shelves. There should also be blanket-closets, for the storing of blankets and 
linen ; these should be accessible from the entries, and may be in the attic. 
Store-closets should also be arranged for groceries and sweetmeats. 

Passages. — Front entries are usually 6 feet wide in the clear ; common pas- 
sage-ways, 3 feet ; these are what are required, but ample passages give an im- 
portant effect to the appearance of the house. The width of principal stairs 
should be not less than 3 feet, and all first-class houses, especially those not pro- 
vided with water-closets and slop-sinks on the chamber-floor, should have two 
pairs of stairs, a front and a back pair ; the back stairs need not necessarily be 
over 2 feet 6 inches in width. 

The Height of Stories. — It is usual to make the height of all the rooms on 
each floor equal ; it can be avoided by furring down, or by the breaking up of 
the stories, by the introduction of a mezzonine or intermediate story over the 
smaller rooms. Both remedies are objectionable. 

The average height of the stories for common city dwellings is : Cellar, 6 
feet 6 inches ; common basement, 8 to 9 feet ; English basement, 9 to 10 feet ; 
principal story, 12 to 1 5 feet ; first chamber floor, 10 to 12 feet ; other chamber- 
floors, 8 to 10 feet — all in the clear. For country-houses, the smaller of the 
dimensions are more commonly used. Attic stories are sometimes but a trifle 
over 6 feet in height, but are objectionable. 

Privies, Water- Closets, and Out-Houses. — The size of privies must depend 
greatly on the uses of the building to which they are to be attached, its position, 
and the character of its occupants. Allowing nothing for evaporation and ab- 
sorption, the entire space necessary for the excrementitious deposits of each 
individual, on an average, will be about seven cubic feet for six months, of 
which seven eighths is fluid. In the country, vaults are usually constructed of 
dry rubble-stone, and the fluid matters are expected to be filtered through the 
earth, the same as in cesspool-waste ; but great care must be taken that they 
neither vitiate the water-supply nor the air of the house. A brick and cement 
vault, air and water tight, with a ventilating-pipe into a hot chimney-flue, is 
the best preventive, and may even be built within the house. In all other cases 
there should be free air-space between the house and privy. In the city, where 
there is adequate water-supply and sewerage, the water-closet should be adopted. 
The water-closet, or privy, with a single seat, should occupy a space not less 
than 4' x 2' 6". The rise of seat should be about 17" high ; and the hole egg- 
shaped, 11" X 8". The earth-closet, when properly taken care of, is an ex- 
tremely useful appendage to a country-house, and the space requisite for it is 
the same as that of a water-closet. 

The forms of modern water appliances, and the means to get rid of house- 
waste, will be illustrated hereafter, under the heads of Ventilation and 
Plumbing. 

39 



594: ARCHITECTURAL CONSTRUCTION. 

For Wood or Coal Sheds or Bins. — In estimating the size of these accesso- 
ries, it may only be necessary to state that a cord of wood contains 128 cubic 
feet, and a ton of anthracite Qgg coal occupies a space of about 40 cubic feet, of 
bituminous coal about 45 cubic feet, of coke from 45 to 50 cubic feet. 

On the Size and Proportion of Rooms in general. — " Proportion and or- 
nament," according to Ferguson, " are the two most important resources at 
the command of the architect, the former enabling him to construct ornamen- 
tally, the latter to ornament his construction." A proportion to be good must 
be modified by every varying exigence of a design ; it is of course impossible to 
lay down any general rules which shall hold good in all cases ; but a few of its 
principles are obvious enough. To take first the simplest form of the propo- 
sition, let us suppose a room built, which shall be an exact cube — of say 20 feet 
each way — such a proportion must be bad and inartistic ; and, besides, the 
height is too great for the other dimensions. As a general rule, a square in 
plan is least pleasing. It is always better that one side should be longer than 
the other, so as to give a little variety to the design. Once and a half the 
width has been often recommended, and with every increase of length an in- 
crease of height is not only allowable, but indispensable. Some such rule as 
the following meets most cases : " The height of the room ought to be equal to 
half its width plus the square root of its length " ; but if the height exceed the 
width the effect is to make the room look narrow. Again, by increasing the 
length we diminish, apparently, the other two dimensions. This, however, is 
merely speaking of plain rooms with plain walls ; it is evident that it will be 
impossible, in any house, to construct all the rooms and passages to conform ta 
any one rule of proportion, nor is it necessary, for in many rooms it would not 
add to their convenience, which is often the most desirable end ; and, if re- 
quired, the unpleasing dimensions may be counteracted by the art of the archi- 
tect, for it is easy to increase the apparent height by strongly marked vertical 
lines, or bring it down by horizontal ones. Thus, if the walls of two rooms of 
the same dimensions be covered with the same strongly marked striped paper, 
in one case the stripes being vertical and in the other horizontal, the apparent 
dimensions will be altered very considerably. So also a deep, bold cornice 
diminishes the apparent height of a room. If the room is too long for its other 
dimensions, this can be remedied by breaks in the walls, by the introduction 
of pilasters, etc. So also, as to the external dimensions of a wall, if the length 
is too great it is to be remedied by projections, or by breaking up the lengths 
into divisions. 

Understanding the general necessities of a dwelling, the proportions of 
rooms, forms of construction, and space to be occupied, the draughtsman is 
prepared to undertake designing, and for this purpose cross-section paper will 
be found of very great use. Taking the side of a small square as a unit — one 
foot, for instance — he can readily pencil in rooms and passages, and alter and 
modify at pleasure. 

Figs. 1445 to 1456 are illustrations of this form of designing. Partitions 
are to be as much as possible one over the other, and the posts or walls ar- 
ranged in the cellar, for the support of these lines of partitions. For the 
sketch, it is sufficient to make door and window openings 3 feet, unless for 
some particular purpose double-fold doors or bow or mullioned windows are 



ARCHITECTURAL CONSTRUCTION. 



595 



required. In arranging the stairs, the whole run may be taken as 1-J- time the 
height of the story between floor and floor ; as square landings have one riser, 




Fig. 1457. 



B 



^ 



r 






1 



S' 



Fig. 1458. 



Fig. 1459. 




the rise will be equal to the square less one tread, say, for 
the design 1 foot. The length of opening in the frame, 
say 12 feet for a straight run. 

Figs. 1447 to 1472 are plans of familiar forms of 
houses, drawn to the scale of 32 feet to the inch, as 
illustrations to the student and as examples to be copied 
on a larger scale. The same letters of reference are used 
on all the plans. Thus, K K designate kitchens, cooking- 
rooms, or laundries ; D D eating-rooms ; S S sleeping- 
rooms ; PP drawing-rooms, parlours, or libraries; pp pantries, china or store 
closets, or clothes-presses ; c c water-closets and bath-rooms. These last are 
not shown in the plans of country houses, but are recognised as a necessity in 
the best of this class. The space occupied by them is given on page 593. 

Figs. 1457, 1458, and 1460 are first-story plans of houses of square out- 
line. Fig. 1459 is the second story of Fig. 1458. 



Fig. 1460. 





Fig. 1462. 





Fig. 1461, 



Fig. 1463. 



Fig. 1464. 



This form of house has the greatest interior accommodations for the outside 
cover, and, although not picturesque in its elevation, is a very convenient 
and economical structure. The kitchen (Fig. 1460) is in the basement, and 
the connection with the dining-room is by a dumb-waiter in the pantry (p). 
In Fig. 1461 the plan is the same as in Fig. 1460, but the kitchen (K) is 



596 



ARCHITECTURAL CONSTRUCTION. 



in an L attached to the house ; there is a small opening between the pantry 
(p) and kitchen, through which dishes are passed to and from the dining- 
room. 

Fig. 1462 is the plan of a very small but convenient floor, of prettier out- 
line than the square ; F is a portico or veranda. No chimney is shown in the 



L 


mill 


- 
















■ 


- 




S 1 




D 1 


- 


3 P 




- S 






I 


: 


E i-o OH 




1 pa^^ 




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JV JV 




i; 


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V 




1 ^ 




" ^ 1 




K 


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1 


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I 


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B 


F 


[G. 1465. 




Fig. 1466. 




Fig. 1467. 


] 


^la. 1468. 



sleeping-room 8\ there should be one either against the stairs or the back 
wall. 

Figs. 1463 and 1464 are first-story plans of houses still more extensive! 
All of the above are adapted to the country, dependent on lights on all sides, 
and ample spaces. 

In the cities, houses are mostly confined to one form in their general out- 



I 



[=1 



IL_ 

D 





1 



i 



s 




Fig. 1469. 



Fig. 1470. 



Fig. 1471. 



Fig. 1472. 



line — a rectangle. Figs. 1465 and 1469 may be taken as the usual type of 
New York city houses. Figs. 1465, 1466, and 1467 are the basement, first and 
second floor plans of a three-rooms-deep, high-stoop house as the first floor is 
reached by an outside flight of steps about 6 feet high. There is usually a 
cellar beneath the basement, but in some cases there are front vaults, entered 
beneath the steps to the front door ; the entrance to the basement itself is also 



ARCHITECTUHAL CONSTRUCTION. 



697 




FIR5T 5TDRY 



Fig. 1473. 



Fig. 1474. 



598 



ARCHITECTURAL CONSTRUCTION. 




Fig. 1475. 



Fig. 1476. 



ARCHITECTURAL CONSTRUCTION. 599 

beneath the steps. The front room of the basement may be used as an eating- 
room, for the servants' sleeping-room, billiards, or library. The usual dining- 
room is on the first floor, a dumb-waiter being placed in the butler's pantry, ^;, 
for convenience in transporting dishes to and from the kitchen. The objec- 
tion to three-rooms-deep houses is that the central room is too dark, being 
lighted by sash folding-doors between that and the front or rear rooms, or both. 
Fig. 1468 is a modification to avoid this objection, the dining-room, or tea- 
room, as it is generally called, being built as an L, so that there is at least one 
window in the central room opening directly outdoors. This was an old 
fashion here, and has lately been revived. 

Figs. 1469 to 1470 are plans of the several floors of an English-basement 
house, so called, distinguished from the former in that the principal floor is up 
one flight of stairs. The first story or basement is but one or two steps above 
the street, and contains the dining-room, with its butler's pantry and dumb- 
waiter, a small sitting-room, with, in some cases, a small bedroom in the space 
in the rear of it. The kitchen is situated beneath the dining-room, in the sub- 
basement. The grade of the yard is in general some few steps above the floor 
of the kitchen. Vaults for coal and provisions are excavated either beneath 
the pavement in front or beneath the yard. The advantages of this form of 
house are the small reception-room on the first floor, which in small families 
and in the winter months is the most frequently occupied as a sitting-room of 
any in the house ; the spaciousness of its dining-room and parlours in propor- 
tion to the width of the house, which is often but 16 feet 8 inches in width, or 
three houses to two lots, and not infrequently of even a less width. The ob- 
jections to the house are the stairs, which it is necessary to traverse in passing 
from the dining-rooms or kitchen to the sleeping-rooms, but this objection 
would, of course, lie against any house of narrow dimensions, where floor-space 
is supplied by height. 

In New York, outside access to the kitchen is from the front, as there is no 
back street or alley. In Philadelphia, where the lots are deeper, and there is 
a street in the rear, the kitchen is usually in a rear L, on the level of the first 
floor, with the dining-room above it on a mezzanine or half-story between the 
first and second floors. 

Figs. 1477 to 1483 are plans and elevations of a country-house in the Flem- 
ish or Queen Anne style. 

Fig. 1486 is the front elevation of a high-stoop house, in New York city, of 
brown stone, a comparatively old but still popular design. 

To accommodate the poor and people of small means in all cities, it was, 
and to some extent still is, the custom to divide houses which were intended 
for single families into small apartments for many, or to let rooms singly for this 
purpose. This was found to be objectionable to both occupants and owners, 
and houses have been constructed especially for parties of limited means. 
Virtually, they are now nearly all apartment-houses, each family having distinct 
rooms or suites to itself. But the term tenement-houses is applied to the cheaper 
kind of apartments, occupied by the poorer class, and situated in the least ex- 
pensive localities. The common form of tenement-house consists of two build- 
ings, one in the front and one in the rear of the lot, with an outer or air space 
between. A hall leads through the first story to the central area ; on each side 



600 



ARCHITECTURAL CONSTRUCTION. 



PLAN OF FIEST FLOOE. 
B 




ARCHITECTURAL CONSTRUCTION. 



601 



PLAN OF SECOND FLOOR. 




Fig. 1478. 



602 



ARCHITECTURAL' CONSTRUCTION. 



FEAMING-PLAN OF FIRST FLOOE. 




Fig. 1479.- 



ARCHITECTURAL CONSTRUCTION. 



603 




604 ARCHITECTURAL CONSTRUCTION. 

ELEVATION OF CHIMNEY OF DINING-EOOM. SECTION. 




Fig. 1481. 



Fig. 1482. 



I...I I 



J I I Feet 



ARCHITECTURAL CONSTRUCTION. 



605 




606 



ARCHITECTURAL CONSTRUCTION. 



ENGLISH EUEAL STYLE. 




Fig. 1484. 



ARCHITECTURAL CONSTRUCTION. 
ITALIAN VILLA, BY UPJOHN. 



607 




Fig. 1485. 



608 



ARCHITECTURAL CONSTRUCTION. 




Fig. 1486. 



ARCHITECTURAL CONSTRUCTION. 



609 



of this hall there may be small stores and apartments. Stairs from the hall 
lead to the apartments above. The 25 feet is divided in two, making two liv- 
ing-rooms on each front ; these are the only rooms opening directly into the 
outer air. Bedrooms are attached to each of these rooms, but take their light 
and air from the staircases, or small light-wells. In the rear houses there are 
two tenements to each story ; they take their light and air from the central and 
back areas. AVater-closets are in the central area. These tenements are 
mostly occupied by work-people, largely of foreign birth, dependent directly 
on small wages. There is a large class, of limited means, to whom these 
accommodations are insufficient; parties who can not well afford an entire 
house, but still wish for the privacy of one. Within the limits of a lot 
25' X 100' it has been found difficult to secure all the necessaries of light and 
ventilation, with the number of suites of apartments adapted to the means of 
the occupants, and satisfactory as an investment to the owners. Fig. 1487 is 
a plan of one of the best of these designs. It provides for four families 




Fig. 1487. 



on each story, although it will be observed by the plan of the stairs that 
the front and rear tenements are not on the same level ; they are separated 
by the half flight of stairs. By means of the cross-shaped court between the 
adjacent houses, every room, including the bath-room, has a window to the 
open air. This is the most commendable feature of the plan. It is remark- 
able, also, however, for providing more conveniences than have been customary 
in dwellings of this class, as, for instance, a small bath-tub as well as a water- 
closet for each family, and two wash-tubs as well as a sink ; also, a dumb- 
waiter (common to two families on each level) for bringing up fuel, provisions, 
etc. The large rooms have recesses for beds, which provide for an extra bed- 
room, while detracting but little from their value as parlors, as the recess may 
be curtained off in the daytime, or the bed turned up. The dimensions of the 
rooms, as marked on the plans, are the average length and breadth. These 
suites are much too restricted for a very large class, but apartment-houses some- 
what on this model are constructed in desirable localities, where the accom- 
modations and conveniences are equal to those of any private house, and not 
bounded by the limits of a single lot nor single story, many unsurpassed in 
luxury of finish and appointments. 

The larger apartment-houses are often designated as flats. The suites should 
be supplied with water, gas, and steam heat ; should be entirely distinct in their 
Tentilation and protected against fire ; some are now lighted by electric light. 
40 



610 



ARCHITECTURAL CONSTRUCTION. 



Fig. 1488 is an illustration of a " flat " situated on the corner of a street, 
and one suite takes its light exteriorly from the streets while the other depends 




Fig. 1488, 



in a measure on the court, with a ventilating passage from the rear beneath 
the fire-escape grating. Kitchens, in the figure, are attached to the suites ; 
the laundries are in the upper story. Many flats are without kitchens or laun- 
dries, and meals are furnished either from without or from restaurants in the 
building. It then corresponds very nearly to a hotel without transient cus- 



ARCHITECTURAL CONSTRUCTION. 



611 




Sidewalk. ^ 



Fig. 1489. 



Fig. 1490. 



612 



ARCHITECTURAL CONSTRUCTION. 



torn, with ample and separate suites. It would seem that hoarding-houses 
might be built on such plans — less extensive in their arrangements and adapted 
to small families of moderate means ; but boarding-houses are almost invariably 
private houses, but little modified for the more public use. 

Stores and Warehouses. — Fig. 1489 is the front elevation of a common type 
of New York city store, occupying a single lot of 25 feet in width. It will be 
observed that there are two stories beneath the level of the sidewalk, the base- 
ment and sub-cellar, and this construction still obtains largely ; but deep base- 
ments only are considei'ed preferable by some, with extra stories at the top 
rather than in the cellar. Fig. 1490 is a section of the front wall, showing 
heights of stories, which of late years have been increased over former practice, 
say to 16' for the first story, 13' for the second, and 12' and 11' for others, the 
light for the interior being taken almost universally from the front and rear, 
and sky lights done awaj with. 

Fig. 1491 is a plan of the first-story floor, with basement in front dotted 
in ; five feet of this space, or that usually allotted for areas, is covered with 




Fig. 1491. 



illuminating tile (Fig. 1492), that is, small glass lenses, set in iron frames, the 
whote water-tight ; or lenses on a skeleton frame of cast-iron set in Portland 
cement. In the extreme rear there is a small area. A, open to the air, of about 





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J^^^^^^^P^^^®®^^P^^^^^^^S^^6^^^^^M^^HfflBl 




l^^^®l®^^P$^®^^^^®^^P^^P^^B^w^^8^^teM®l 




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IP mmimmmmmimmmmmmmmmmm^^mm^mmm^mm 




m0im'^^Om9M&&MQQ<B^'MM&&O^&&^^awm 







Fig. 1492. 



5 feet, for light and air to the basement and cellar. The offices of the first 
story are situated at B, over which there is usually a curved lean-to of illumi- 
nating tile. The main wall above this story is on the line a Z*— plain brick— 
with iron shutters. When shutters are used to close the first-story front they 
are mostly rolling shutters of sheet-steel. The hoist-way to the upper stories 
is at c, a position somewhat objectionable as interfering with the use of the 



ARCHITECTURAL CONSTRUCTION 



613 



!liiiiliii!i!iiiii!i!i!1il^^^^ 




■''■'''''1ii|l|liii|jlli!|'ii-i|i|i;||l'r 



•ID! II"' 



614 



ARCHITECTURAL CONSTRUCTION. 



stairs, when a common hoist- wheel is used ; but if it is a power-hoist, then it is 
put close to the wall, guarded by a rail, with a passage round to the stairs. In 
50-feet-front stores the hoist is put on the opposite corner from the stairs, as 



i 



L 




pq~; • • I — 



Fig. 1493. 

at D, but this cuts off considerable light from the first-story front. In some 
the arrangement is as in Fig. 1493, in which the hoists c c are in the rear of 
the stairs. The arrangement for ofiflces in the rear of the first story is in a T, 
with spaces at the sides for the ventilation and light of the lower stories. It 
will be observed that there is no central door, as in the elevation (Fig. 1489), 
which last most usually obtains for wholesale stores. Formerly illuminating 
tile on iron quadrant frames over rear extensions of stores were common, but 
were objectionable from the inside condensation and drip. It is very common 
to leave open areas at the sides, inclosed by brick walls (Fig. 1493), with the 
windows protected by iron shutters. For deep stores the area should be at one 
side and central, say from 30 to 40 feet long and 6 feet wide, which may be 
covered in the first story with glass. If this recess is on the side occupied by 
the staircases, it does not detract from the inside finish of the stores. 

Hoists now in large stores are power-hoists — that is, worked by either 
steam, water, or electricity. The platform of a freight-hoist is usually 5 feet 
square ; for passenger-hoists, in wholesale stores, somewhat less — 4' X 5'. For 
the raising of goods from the basement or sub-cellar, to the sidewalk there is 
a hatch in the front light platform, opposite some window, and the space is 
like that of freight-hoists, 5' X 5' ; these may be power or hand hoists. For 
the delivery of goods into these lower stories there is often a slide or incline, 
iron-plated, ending at the bottom with an easy curve to the horizontal, down 
which boxes and bales are slid. 

Fig. 1494 is a perspective view of a city machine and blacksmith shop. It 
was built for a purpose, and to express the purpose constructionally and eco- 
nomically. As regards convenience and strength, it was found to be, on occu- 
pation, all that could be wished. Posts, lintels, window-frames, sashes, and 
ornamental letters were of iron, and painted a very deep green; the structure 
was of brick, with sills and bands of rubbed Ulster bluestone, roof of Welsh 



ARCHITECTURAL CONSTRUCTION. 



615 




Fig. 1495 



TTni^c 



I I I I I 



I I I I i I 



w£-' 




Fig. 1496. 



616 



ARCHITECTURAL CONSTRUCTION. 



slate. The chimneys shown in front, although not dummies, were never used. 
Power and heat were supplied by steam-boilers in the front vault, with a long 
flue, slightly rising, leading to a chimney at the centre of the side blank wall. 
On each side of this chimney, and separated from it by a thin ivitJi^ there were 
flues. Forges occupied all the exterior walls of the basement, front and side 
areas, and the draught was upward and then down into the nearly horizontal 
flues connected with the central flues, and the draught was invariably good. 
Care was taken that all angles, horizontal and vertical, were rounded. 

School- Houses. — Figs. 1495 and 1496 are an elevation and plan of a country 
district school-house, with seats for forty-eight scholars. There are two en- 
trances, one for each sex, with ample accommodations of entry or lobby-room 
for the hanging up of hats, bonnets, and cloaks. A side door leads from each 
entry into distinct yards, and an inside door opens into the school-room. The 
desk, T, of the teacher, is central between the doors, on a platform, P, raised 
some 6" or 8" above the floor. In the rear of the teacher's desk is a closet or 
small room, for the use of the teacher. The seats are arranged two to each 
desk, with two alleys of 18" and a central one of 2'. The passages around the 
room are 3'. 

Figs. 1497 and 1498 are the elevation in perspective and plan of an English 
country school-house, introduced as suggestive — whether a one-story plan might 
not be better suited, and of more beautiful effect in our own country towns, 
where there is plenty of ground space, than the imitation of city edifices of 
many stories. 

On the Requirements of a School-House. — Every scholar should have room 
enough to sit at ease, his seat should be of easy access, so that he may go to and 
fro, or be approached by the teacher without disturbing any one else. The 
seat and desk should be properly proportioned to each other and to the size of 
the scholar for whom it is intended, who should not sit in a cross-light, the 
light should come from a single direction as near as possible over the left shoul- 
der. The seats, as furnished by the different makers of school furniture, vary 
from 9" to 14" in height ; and the benches from 17" to 28" ; measuring on the 
side next the scholar. The average width of the desk is about 18", and it is 
formed with a slope of from IJ" to 2i", with a small 
horizontal piece of from 2" to 3" at top. There is a 
shelf beneath for books, but it should not come within 
about 3" of the front. The width of the seat varies 
from 10" to 14", with a sloping back, like that of a 
chair ; it should, in fact, be a comfortable chair. In 
the figure, two scholars occupy one bench. Fig. 1499 
represents another arrangement, in which each scholar 
has a distinct bench ; this is more desirable, but not 
quite so economical in room. In primary schools desks 
are not necessary; and in many of the intermediate 
Fig. 1499. schools the Seat of one bench is formed against the 

back of the next bench ; but seats distinct are preferable. 
The teacher's seat is invariably on a raised platform, and had better be against 
a dead wall than where there are windows. Blackboards and maps should be 
placed along the walls. Care should be taken in the warming and ventilation ; 



[ZPCPD°0 



& 






ARCHITECTURAL CONSTRUCTION. 



01 r 



warm air should be introduced in proportion to the number of scholars, and 
ventiducts should be formed to carry off the impure air. 




Fig. 1498. 



In cities and large towns it is almost indispensable to build school-houses 
many stories in height, dividing the rooms in each story according to the neces- 



618 



ARCHITECTURAL CONSTRUCTION. 




ARCHITECTURAL CONSTRUCTION. 



619 



sities of their occupancy. The management of schools differs in different locali- 
ties. This will be seen in the illustrations given below, showing the arrange- 
ments of school-houses in the city of New York and of Cleveland, Ohio. 

Fig. 1500 is an elevation in perspective of one of the largest of the New 
York city schools, showing the yards around it. Fig. 1501 is the plan of the 




Fig. 1501. 



grammar-department floors of this house ; and Fig. 1502 the plan of the same 
floors of another house of a different outline. 

Figs. 1503 to 1506 are plans of school-houses, built at Cleveland, Ohio, a 
type inaugurated under the supervision of the then superintendent, Mr. A. J. 
Rickoff. Figs. 1503, 1504, and 1505 are plans of the High-School house. Fig. 
1503 is the plan of the third story ; Figs. 1504 and 1505 of those portions of 
the second and first stories which differ from that of the third. There is a rear 
vestibule in the first story to correspond with the one in front, shown in the 
figure. In the whole building there are 14 session-rooms, each 37' X 30' X 
16' ; each having its connecting cloak-room ; one general assembly-room, 94' X 
o6' X 38' high, with a seating capacity for at least 1,000 persons ; one lecture- 
room, with seats for 100, with an apparatus-room ; one room for drawing, 30' x 
55', with a room for models, drawing-boards, etc. ; two rooms for the principal 
and reception-room ; five rooms for library and recitation-rooms. 



620 



ARCHITECTURAL CONSTRUCTION. 



Fig. 1506, a plan of one half of one story of the Walton Avenue School, on 
a larger scale, explains more fully the arrangement of seats and the ventilation. 
Four ventilating educts, of 8 square feet of section each, may be heated to any 
required temperature for the purposes of circulation by four upright %" steam- 
pipes ; six ducts of 1 square foot section lead from different points in the floor 



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B 



Fig. 1502. 



of each session-room, (as shown in dotted lines in the figure) into the ventilating 
educts. There are besides other registers opening directly into the educts. 
The building is heated by steam coils or radiators placed under the windows of 
the rooms, with provision for the admission of fresh air under the stone sills 
behind the radiators. The main light of every room is admitted at the left 
hand of the pupil, so that in writing the shadow of the. hand does not fall on 
the space to be written on. There are none of the cross-lights that so seriously 
impair the vision. The wall facing the pupil and behind the teacher is un- 
broken by windows, affording large and convenient spaces for blackboards. 

Churches, Theatres, Lecture- Rooms, Music and Legislative Halls. — To the 
proper construction of rooms or edifices adapted for these purposes some knowl- 
edge of the general principles of acoustics, and their practical application, is 
necessary. In the case of lecture-rooms and churches, the positions of the 
speaker and the audience are fixed ; in theatres, one portion of the inclosed 
space is devoted to numerous speakers and the other to the audience; in legis- 
lative halls, the speakers are scattered over the greater part of the space, and 
also form the audience. 



ARCHITECTURAL CONSTRUCTION. 



621 






ARCHITECTURAL CONSTRUCTION. 




Mil I I I I I Fept 



ARCHITECTURAL CONSTRUCTION. 628 

The transmission of sound is by vibrations, illustrated by the waves formed 
by a stone thrown into still water ; but direction may be given to sound, so that 
the transmission is not equally strong in every direction ; thus, Saunders found 
that a person reading at the centre of a circle of 100 

feet in diameter, in an open meadow, was heard most dis- ,.- " -^.^ 

tinctly in front, not as well at the sides, but scarcely at ■'''^^^" — '^\ — ~"^0\ 
all behind. Fig. 1507 shows the extreme distance every /^..^j.... J 75-™* 
way at which the voice could be distinctly heard : 92 feet ^i^ j 

in front, 75 feet on each side, and 31 feet in the rear. \ ^ / 

The waves of sound are subject to the same laws as those \ ■ / 

of light, the angles of reflection are equal to those of in- ^^.^1 ^^ 
cidence ; therefore, in every inclosed space there are re- 
fleeted sounds, more or less distinct, according to the po- 
sition of the hearer, and to the form and condition of the surfaces against 
which the waves of sound impinge. Thus, of all the sounds entering a para- 
bolic sphere, the reflected sounds are collected at the focus. Solid bodies 
reflect sound, but draperies absorb it. As, in all rooms, the audience can never 
be concentrated at focal points, nor is it possible in any construction to make 
calculation for all positions, it is in general best to depend on nothing but the 
direct force of the voice, and not to construct larger than can be heard directly 
without aid from reflected sounds. 

There is great difference in the strength of voice of different speakers ; the 
limits as given in the figure are for ordinary reading in an open space. In in- 
closed spaces, owing to the reflected sounds or some other cause, there are cer- 
tain pitches or keys peculiar to every room, and to speak with ease the speaker 
must adapt his tone to those keys. The larger the room, the slower and more 
distinct should be the articulation. 

It has been observed that the direction of the sound influences the extent to 
which it may be heard. The direction of the currents of air through which 
the sound passes affects the transmission of the sound, and this may be made 
useful when the rooms are heated by hot air, by introducing the air near the 
speaker and placing the ventilators or educts at the outside of the rooms, and 
by placing their apertures rather nearer the bottom of the room than at the 
top. It would seem much better and easier to make a current of air a vehicle 
of sound rather than depend on reflection. 

In the "Baltimore Academy of Music," designed by Mr. J. Crawford Neil- 
son, architect, the ventilation was arranged to obstruct the formation of air- 
currents of unequal density. The whole supply of fresh air is admitted at the 
back of the stage, is there warmed, crosses the stage horizontally, and passes 
through the proscenium and then, somewhat diagonally toward the roof, across 
the auditorium in one grand volume and with gentle motion so as to almost 
entirely prevent the formation of minor air- currents. It is exhausted partly 
by an outlet in the roof and partly by numerous registers in the ceilings of 
the galleries. From this central outlet and from the large flues of the reg- 
isters the air passes into the ventilating-tower over the great chandelier, which 
supplies, in its heat, a part of the motive power of the circulation. It is 
further expelled from the tower by means of large valves, offering no obstacle 
to the egress of air^ but completely cutting of its entrance. 



624 



ARCHITECTURAL CONSTRUCTION. 





Fig. 1508. 



Fig. 1509. 



The direction of the air-currents within the house was determined by thistle 
balls, and the quantity, as found by anemometers, was about 15,000 cubic feet 
per minute. This amount, sufficient to ventilate the house, is that required to 
impress the proper movement on its atmosphere. It is amply sufficient for 
ventilation, as is shown by the fact that the thermometers of the upper circle do 
not vary perceptibly from those of the orchestra circle. The seating capacity 
of the house is about sixteen hundred persons. The acoustics are satisfactory. 
071 the Space occupied hy Seats in general. — A convenient arm-chair occu- 
pies about 20" X 20", the seat itself being about 18" in depth, and the slope of 

the back 2" ; 18" more affords am- 
ple space for passage in front of 
the sitter. In churches the seats 
are arranged by pews or stalls, the 
width of each pew in general being 
about 2' 10". In the arrangement 
of theatre seats the bottom turns 
up (Figs. 1508 and 1509), and 29" 
only is allowed for both seat and 
passage-way, and 18" for the width 
of seat, which may be taken as the 
average allowance in width to each 
sitter in comfortable public rooms. 
In lecture-rooms, benches and set- 
tees are often used, the space there occupied by seat and passage being about 
2' 6". 

In the earlier churches, ceremonies and rites formed a very large part of the 
worship, the sight was appealed to rather than the hearing, and for this pur- 
pose churches were constructed of immense size, and with all the appliances 
of ornament and construction, with pillars, vaults, groins, and traceried win- 
dows. In the churches of this country, the great controlling principle in the 
construction of a church is its adaptation to the comfortable hearing and seeing 
the preacher. In this view alone, the church is but a lecture-room ; the ceiling 
should be low, and pillars and transoms should be little used ; but since even 
the character of the building may tend to devotional feelings in the audience, 
and since certain styles and forms of architecture have long been used for 
church edifices, it has been the custom to follow these time-honoured examples, 
adapting them to modern requirements of church worship, with adequate means 
of heating and ventilation. 

Fig. 1511 is a plan of an ancient basilicon or Romanesque church. Fig. 
1510 is a sectional elevation of the same. Fig. 1512 is a plan of a Gothic 
church, in which C is the chancel, usually at the eastern extremity, T T the 
transept, and N the nave. In general elevation the Gothic and Romanesque 
agree : a high central nave and low side aisles. In the later Romanesque the 
transept is also added. 

The basilicas aggregated within themselves all the offices of the Romish 
church. The circular end or apse, with the raised platform, or dais, in front 
appropriated to the altar ; in the rear the confessional and the sacristy ; beneath 
was the crypt, where were placed the bodies of the saints and martyrs, and pul- 



ARCHITECTURAL CONSTRUCTION. 



625 



pits were placed in the nave, from which the services were said or sung by the 
inferior order of clergy. 

The plan (Fig. 1512) is that of the original Latin cross, the eastern limb 
or chancel being the shortest, and the nave the longest. Sometimes the eastern 




ik. 



- .77 



m 



Fig. 1510. 



Fuj. 1511. 



N 



+^ -H- 

FiG. 1512. 



limb was made equal to that of the transept, sometimes even longer, but never 
to exceed that of the nave. In the Greek cross all the limbs are equal. In 
most of the French Gothic churches the eastern end is made semicircular, often 
inclosed by three or more apsidal chapels, that is, semi-cylinders, surmounted 
by semi-domes. 

The Byzantine church consisted internally of a large square or rectan- 
gular chamber, surmounted in the centre by a dome, which rested upon 
massive piers ; an apse was formed at the eastern end. Circular churches 
were built in the earlier ages for baptisteries, and for the tombs of saints and 
emperors. 

The Greek, Eoman, and English churches conform in their cathedrals and 
larger edifices nearly to the Eomanesque or Gothic models. But as the general 
requirements for church services now are those of a lecture-room, modern 
churches are constructed adapted to these purposes, and, in cities, to the size 
and form of the lots, with some ecclesiastical accessories of towers and steeples, 
windows and doors and interior finish. 

Fig. 1513 is the plan of the English church at The Hague. 




scAi.e c 



Fig. 1513. 



Fig 1514 is the plan of a Wesleyan chapel in London ; the requirements of 
the service have been well adapted to the necessities of the lot. 
41 



626 



ARCHITECTURAL CONSTRUCTION. 



Fig. 1515 is the cross-section of a common form of small country church, 
with nave n, aisles a a, and clear-story c. The effect, both inside and out, is 




so 60 ■;srr 



Fig. 1514. 



good, but there are objections to large or masonry-columns, which cut off the 
view of the desk and the altar from many sitters, and to the windows of the 




Fig. 1515. 



ARCHITECTURAL CONSTRUCTION. 



627 



clear-story, which in winter act as coolers to the air descending in draughts 
upon the heads of the congregation beneath them. Neither columns nor clear- 
story are constructively necessa- 
ry ; the span can readily be met 
by a single roof, and suflQcient 
light can be obtained from the 
sides. 

Figs. 1516, 1517, and 1518 
are examples of open-timbered 
Gothic roofs of churches. 

The technical names (Fig. 
1516) are : 1, Principals ; 2, Pur- 
lines; 3, Collars; 4, Braces; 5, 
Wall-pieces ; 6, Wall-plates ; 7, 
Struts ; 8, Eaf ters. 4 and 5 are 
shown in section. 

The length of pews is vari- 
ous, being of two sizes, adapted 
to either small or large families, 
say from 7' 6" to 12' 6", 18" be- 
ing allowed for each sitter. In 
arrangement it is always consid- 
ered desirable that there should 
be a central aisle, and if but 
four rows of pews (often of two 
sizes in the same church), an 
aisle against each wall ; if six 
rows, one row on each side will 
be wall-pews. Formerly it was 
the universal practice to con- 
struct pews with doors, but of 
late it is more customary to omit 
the doors, making the pews open 
stalls. 

Few churches are now with- 
out an organ ; its dimensions 
should of course depend on the 
size of the church. In form it 
may be adapted somewhat to the 
place which may be appropriated 
to it — either in a gallery over 
the main entrance or above the 
pulpit or at the side of the chan- 
cel, as in Fig. 1513. Sometimes 
there are two, one at each ex- 
tremity of the church, one organist playing on both by electric connection. In 
general, it is oblong in form, the longer side being with the keys. The di- 
mensions suited to a medium-sized church are about 9' X 15', and 12' in height. 




Fig. 1517. 




028 ARCHITECTURAL CONSTRUCTION. 

The vestry-room, if used for the purposes of its nieetings, should be adapted 
in size to the purpose ; but if only for a withdrawing or robing room for the 
clergyman, it may be of very small dimensions, and should be accessible from 
without. The Sunday-school room, in general, requires in plan about half 
the area of the church. From motives of economy it is usually placed in the 
basement of the church ; but, in the country especially, it is better that it 
should be a separate building, and form one of the group of church, parson- 
age, and Sunday-school house. 

In elevation, city churches are generally Romanesque and Gothic, occasion- 
ally Byzantine. The Greek have no tower, but often a spire above the portico ; 
the Romanesque and Gothic generally one tower, over the central door of en- 
trance, or at one corner ; sometimes two, one at each side of the principal door, 
almost invariably surmounted by spires, high and tapering, usually of wood, but 
in some instances of stone. 

Theatres. — In theatres and opera-houses it is not only necessary that the 
audience should have a good position for hearing and seeing the performance 
upon the stage, but also to see each other. The most approved form, now, for 
the body of a dramatic theatre is a circular plan, the opening for the stage 
occupying from one fourth to one fifth of the circumference, the sides of the 
proscenium being short tangents ; but for a lyric theatre, where music only is 
performed, and where, consequently, hearing is easier, the curve is elongated 
into an ellipse, with its major axis toward the stage. 

In the general position of the stage, proscenium, orchestra, orchestra seats, 
parquette, and boxes, but one plan is followed. The line of the front of the 
stage, at the footlights, is generally slightly curved, with a sweep, say, equal to 
the depth of the stage, and the orchestra and parquette seats are arranged in 
circles concentric with it : of the space occupied by seats we have already 
spoken. The entrance to the parquette may be through the boxes, near the 
proscenium, and centrally, but better at the sides, dividing the boxes into three 
equal benches ; the seats in the boxes are usually concentric with the walls, and 
more roomy than those of the parquette. The orchestra seats are of a height 
to bring the shoulders of the sitter level with the floor of the stage, and the 
floor of the parquette rises to the^outside, 1 in 15 to 18. The floor of the first 
row of boxes is some 2 to 3 feet above the floor of the parquette at the front 
centre, and rises, by steps at each row, some 4 inches ; in the next tier of boxes 
the steps are considerably more in height, and so on in the boxes above. In 
general, three rows of boxes are all that is necessary ; in front, above the sec- 
ond, the view of the stage is almost a bird's-eye view. The floor of the stage 
descends to the footlights at the rate of about 1 in 50. In large theatres it is 
of the utmost importance that all the lobbies or entries should be spacious, and 
the means of exit numerous and ample — the staircases broad, in short flights 
and square landings, and not circular, as, in case of fright, the pressure of 
persons behind may precipitate those in front the whole length of the flight. 
Ladies' drawing-rooms should be placed convenient to the lobbies, of a size 
adapted to that of the theatre, also rooms for the reception of gentlemen's 
canes and umbrellas, both with usual water arrangements. The box-office 
should be near the entrance and arranged to interfere as little as possible with 
the approach to the doors of the house. At the entrance there should be a 



ARCHITECTURAL CONSTRUCTION. 



629 




Fig. 1519. 



PLAN. 



very spacious lobby, or hall, so that the audience may wait sheltered from the 
weather ; if possible, there should be a long portico over the sidewalk, to cover 
the approach to the carriages. Only single 
entrances are necessary to distinct parts of 
the house, but the greater the number of, 
and the more ample places for exit at the 
conclusion of the piece, or for the contin- 
gency of fire, the better. 

Fig. 1519 is a plan suggested by Fer- 
guson of keeping the centre of the bal- 
conies perpendicular over one another, and 
then, by throwing back the sides of each 
balcony till the last is a semicircle, the 
whole audience would sit more directly 
facing the stage, would look at it at a bet- 
ter angle, and the volume of sound be con- 
siderably increased by its freer expansion 
immediately on leaving the stage. 

Figs. 1520 and 1521 are a plan and section of Wagner's theatre. 
In cities, the auditoria of dramatic theatres conforming to the shape of the 
lots are rectangular in their outline, and seldom exceed a seating capacity of 

1,500. Lyric theatres are 
much larger, both in seat- 
ing and scenic capacity. 
Lecture-rooms are usually 
arranged with the au- 
dience-floor flat, room rec- 
tangular, with reading-desk 
or platform raised, and 
with or without galleries. 
The same form usually ob- 
tains for music-halls, only 
they are much greater in 
extent, the first being capa- 
ble of containing from 500 
to 1,000 persons ; whereas 
some music-halls will con- 
tain 2,500, and Ferguson 
thinks that a music-hall 
might be arranged so that 
even 10,000 might hear as 
well as in those of present 
construction. The lecture 
and music halls are seldom 
devoted to a single purpose, 
but are used for political 
meetings, for fairs, and dances, and the constructon must be such as to serve 
these other purposes. 




Fig. 1520. 



SECTION. 



4 



ii 



ORCHESTRA 



^^-^ 



> 



Fig. 1521. 



630 



ARCHITECTURAL CONSTRUCTION. 



COMPARATIVE TABLE OP THE DIMENSIONS OF A FEW THEATRES. 



Name and Location. 



Alexandre, St. Petersburg. 

, Berlin 

La Scala, Milan 

San Carlo, Naples 



Grand Theatre, Bordeaux 

Salle Lepelletier, Paris 

Covent G-arden, London 

Drnry Lane, London 

Boston, Boston 

Academy of Music, New York. . . 
Grand Opera-House, New York. . 
Opera-House, Philadelphia 



distance, in feet. 






m 



65 
62 

77 
■77 
46 
67 
66* 
64* 
53 
74 
54 
61 



0)73 



11 

16 
18 
18 
10 
9 



18 
13 
Si 
17 



a; 73 

CO 



84 
76 
78 
74 
69 
82 
55 



71 
63i 

72 



58 
51 
71 
74 
47 
66 
51 
56 

62 

48 
66 



56 
41 
49 
52 
37 
43 
32 
32 
46 
48 
44 
48 



■B a 



75 
92 
86 
66 
80 
78 
86 
48 
87 
83 
76 
90 



height, in feet. 



So 



53 
43 

60 

81 

50 

52 

54 

60 

55^ 

74 

52 

m 



58 
47 
64 
83 
57 
66 



58 

67 

74 



* These dimensions include the distance between the footlights and curtain. 

Legislative Halls. — Although much has been written about their construc- 
tion in relation to acoustic principles, there is great disagreement in practical 
examples, and in the deductions of scientific men. The Chamber of French 
Deputies was constructed, after a report of most celebrated architects, in a 
semicircular form, surmounted by a flat dome, but as the member invariably 
addresses the house from the tribune, at the centre, in its requirements it is but 
a lecture-room. Mr. Mills, architect, of Philadelphia, recommends for legisla- 
tive or forensic debate a room circular in its plan, with a very slightly concave 
ceiling. Dr. Reid, on the contrary, in reference to the Houses of Parliament, 
gave preference to the square form, with a low, arched ceiling. The Hall of 
Representatives at Washington is 139 feet long by 93 feet wide, and about 36 
feet high, with a spacious retiring gallery on three sides, and a reporters' gal- 
lery behind the Speaker's chair. The members' desks are arranged in a semi- 
circular form. The ceiling is flat, with deep-sunk panels, openings for ventila- 
tion, and glazed apertures for the admission of light. The ventilation is 
intended, in a measure, to assist the phonetic capacity of the hall, the air 
being forced in at the ceiling and drawn out at the bottom. 

In reviewing the general principles of acoustics, it will be found that those 
rooms are the best for hearing in which the sound arrives directly to the ear, 
without reflection ; that the sides of the room should neither be reflectors nor 
sounding-boards, and that surfaces absorbing sound are less injurious than 
those that reflect. Slight projections, such as ornaments of the cornices and 
shallow pilasters, tend to destroy sound, but deep alcoves and recessed rooms 
produce echoes. Let the ceiling be as low as possible, and slightly arched or 
domed ; all large external openings should be closed ; as M. Meynedier ex- 
presses it, in his description of an opera-house, " Let the hall devour the sound ; 
as it is born there, let it die there." 

Hospitals. — In large cities, hospitals, by necessity, are confined to narrow 
spaces, but they should be placed, if possible, on river fronts or on open parks, 



ARCHITECTURAL CONSTRUCTION. 631 

to secure as much open-air ventilation as possible. They are usually many 
stories in height, with large wards one above the other. Sir J. T. Simpson 
alleges a very high rate of mortality in hospitals after surgical operations as 
compared with the mortality after the same operations when performed at the 
homes of the patients, and asserts that the mortality after operations performed 
in hospitals containing more than 300 beds is in excess of that in hospitals con- 
taining less ; that great hospitals are great evils in exact proportion to their 
magnitude, and suggests the construction of smaller hospitals. 

Figs. 1522 and 1523 are an elevation and plan of an English country hos- 
pital. 

Stables.^Undev this general name are included the barn, or the receptacle 
of hay and fodder, the carriage-house, and the stable proper, or lodging-house 
for horses and cows. The first two may be included under one roof, the car- 
riages on the first floor, and hay in the loft ; but the lodging-place should be 
distinct, in a wing attached to the barn, that the odours from the animals may 
not impregnate their food, or the cloth- work of the carriages, or the ammonia 
tarnish their mountings. 

Hay in bulk, in the mow, occupies about 340 cubic feet per ton ; bales aver- 
age 2' 4" X 2' 6" X 4', and weigh from 220 to 320 pounds. The door-space for 
a load of hay in the bulk should be from 12 to 13 feet high and 12 feet wide. 
The floor beneath the hay should be tight, so that dust and seed may not drop 
on the carriage. A door for carriages should be 10 feet 6 inches high by 9 feet 
wide. 

The horse is to be treated with greater care than any other domestic animal. 
His stable is to be carefully ventilated, that he may have fresh air without 
being subject to cross-draughts. Preferably the floor should be on the ground, 
that there may be no cold from beneath. He should stand as near as possible 
level; and for this purpose a grated removable floor, with small interstices, 
should be laid over a concrete bottom, with a drip toward the rear of the stall, 
and the urine should be collected in a drain and discharged into a trapped 
manure- tank outside the stable. In Fig. 1524 the pitch of bottom of stalls is 
to the centre and outward. The manure should never be deposited beneath 
the stable, but should be wheeled out and deposited in a manure-yard or tank 
daily. It is as essential that all excrements should be removed entirely from 
the stable as that the privy should be placed outside the house. 

The breadth of stalls should be from 4 feet 6 inches to 5 feet in the clear; 
the length, 7 feet 6 inches to 8 feet ; the rack and feed-box require two feet in 
addition, to which access is given in the best stables by a passage in front. 
Rack and feed-boxes are often made of iron, and the upper part of stalls fitted 
with wrought-iron guards. Box-stalls, in which horses are shut up but not 
tied in cases of sickness or foaling, are about 10 feet square. 

In large stables in cities the first floors are often occupied by the carriages, 
while the horse-stalls are in the basement or upper stories, with inclined ways 
of access. In the basement provision must be made for light and ventilation. 
In the upper stories these may be secured more readily, but the floors must be 
made tight and deafened, that the urine may not leak through, nor the cold 
come through from below to make too cool a bed for the horse. 

Fig. 1524 is an elevation in perspective of two first-class stalls, a box shown 



632 



ARCHITECTURAL CONSTRUCTION. 




Fig. 152;i. 
GROUND PLAN. 




Fig. 1523. 



scale: of FE.e.7 



ARCHITECTURAL CONSTRUCTION. 



633 



with the door open, and a single stall. The lower part of the inclosures is of 
plank, with wrought-iron guards and ramp above. The posts are of oak, and 




Fig. 1524. 

the hay -boxes or mangers of cast-iron ; the hay-rack in the box-stall is of 
wrought-iron. These are of common manufacture, and are of varied patterns ; 
but in the country they are usually made of wood, and connected with 
the stall. 

Fig. 1525 is the plan of a small country stable, showing the desirable pas- 




Shed 




Fig. 1525. 

sages around the stalls and exterior windows in front of each stall, that the 
horses may not only have light and air, but can see out. 

Cow-houses^ for cows giving milk, should be constructed with care for ven- 
tilation, light, and cleanliness. Other cattle are usually left out, with sheds 
under which they can go for shelter. For those housed, the spaces occupied 
should be about the same per head as the single horse-stall. The manger 
should be on the floor, 12" to 18" high, and about 18" wide. It is not usual to 



634 



ARCHITECTURAL CONSTRUCTION. 



have partitions, but there ought to be between every pair, reaching from the 
manger half-way to the gutter behind. The floor should be level, grated, with 
a drip beneath, and cleansed by washing out. The partition and 
mangers are often of cast-iron, and on sale, but for large stables and 
in the country they are commonly of wood. 

Greenhouses. — Fig. 1526 is the section of a greenhouse, 
with shelves for plants. The floor is of concrete and 
the walls are of masonry ; the northern exposure is 
a blank wall. 

Fig. 1527 is the details of windows. 
The sides are box-sash, hung with ^,i^^^ ^^^^^^^^\ 

weights {w, w, Fig. 1528). ^^^^^^ .^<:^^^^^V~ 

The lower roof sash is 
firmly fixed, but 
the upper 




Fia. 1526. 



Feet 



one can be slid down ; it is usually retained in place by a cord attached to the 
lower part of the sash, passing over a pulley on the upper bar of the frame, 
with the loose end within reach of the gardener, who can fasten it to a cleat. 

Ventilation and Warming. — The purposes of ventilation are not changes of 
air merely, but the removal of foul and vitiated air, and the substitution there- 
for of pure air ; and this air may be warm or cool according to the necessities 
of the season and personal requirements. Open space is not necessarily well 
ventilated ; there must be circulation, outward and inward — the latter from 



ARCHITECTURAL CONSTRUCTION. 



635 



purer sources than the former. With an equal discharge and sup- 
ply of pure air, the smaller the room, the more frequent the change 
of air, the better its distribution and the better the ventilation. 
But if the means of removal, supply, and distribution of 
air be proportioned to the size of the room, then 
the larger the room the better. Apertures ^^^^^<^ 

do not necessarily mean circulation 
flue may draw or it may not 
draw, it may be inert, or 
the air may come 




Fig. 1527. 



636 ARCHITECTURAL CONSTRUCTION. 

down ; a window may be open, with little or no inward or outward movement 
of air. In a house exposed to a fresh breeze, on the windward side there is an 
air-pressure, on the leeward side there is an eddy or vacuum. Air is forced in 
on the first through every crack of door and window — often down chimney- 
flues — and drawn out on the other side. This often happens even with -fires in 
the chimneys, and with insufficient heat in ventilating educts. If one will 
make an experiment in cold weather, when the windows are closed and there 
are fires in some rooms, he will often find that there is cold air coming down 
the unused flues, and will feel the cold current flowing down the stairs and 
along the floors to the fires. Architects have placed kitchens in the basement 
and in the attic, and the smell of cooking rises through the house from the 
former, and usually descends from the latter when the air is light and muggy. 

Every room should have its distinct flue ; if the current is not upward it 
will probably be downward, affording a fresh supply of air for ventilation if 
there is an escape elsewhere. A chimney-flue may be too large for the purposes 
of a fire; for most fires a fine 8" X 8" is amply sufficient, and will serve for 
ventilation in the common occupation of a house. If the throat of the chim- 
ney be made with rounded corners and a diverging sectional area, or a 
damper hinged at the bottom, for like effect, it should increase upward, and 
prevent back draught. 

Small circular flues of from 6" to 8" diameter, or of equivalent rectangular 
section, are now made in concrete or stoneware, which, as they are smoother 
and with less joints than brickwork, give greater velocities of current with less 
section, and, laid with care, changes in direction aiford but little obstruction.' 
In an ordinary chimney with natural draught the velocity of ascending current 
is about six feet per second. 

It is usual to depend largely on windows for ventilation, but the space on 
which they open may be too circumscribed to afford the requisite change of air, 
or the outer air itself may be too hot, or too cold, or too malarial or offensive, 
to make the change of air sanitary or pleasant. In tenement or apartment 
houses care should especially be taken that the inner windows on different flats 
open into as large air-shafts as possible, and that these shafts should have free 
opening to the outer air below and at the top, without skylights ; and that the 
floors should be tight, so that the smells may not pass from one flat to another. 
Nothing more surely shows faults in ventilation than the diffusion of kitchen 
smells or tobacco smoke. Distinct flues should be constructed for each room, 
extending independently well above the roof; and not into an attic with a 
ventilating louvre, as the air may ascend one flue and descend another, and 
not out of the louvre. Pipe flues may lead into a single stack if each branch is 
given the direction of the main current at its connection, without obstructing 
its flow, as in sewer branches. 

The quantity of air taken into and expired from the lungs by a single indi- 
vidual is quite small, probably about 14 cubic feet on an average per hour. 
The usual gas-burner delivers from 4 to 6 cubic feet per hour, under a pressure 
of 1" and 2" of water. It will be seen, therefore, how small apertures are neces- 
sary to supply the lungs of a person, if it could be provided directly to him and 
taken away without vitiating other air. But, in addition, air is vitiated by 
personal emanations and consumed by lights. These last can readily be ar- 



ARCHITECTURAL CONSTRUCTION. 637 

ranged in connection with flues, not only to remove all their products of com- 
bustion, but also improve the ventilation of the room. 

All systems of ventilation are based on the idea that so many individuals 
within a room and so many lights burning vitiate so much air, and that conse- 
quently a very large quantity of outer air must be introduced to reduce the 
percentage of vitiation, and generally with very little consideration as to the 
distribution of this air, although it is in every one's experience that the air in 
some portions may be fresh, in others stifling ; that in hospital wards there are 
often dead ends where the air does not circulate, and where patients do not as 
a rule recover. The system is to provide, somewhere in a room, air enough and 
trust to chance for its distribution. 

Some architects make the educts at the ceiling, some at the floor, some at 
both, with registers to control the openings. For sleeping apartments, if there 
is a fireplace this is all that will be necessary ; if the air goes up or comes down 
it does not make draughts about the heads of the occupants. 

To make flues draw, various forms of chimney-tops or cowls are adopted. 
The best and simplest are the Emerson (Fig. 1529) and a modification of the 
same (Fig. 1530) ; there are also various forms 
of self-acting flaps, turn-cowls, etc., the prin- 
ciple being to take advantage of the wind to 
make a draught. With the wind blowing 
across the top of a chimney, a bit of square- 
ended iron pipe extending above the chimney 
will answer as an expirator, but without a 

wind the draught must depend on circum- ^^^ ^.^g fig i530 

stances within the dwelling and artiflcial 

draught. When sufficient circulation can not be obtained from natural differ- 
ences of temperature in the atmosphere, or from winds, it is usual to have 
recourse to fans to force air into or draw it from a building, or by heat applied 
to the air in flues, ducts, or chambers in the hot-air furnaces. Both the air 
and the heat are necessary. 

" Xo systematic ventilation, however well devised and constructed, however 
extensive its supply of fresh air, however regularly or judiciously operated, can 
afford to dispense with the repeated displacement of the air of rooms and sub- 
stitution of entirely fresh air through open windows and doors, at times, during 
all seasons of the year" (Briggs). 

Methods of Heating. — The open fireplace grate heats by radiation, com- 
municating heat to objects, which by contact transfer it to the air. Persons 
coming in contact with rays are themselves heated, while the air around them 
is cool and invigorating for breathing ; the bright glow has a cheering and ani- 
mating effect upon the system, somewhat like that of sunlight. As a ventilator, 
an open fire is one of the most important, drawing in air not only for the sup- 
port of combustion, but also, by the heat of the fire and flue, making a very 
considerable current through the throat of the chimney above the fire. From 
this cause, although there is a constant change of air, yet there arises one great 
inconvenience of disagreeable draughts, especially along the floor, if the air- 
supply be drawn directly from the outer cold air; but in connection with prop- 
erly regulated furnaces or stoves, the open fireplace becomes the most perfect 





638 



ARCHITECTURAL CONSTRUCTION. 




Fig. 1531. 



means of heating and ventilation. As a heater merely, the open grate in very 
cold weather is not satisfactory ; its influence is only felt in its immediate 
vicinity, and but from 10 to 15 per cent, of the heat of the fuel is rendered 
available. 

Fig. 1531 represents an old form of open fire used in a tavern bar-room and 
ofiBce, which answered admirably for heating and ventilation, and admitted of 

access to many persons. It con- 
sisted of a circular grate at the 
level of the floor in the centre of 
the room. In the cellar beneath 
was an ash-pit, «, in brickwork, 
with an opening, o, to supply air 
for the combustion of the fuel. 
Above the grate was a counter- 
weighted sheet-iron hood, h, con- 
nected by a pipe with the chimney, 
which could be raised or lowered 
to suit the required draught. 
Around the grate was a ring-guard 
to rest the feet on, and the cus- 
tomers ranged themselves in a circle 
round the fire. 
Stoves. — Open stoves heat by direct radiation, and by heating the air in con- 
tact with them, and close stoves by the latter way only ; as economical means- 
of heating the latter are the best, and, when properly arranged, give both a com- 
fortable and wholesome atmosphere. There should be some dish of water upon 
them to supply a constant evaporation, sufficient to compensate for increased 
capacity of the air for moisture due to its increased heat. In the hall there will 
be no objection to a close stove, letting it draw its supply of air as it best can ; 
but in close rooms the open stove is best, on the plan of the old Franklin stove, 
or, if a close stove, somewhat on the plan of a furnace, with an outer air-supply 
for combustion and ventilation. 

Stoves are made of sizes adapted to large and small rooms, in every style and 
with all possible appliances for comfort, convenience, and economy : self-feed- 
ers, in which the coal is furnished to the fire in a close chute from the top 
downward and in proportion to the coal consumption below ; base-burners, in 
which the draught is reversed so that the base becomes a portion of the heating 
surface ; doors with mica panels around the circumference, by which the fire 
is seen with the advantage of radiant heat .and easy access to the fire-pot. 
Stoves are usually coal-burners, but plain box-stoves in cast or sheet iron are 
well adapted for wood-burners and for holding fire and retaining heat. They 
have appliances for controlling draught by dampers or by opening the smoke- 
pipe or flue to the room, thereby reducing the velocity of draught, but not 
throwing the products of combustion outward into the room, as is done by 
dampers. 

Hot-air furnaces are close cast-iron stoves, inclosed in air-chambers of brick 
or metal, into which external air is introduced, heated, and distributed by metal 
pipes to the different rooms of a house. Furnaces have been of late very much 



ARCHITECTURAL CONSTRUCTION. (539 

decried, but under proper regulation they are a very cheap, economical, and 
even healthful means of ventilation and warming. The heating surface should 
be very large, the pot thick, or even incased with fire-brick, that it may not be- 
come too hot ; there should be a plentiful supply of water in the chamber for 
evaporation, perhaps also beneath the opening of each register ; the air supply 
should always be drawn from the outer air and unobjectionable sources, through 
ample and tight ducts, without any chance of draught from the cellar ; the pot 
and all joints in the radiator should be perfectly gas-tight so that nothing may 
escape from the combustion into the air-chamber. With these provisions on a 
sufficient scale, and proper means for distribution of the heated air and escape 
of foul air, almost any edifice may be very well heated and ventilated. The air 
should be delivered through the floor or the base-board of the room, and at the 
opposite side from the flue for the escape of foul air, making as thorough a 
current as possible across the room, and putting the whole air in motion. In 
dwelling-houses the fireplace will serve the best means of exit ; in public rooms 
distinct flues will have to be made for this purpose, and they should be of 
ample dimensions and well distributed, with openings at the floor and ceiling 
with registers, and means should be provided for heating the flues. An archi- 
tect, in laying out flues for heating and ventilation, should, both in plan and 
elevation, fix the position of hot and foul air flues, and trace in the current of 
air, always keeping in mind that the tendency of hot air is to rise ; he will then 
see that, if the exit-opening be directly above the entrance-flue, the hot air will 
pass out, warming the room but little ; if the exit-opening be across the room 
and near the ceiling, the current will be diagonal, with a cold corner beneath, 
where there will be very little circulation or warmth. To heat the exit-flue, a 
very simple way is to make the furnace-flue of iron, and let it pass up centrally 
through the exit-flue ; but the current may be obstructed by a high Avind. ■ 

Fig. 1532 is one of the many forms of furnaces which consist of the most 
approved stoves, with a large heating-chamber above — in the figure of cast-iron, 
and composed of numerous flues, but very often a drum of wrought-iron. The 
whole is inclosed in a brick chamber ; in those denominated portable furnaces 
the case is of galvanized iron. The figure contains the usual appliances ix)r 
feeding and clearing fires, with a check draught opening from outside into the 
smoke flue, and dust damper and flue so arranged that when the grate is shaken 
no ashes or dust comes into the hot-air chamber. The air is introduced at the 
bottom of the case, passes up and around the stove, and out through the ducts 
to different parts of the building. The water-pan is indispensable to the hot- 
air furnace, and should be of capacity enough for a day's supply, or have auto- 
matic means of keeping up the supply. 

Air in winter is very dry, but as its volume is enlarged by heat it draws a 
supply of moisture from everything with which it comes in contact — from the 
skin and lungs, creating that parched and feverish condition experienced in 
many furnace-heated houses ; from furniture and woodwork, snapping joints 
and making unseemly cracks. Thus, taking the air at 10° and heating it to 
70°, the ordinary temperature of our rooms requires about nine times the mois- 
ture contained in the original external atmosphere, and, if heated to 100°, as 
most of our hot-air furnaces heat the air, it would require about twenty-three 
times. 



640 



ARCHITECTURAL CONSTRUCTION. 



The portable furnace is not so economical as the furnace set in brickwork, 
as more heat escapes through the metallic case. The former are usually made 




Fig 1532. 

from 12" to 36" diameter of pot, from 2' to 6' outside diameter, and 5' to 6' 
height of case. The brick-set furnaces are from 20" to 32" pot, outside brick- 
work from 5' to 6' square, walls 4" thick, height 6' to 7'. It is difficult to give 
any rule for the heating capacity, A 22" pot should be adequate for the heat- 
ing of a common 25' X 60' city house, and the higher the air-duct the less its 
diameter. 

The total sectional area of the hot-air educts should be equal to that of the 
fire-pot ; that to the first floor should be larger than to the other floors, since 
the column of hot air is shorter it will have less velocity. Air ducts that have 
outlets at the same level under the same conditions should have greater area if 
the horizontal pipes are longer. The cold-air duct should have about the same 
area as the grate, and the inlet should be above the level of the street or back 
area to avoid dust. If air ducts lead from both sides of the building to the 
furnace-chamber, the current can be controlled according to the wind, and the 
hot air distributed more equably through the building. 



ARCHITECTURAL CONSTRUCTION. 



641 



The Baltimore heater (Fig. 1533) was the 
earliest union of the stove with the furnace. 
A stove is set in the fireplace of a room in a 
lower story, of which the exterior or orna- 
mental half is exposed for the heating of 
this room, while the inner half acts as a fur- 
nace for the upper rooms. The smoke-piiie 
passes up into a chimney above, and is in- 
closed by an air pipe or jacket to which heat 
is communicated and distributed by drum 
pipes and registers to upper stories. 

Steam and hot-ivater circulation are ap- 
plied to the heating of buildings by means 
of wrought- or cast-iron pipes connected 
with boilers. In the simplest form, as com- 
mon in workshops and factories, steam is 
made to give warmth without ventilation by 
direct radiation from wrought-iron pipes. 
The general arrangement is by rows of 1" to 
ly pipe hung against the walls of the room, 
or suspended from the ceilings, 3' of 1" pipe 
being considered adequate to heat 200 cubic 
feet of space ; if there are many windows in 
the room, or the building is very much ex- 
posed, more length should be allowed. 

Steam, as a means of heating, is the most 
convenient and surest in its application to 
extensive buildings and works. From boilers, 
located at some central point, steam can be 
conveyed to points so remote that in many 
cities it is a matter of sale both for heating 
and power purposes. The limits of the ex- 
tension of steam -pipes economically have not 
yet been determined, but within the range of 
the buildings occupied by any single textile 
manufacturing industry steam-heating has 
proved satisfactory, and is almost universally 
adopted. For stores, warehouses, large build- 
ings of all sorts, where there are extensive or 
numerous rooms to be heated, steam has been 
long used, and the appliances for its use can 
be as readily obtained in all our cities and 
large towns as stoves or grates. Steam' is 
used for heating at either high or low pres- 
sures ; under 5 or 6 pounds would be consid- 
ered low pressure. A low-pressure apparatus 
may draw direct from a boiler, or be supplied 
from the exhaust of a steam-engine ; if from 
42 




w/^^'!j!;::;i^*^jg^qg^ 



Fig. 1533. 



642 ARCHITECTURAL CONSTRUCTION. 

the latter, a certain amount of back pressure must be put on the engine to es- 
tablish a circulation in the steam-heating pipes. But the loss in power is more 
than repaid by the utilization of the heat in the steam. If the heating-pipes 
are ample, they may be arranged to act as condensers, reducing the back 
pressure below atmosphere and supplying low steam for heating. 

In the operation of heating by steam, the steam, in giving off its latent 
heat through the pipes to the air of the room, returns to water ; the apparatus 
would then be nothing but pipes to convey the steam to radiators to condense 
it, and pipes to return the water to the boiler, were it not for air invariably in 
water and steam. This necessitates a more complicated circulation; there 
should be a regular flow outward of steam from the boiler, and inward of water 
and steam to it, which must be provided for in the design and by care in con- 
struction that there are no corners or angles forming eddies where air can 
lodge, and with provision for its continuous movement. 

When hot water is used for heating, there must be circulation throughout 
the system ; the water flows out from the top of the boiler, gives out its heat, 
and returns, practically of the same bulk, cold to the bottom of the boiler, and 
any radiator out of the line of this current is of no use. 

Both steam and water are used for heating rooms either directly or indirectly. 
Direct heating is like that of common stoves, without any considerations for 
ventilation ; indirect heating, like that of hot-air- furnaces. Radiators are in- 
closed in a box or chamber, into which air is drawn or forced, and then dis- 
tributed by ducts to the rooms to be warmed and ventilated. With steam or 
hot-water heating, the metallic surfaces brought in contact with the air usually- 
range from 212° to 250°, while the pot of the air-furnace is often from 900° 
to 1000°. In a sanitary point of view hot-water or low-steam coils in air- 
chambers are a more surely healthy means of warming and ventilation ; the 
greatest objection is their expense, the care requisite in attending them, and 
the danger of freezing and bursting the pipes if worked intermittently in win- 
ter. In the arrangement it is usual in dwelling-houses to place the coils at 
different points in the cellar, as near as possible beneath the rooms to be heated. 
In public buildings frequently a very large space in the cellar is occupied by 
the coils, into which the air is forced by a fan, and then distributed by flues or 
ducts throughout the building. 

All inlet or outlet ventilating flues should be provided with dampers or 
registers to control the supply or discharge of air, cutting it off when suffi- 
cient heat is secured, or retaining the warmth when ventilation is not re- 
quired. 

Fig. 1534 is an elevation showing the usual arrangement of mains, s 5, and 
returns, r r, when the horizontal distance from the boiler is small and the 
risers few. The inclination of the mains is toward the boiler, and their con- 
densed water returns by them to the boiler. 

Fig. 1535 is the better practice, and necessary if the steam is high pressure, 
the mains extended, and the branches numerous. The inclination of the mains, 
s 5, is from the boiler, and the condensed water flows down to the lowest angle, 
where it is connected with the return, r, and is by this brought back to the 
boiler. 

The size of the boiler for a steam-heating apparatus is based on the amount 



ARCHITECTURAL CONSTRUCTION. 



643 




of radiating surface, which must include that of the steam-mains and of the 
returns. 

In Fig. 1535 the steam riser, s, descends from the boiler to the last riser, 
which is connected at this point with the return, and this should obtain in all 
forms of steam-heating, keeping the flow of condensed water as far as possible 
in the direction of the flow of 
the steam, and removing it 
from the steam-pipes. 

Figs. 1536 to 1538 are com- 
mon forms of distributing steam 
and return pipes of different 
systems of heating. 

In Fig. 1536 the riser pro- 
ceeds from the boiler and leads 
directly to the highest point of 

service. Provision is made for the condensation in the pipe by a direct con- 
nection. 

In Fig. 1537 the risers are as in Fig. 1536, but there are separate returns 
for each radiator. 

In Fig. 1538 the main riser is carried directly to the highest story to be 
warmed, and the distributing mains are led from it with a pitch from the riser, 
and the descending pipes conveying the steam to the different radiators and 
the condensed water to the hot well and boiler. This should be the quietest cir- 



Fio. 1534. 




Fia. 1535. 



culation, as the steam, except in the main riser, does not interfere with the flow 
of the condensed water. 

Valves are introduced in the mains or returns where necessity or conven- 
ience may require the shutting off of any of the radiators or mains, and air- 
cocks to relieve stagnation in angles or pockets where circulation must be 
established before the whole of the heating surface can be utilized. 

The amount of radiating surface depends on the cubic feet of air to be 
heated and the number of degrees to which it is to be heated. These are de- 
termined from the outer exposure of the building or room, its plan, material, 
and construction, whether there is more or less window surface, and its occu- 
pancy ; whether for living rooms or for business, sedentary or active ; in the 
store the bookkeeper needs much more heat than the salesman. 

On an average, 100 to 150 cubic feet of room space can be heated from 0° 
to 70° by 1 square foot of radiating surface— say 3' of V pipe. This covers an 
average glass exposure which may be taken, according to Mr. Briggs, at 100 
cubic feet of space to each square foot of glass. 

The effect of glass under air exposure is to be noticed in the different con- 



644 



ARCHITECTURAL CONSTRUCTION. 




'1 

J 


■ 


H^i 


1 


^1 


r 

1 — 1 





Fig. 1536. 



Fig. 1537. 



Fig. 1538. 



ARCHITECTURAL CONSTRUCTION. 



645 



ditions experienced in cars while in motion and when stopped in cold weather, 
and the advantages of double windows in these conveyances. 

Proportions of mains to radiating surface : one of 1" diameter will serve for 
75 feet of radiating surface, including that of the mains. One and a half inch 
diameter for 250 square feet, 2" diameter for 500 square feet, 3" diameter for 
1,250 square feet, 4" diameter for 2,500 square feet. 

For the returns, one size less than that of the steam mains is the rule ; thus, 
a f" return for a 1" pipe, but 'no pipe of less diameter than f" is used ; for a 
2i" steam a 2" return, and a larger than 2" is seldom used. It may not be 
always practicable to return the condensed water, as shown in the figures 
above, by gravitation, but there are various forms of receivers or traps in which 
the water is collected and returned by hand or automatically pumping to the 
boiler. 

Fig. 1539 is a float trap, in which jt? is the pot with a tight cover, /an open 
float sliding on the stem, s, at the foot of which is a valve, v ; the condensed 
water flows in through the inlet, i, raises 
the float, /, and closes the valve, v ; event- 
ually the condensed water overflows into/ 
till it sinks and opens the valve, v, and the 
condensed water flows out through the 
valve, V, under the pressure of steam at the 
inlet ; when blown out, / rises and v closes 
for another charge. The condensed water 
is either wasted or returned to the boiler by 
a pump. The hand valve, A, is an inde- 
pendent relief to the trap. 

There are traps which return the con- 
densed water directly to the boiler, in 
which the condensed water is forced into 
a chamber above the level of the water in the boiler and the steam pressure 
then brought upon the chamber, and the water flows down from it into the 
boiler. 

Heating by indirect radiation is like that by hot-air heaters ; the heaters 
are inclosed in chambers to which cold air is introduced and the heated air 
conveyed into different rooms by pipes. It is usual to place the hot-air cham- 
bers in the cellar and basement, as directly beneath the room to be heated as 
possible, and extending the cold-air duct to the hot chamber. The chamber is 
usually made of galvanized iron in a wooden box, and often suspended from 
the ceiling of the cellar. Where the heating is indirect, as there are more cubic 
feet of air to be heated, the radiating surface is to be increased, usually to about 
three times that of the direct heating. 

Heating by Hot Water. — The principle of it is based on the fact that water 
when heated becomes of greater volume and less density, and rises; coming in 
contact with cooler surfaces, it loses its heat and descends ; the water circulates 
by the addition and reduction of heat. The possibility of a rapid and thorough 
circulation gives efficiency to the apparatus. One of its greatest advantages is, 
that when necessary the circulation will continue with a water temperature at 
an extremely low point, say 110°, and a proportionate consumption of coal. 




646 



ARCHITECTURAL CONSTRUCTION. 



Fig. 1540 exhibits the application of hot water to the heating of a building. 
The boiler shown will serve as an illustration of the water circulation; it is of 

cast-iron, of which there are numerous 
forms in this material, as well as wrought- 
iron. 

The main rises directly to the top, 
where there must be an expansion cham- 
ber, 0, in connection with it, to provide 
for the increase of volume in the water 
due to the heat. It is usual to have this 
chamber open at the top, and water may 
be poured down through the funnel noz- 
zle. A glass at the side shows the level 
of the water. 

The mains are of a little larger diame- 
ter than in steam, and reduced in size as 
the current is distributed into the radia- 
tors on which valves are placed to control 
the current ; these valves should be gates, 
to provide for full water-way. The re- 
turns are to be of the same diameter as 
the rising mains. The surface of the ra- 
diator should be greater than for steam, 
as the temperature of the water is less. 
When the radiators are vertical, as shown 
in the first and second story, there must 
be air-cocks, «, as shown, for air effectu- 
ally cuts off circulation. Hot-water cir- 
culation can be used for direct or indi- 
rect heating with like appliances as for 
steam. 

Boilers are of such varied forms and 
proportions to the area of grate that it is 
impossible to determine the value of the 
heating surface except by actual test. As 
a unit it is better to refer to the area of 
grate as a measure, of the capacity of the 
boiler, the evaporation of water by the 
combustion of pounds of coal being the 
standard of efficiency. 

Under the head of chimneys it is 
stated that two square inches of flue is 
sufficient for the combustion of each 
pound of coal per hour. This has been 
found in excess for a 5-foot diam. chimney, 
where provision has been made for avoiding eddies by the rounding of corners, 
and where there is a good natural draught, but there must be a factor of safety 
when care has not been taken in the location and construction. For the small 




Fig. 1540. 



ARCHITECTURAL CONSTRUCTION. 



647 




Fig. 1541. 



flues connected with the heating of common buildings this rule will not obtain ; 
flues for this purpose should be at least 8" X 12". But as a large area of chim- 
ney flue does not interfere with the draught, and as the necessities of chimneys usu- 
ally increase by the extension 
of works, it is safer to make 
the flue larger, but without 
omitting care in construc- 
tion. 

The combustion of coal 
on small grates may be taken 
at 4 to 6 pounds of anthra- 
cite coal per square foot of 
surface ; on grates 4' X 4', 8 
pounds ; on grates of larger area, 10 pounds, which would be a fair average of 
this class, and the vents of large chimneys may be calculated on this data, 
although the draught under equal conditions is in favour of the chimneys of 
large diameter. 

With forced draught by fans, ejectors, or, as in locomotives, by the exhaust, 
very large quantities of coal can be consumed on grates. 

The air-ducts from boiler and heaters for smaller and private dwellings have 
a natural draught ; but for schoolhouses, churches, and other public edifices a 
forced draught is usual, is under surer control, and with adequate indirect 
heaters the quantity of air can be readily furnished. It is common to intro- 
duce local fans driven by electric motors to supply air at varied points and in 
quantities suited to the needs of the position. By the use of dampers or valves 
air of any temperature, from that of the outside to that of the radiator, may be 
distributed. 

In Figs. 1536, 1537, 1538, and 1540 illustrations are given of the usual radi- 
ators : the wall coil with return bends, which may be more or less open (with 
branch Ts and multiple coils they are called box coils), wall coils with branch 




Fig. 1542. 



Fig. 1543. 



648 



ARCHITECTURAL CONSTRUCTION. 



Ts, vertical tube radiators with box bases of eifective heating surface, cast-iron 

radiators of similar design, ornamented and of great variety. Indirect radia- 
tors, Fig. 1541, in cast-iron with 
pin or iron projections, and 
wrought-iron pipes covered with 
compound coils of wrought-iron 
ribbons, increase heating surface. 
In measuring the surface of cir- 
culating coils include the lengths 
of angles and all fittings ; in the 
vertical radiators include the base. 
Figs. 1542 and 1543 are the 
end and side elevation of a radia- 
tor for live or exhaust steam, in- 
closed in a case for indirect heat- 
ing. Air is forced through the 
case into the building by a fan. 

By the location of the radia- 
tors in an independent chamber 
and a valve. Fig. 1544, the air may 

be forced through it hot, or mixed with cold air or without connection with the 

chamber cold. 




Fig. 1544. 




Fig. 1545. 



ARCHITECTURAL CONSTRUCTION. 



649 



Fig. 1545 is the plan of a portion of a large building heated by steam. B B 
are two boilers, either of which would be sufficient for the purpose ; the steam 
mains are shown by black lines following those of the building, with the sizes 
marked upon them ; the risers by inclined lines, with the square foot of radiat- 
ing surface on each story marked. This is a very convenient form of drawing, 
explanatory of the system. It is usual to draw the steam mains and risers in 
red and the returns in blue, with the diameters on each. 

Plumbing. — The conveniences for comfort in modern buildings require the 
introduction of water and its removal. Most cities have water-supplies and a 
system of sewers, and the plumber makes the connections with both. In the 
country, where there are not these public conveniences, their places are largely 
supplied by pumps and elevated tanks and by cesspools. The quantity used in 
each household varies with the wants and habits of the occupants. An average 
bath will take 25 gallons ; each use of a water-closet from 1 to 3 gallons. A 
wash-tub will hold from 10 to 20 gallons. If the water is to be pumped by 
hand, from 7 to 10 gallons may be reckoned as the daily use by each person ; if 
from aqueduct, 30 to 50 gallons is ample. With the popular style of water- 
closets the use of water has been largely increased, and by carelessness in the 
selection and use of fixtures the waste has become greater. 

The regulation size of taps for city mains is from -J-" to 1", and the pipes 




Fig. 1546. 



650 



ARCHITECTURAL CONSTRUCTION. 



leading into the house from f " to 1" diameter. The pipes are usually of lead, 
as most waters are not affected sensibly by lead, if the pipes are always kept 
full, but water which has stood for some time in the pipe should not be used 
for drinking, and lead-lined tanks should be coated with asphalt varnish. In 
some cases block-tin pipes are used ; or iron, galvanized, or coated with some 
preparation of asphalt, or glass-lined. 

The soil or house-sewer pipe connections with the main sewer or cesspool 
are usually vitrified stoneware pipe, from 4" to 6" diameter, the large size is 
for the discharge of the sewage, and the rainfall from the roof. Within the 
house the pipe is either of stoneware or cast-iron ; invariably of the latter if 
the pipe is exposed. The rising pipe to the roof is here, also, usually of cast- 
iron, and 4" diameter may be considered ample for a common house ; branches 
as small as 2" are usually of lead. 

Fig. 1546 is the perspective of a kitchen-range boiler and sink : c is the 
cold-water pipe leading to the sink and to the boiler ; it enters the top of the 
boiler, and is led down nearly to the bottom. The hot water is drawn from 
the top, through the pipe 7^, is led down to the sink and up 
for distribution through the house. The water is heated in 
the boiler by the water-back, which consists of a closed-box 
casting, forming the back of the range, r, with two connec- 
tions with the boiler, the one at the bottom introducing cold 
water, and the one at the extreme top discharging it heated 
into the boiler above, the circulation taking place as in hot- 
water heating ; the water flows through the pipe, Z, is con- 
nected with the lower part of the water-back, and returns by 
the pipe, u^ from the top of the water-back to a higher point 
in the boiler; b is the blow-off pipe. Stoves are arranged 
with water-backs. 

The pipes, a a, are carried above the draw-cocks over the 
sink, forming air-chambers, to cushion the blow of the water- 
hammer when the cocks are shut quickly. Beneath the sink 
there is a trapped connection with the sewer-pipe. 

Tig. 1547 is the elevation of a galvanized-iron boiler, but 
those in general use here are of copper. 

Fig. 1548 is the perspective drawing of a cast-iron sink, 




1 





Fiu. 1547. 



Fig. 1548. 



of the usual form and material. They are to be obtained of all suitable dimen- 
sions, rectangular, from 16" X 12" X 5" deep, to 96" X 24" X 10" deep; also, 
half-circle and corner sinks, and deep and slop sinks. 



ARCHITECTURAL CONSTRUCTION. 



651 



In the kitcheu, or a lanndry-room adjacent, tubs are set for washing, with 
hot and cold water service. The water-pipe connections are usually f ", the 
waste connections 2''. The tubs themselves are mostly of wood, but there are 
many of cast-iron (Fig. 1549), galvanized or enamelled, of slate, of earthen- 
ware, and of soapstone. 

In the butler's pantry there is usually a sink of planished tinned-copper, 
with hot and cold water connections. In the chambers and dressing-rooms 




Fig. 1549. 



wash-basins, usually of porcelain or porcelain-lined cast-iron, are set with like 
connections. The sizes of basins vary from 12" to 18" outside diameters. 

Fig. 1550 shows the usual form of setting of a wash-basin in a countersunk 
marble slab, with a back of the same material ; swing faucets for the supply of 
hot and cold water ; self - closing faucets prevent waste, and compression 
cocks are best suited for high pressures. The waste is closed by a metal or 
rubber plug, attached to a 
chain, with the other end 
fastened to a pin in the 
marble slab. The sides 
are inclosed with wood, 
forming a closet beneath 
the basin, with usually 
small drawers for towels 
at each side of the closet. 
It is cleaner and neater 
to support the slabs and 

basins by a metal frame and posts or brackets, with the traps and pipes ex- 
posed. A later form of wash-basin is an oval (largest size 19" X 15", outside 
measure), which admits of the washing of the head and shoulders, with a 
standard waste or hollow pipe overflow, preventing offence in the oxidation of 
the soapy waste which obtains from pipes, formed on the basin, and which can 




Fig. 1550. 



652 



ARCHITECTURAL CONSTRUCTION. 



not be readily cleaned. Fig. 1551 is a plan, and Fig. 1552 a section, of a cast- 
iron bath-tub porcelain-lined ; there are cocks for hot and cold water ; for the 
discharge there is a standard waste, which can be taken out entirely, but there 
is often a common plug and an overflow by an independent pipe. 

The dimensions of tubs are varied to suit the rooms in which they are to 
be placed ; the largest are 6' X 24", 18" and 19" deep. They may be reduced 
to 3' 6" in length, but should then be made deeper. Tubs of porcelain are set 
up on blocks ; porcelain-lined, on cast-iron legs, about 6" in height. Bath- 
tubs are more generally made of planished tinned- copper in a wooden box for 
support, and inclosed by wooden panels. In most bath-rooms there are basin 





Fig. 1552. 



Fig. 1551. 



and water-closet — often a foot-bath and bidet-pan — but it is preferable to make 
the water-closet a separate room, distinct, with its own water and sewer-service 
and means of ventilation. 

The construction of one form of water-closet, with all the modern appli- 
ances for the removal of soil and for ventilation, will be understood from the 
section (Fig. 1553). The seat is not shown, but is just above the basin, B, 
which contains some water to receive the defecations, to prevent the soil attach- 
ing to the side of the basin, and in a measure to check its offensive smell. T 
is the trap or water-seal which prevents the smell from the soil-pipe S passing 
up through the basin. The water-discharge from the pipe W is through a rim- 
flush around the edge of the basin. The sudden discharge washes out the basin 
B into the trap T, which is also cleaned by the rush of water. The soil-pipe S 
extends up through the roof, and may or may not also serve as a rain-leader. 
A sudden flow of water down the soil-pipe often acts as an ejector to draw the 
water out of the trap T, and break the water-seal ; to prevent this there is a 
back-air connection. A, leading also to the top of the house. But as the offence 
of a water-closet is largely due to its recent use, and as smell once getting into 
the room is with difficulty removed, but generally diffused, there is a ventilat- 
ing-pipe, V, connecting the basin B with a ventilating-flue ; this is the most 
important part of the apparatus ; connected with a chamber commode, it would 
remove all smell, and if there were no trap to the soil-pipe, or were the water- 
seal broken, it would still prevent any offensive smell from penetrating the 
house. If the soil-pipe be made also a ventilating-pipe, as is frequently done 
by its connection with the hot-air flue, then the trap and pipes A and V are 
unnecessary. 

Many sanitary engineers object to the back-air pipe as imperfect in its 



ARCHITECTURAL CONSTRUCTION. 



653 



action (a sudden suction will draw the water out of the trap before the suction 
can be relieved through a back-air pipe), that it is expensive, and that there are 
many better ways of protecting the seats by anti-siphon traps or diverging Y- 




FlG. 1553 



Fig. 1554. 



branches. In Fig. 1554 is shown a branch by which the flow from the up- 
per pipe dripping into the lower trap preserves the water seal. As the water- 
closet must be ventilated, it is better to have a regular flue in the wall with 
an induced ventilation by heat in some form, or electric fans, and air supplied 
from outer rooms or windows. 

Fig. 1555 is an elevation of the simplest 
form of closet — the hopper-closet — and in many 
respects the best. A standard waste in the cis- 
tern c will serve both for the disk-valve and the 
overflow. A rim-flush is supplied through the 
pipe W, controlled by a plain cock or by a han- 
dle 7i, as in Fig. 1556, lifts the disk valve, clos- 
ing automatically ; or by cock connecting with 
the seat, which, when down for occupancy, 
opens the flush, and, as the sitter rises, the 
counterbalanced lid rises and closes the cock. 

The service box beneath the cistern continues a temporary flow after the valve 
is dropped. V is a ventilator branch. 

Fig. 1557 is the section of a pan-closet, for many years the most popular 




Fig. 1555. 



654 



ARCHITECTURAL CONSTRUCTION. 



closet. The copper pan, when shut, cuts off the view of the trap below and 
any odour from it ; with a small flow of water the basin is readily kept clean, 

but soil is apt to lodge in the iron re- 
ceiver, and the odour to arise from it 
when the pan is down. There is an 
annular ventilating-tube beneath the 
seat, with an air-shaft attached, but of 




Fig. 1556. 



Fig. 1558. 



SIPHON JET CLOSET, 
f 



altogether inadequate dimension for the purpose, as may be said of all such 
vents attached to water-closets. There is also the air- vent to prevent the water 
being drawn from the trap. No water connections are shown in the figure. 

If the 2" vent be removed, and the air- 
draught pipe be enlarged and connected 
with a positive draught-flue, all offence 
from either recent or former use of the 
closet will be cut off. 

Fig. 1558 is the section of a, flap-closet^ 
in which a flap-valve supplies the place of 
a pan. 

Fig. 1559 is the section of a siphon-jet 

closet. In addition to the fa7i flush, /, 

into the basin, it has a jet-pipe, j\ at its 

bottom, inducing a current in the direction of the inclined leg of the trap, and 

by flush and jet the water is siphoned from the basin. 




Fig. 1559. 



ARCHITECTURAL CONSTRUCTION. 



655 



Traps are varied in their form, but all to cut off the air-connection of the 
soil-pipe with the room in which the appliance is placed. The smaller traps 
are invariably lead, the larger cast-iron. 

Figs. 1560 to 1567 represent the usual forms of lead traps. There are 
screw-plugs at the bottom of the traps, which can be taken out to remove 



Short Bend. Long Bend. 




Fig. 15i 



Fig. 1.567. 



any obstruction. As the water may be drawn out of any trap by the passage 
of water down the pipe with which it is connected, air-vents, as already de- 
scribed, in the water-closet trap, are put on these small traps. But if upper 
waste pipes be inserted, as in Figs. 1560 and 1561, at a a^ and shown in sec- 
tion (Fig. 1554, p. 653), loss of seal is cut off. 

Figs. 1568 and 1569 are cast-iron traps, with a cap that may be removed to 
clean the trap, or the aperture may be used for air- vent connection. 

Fig. 1570 is the section of a Z'e^^trap, used on sinks, with a strainer, S, 
above it. 

Fig. 1571 is a plate with plug, for the bottom of basins and bath-tubs. 



S-Trap. 



Trap with Side Outlet. 







Fig. 1568. 



Fig. 1569. 



Fig. 15r0. 



Fig 1571. 



Figs. 1572 to 1577 are common cast-iron bends or angles. 

Figs. 1578 to 1583 are cast-iron branches. The T-branch and cross 
are objectionable, as the flows from the branches and mains are at right angles, 
and mutually obstructive ; whereas in the Y, especially in the full Y, the flows 
are at acute angles with each other, and the currents converge. Similar fittings 
are used for water, but they are much heavier. 



QtrABTER 


Double Hub, 


Eighth 


Sixth 


Sixteenth 


Eeturn 


Bend. 


Quarter Bend. 


Bend. 


Bend. 


Bend. 


Bend. 






Fig. 1572. 



Fig. 1.573. 



Fig. 1574. 



Fig. 1575. 



Fig. 1576. 



Fig. 1577. 



Most water-closet basins are inclosed by a lidded seat and riser, but the less 
wood-work about a basin the better. The seat is generally hung with hinges 
of brass or composition, so that it can be raised, and the basin makes the 



656 



ARCHITECTURAL CONSTRUCTION. 



T-Branch. 



Cboss-Head. 



-Branch 





Fig. 1578. 



Fig. 1579. 



Fig. 1580. 



Double 
Y -Branch. 



Double Half 
Y-Branch. 




Fig. 1581. 



Fig. 1582. 



Fig. 1583. 




Fig. 1584. 



best urinal for men, the upper edge of the basin being covered with an earthen- 
ware tray, sloping toward the basin. Instead of the tray, if the rim of the 

basin be made square, of suflQcient width to 
support the seat, sloping to the basin, and 
overhanging, it will make the better urinal, 
and afford space for an adequate ventilating 
pipe. 

Urinals, of which one form for males is 
shown (Fig. 1584), are often used in public 
buildings, and in open stalls. Although they 
have water connections, w, and a rim flush, 
it is almost impossible to keep them sweet ; a 
cake of carbolic soap is often put in the ba- 
sin, but the most effectual means adopted on 
many railway-cars is a piece of ice. 

As direct supply from the service is uncer- 
tain if there is a draught in another quarter, 
it is now common to have small cisterns for 
closets, shown in Fig. 1556. The water from 
the service pipe is discharged well below the 
surface overflow, generally through a pipe attached to the goose-neck on the 
ball- valve pipe, to avoid the noise of running water. 

Lighting is one of the present necessities of civilization, and for a great 
many years gas has been used for lighting in domestic and industrial buildings. 
Gas fittings are in all forms — brackets and pendants, wide branches with 
fixed, swing, and slide joints ; and burners in great variety — bat wings, fish- 
tail tips, and Argand burners, and many patents for increased light and econ- 
omy of consumption. 

Service mains are seldom placed in buildings less than f " diameter for 10 
burners and 100 feet of pipe, to If" and 200 feet length. 

Electric lighting, although not superseding gas for common use, is now 
largely employed in industrial operations, and for all shows and brilliant illu- 
minations. 

The three accompanying drawings (Fig. 1584, A, B, C) illustrate three 
methods of wiring for electric lighting. 

Fig. A is a series installation. The lamps are in series and dynamo series 
wound. The wires may be led in any direction, care being taken to insulate 
them properly and avoid proximity to inflammable substances. The current 
leaves the dynamo at -j-, passes through each lamp, and returns to the dynamo 



ARCHITECTURAL CONSTRUCTION. 



057 



at — . This current is maintained at a constant strength required by the con- 
struction of each style of lamp, and determined by the E. M. F. of the dynamo, 
and the full resistance of the entire circuit, including the dynamo, the lamps, 
and the conducting wires. The strength of the current required varies greatly, 
ranging from ten to twenty amperes for series installations in the various lead- 
ing arc-light systems for which this method is used. 

Fig. B. — One method of wiring is shown for incandescent electric lighting, 
and is known as the multiple-series installation. Between two main conductors 
extending from the dynamo are placed, in parallel, several short lines connect- 




FiG. 1584. 

ing with the lamps, the current being thus divided among the lamps in pro- 
portion to their number and resistance, while in the series system the entire 
current passes through every lamp. This method is common to both the 
direct and alternating current system, and is convenient for lighting a large 
room or hall where many lamps are required at one time. A simpler and 
better arrangement for most purposes is the parallel system, in which two 
mains are led from the dynamo, and each lamp is placed on a separate branch 
between the mains, so that it can be lighted or extinguished without inter- 
fering with the remaining lamps. 

Fig. C shows the Edison three-wire system for incandescent lighting. Two 
dynamos are joined in series as shown. Each lamp has the same advantage of 
independent connection with the dynamo as in the two- wire system, shown at 
B. If an equal number of lamps are burning simultaneously in each row the 
current will flow through the parallel branches from one dynamo to the other, 
the central wire remaining neutral ; but if the number is varied by the extin- 
guishing of lamps or otherwise, the third wire furnishes a path for the surplus 
current required by the row having the greater number lighted, which will flow 
to that side in consequence of the reduced resistance resulting from the greater 
number of branches open through the lighted lamps. 

The chief advantage of this system is in the reduced amount of copper used 
for conductors, three wires instead of four being used, and each only one half 
the area, a saving of five eighths being thereby effected. 

A diagram in the Appendix illustrates a graphic method for obtaining the 
size of wire to be used in electric lighting. 
43 



658 ARCHITECTURAL CONSTRUCTION. 

GREEK A:N^D EOMAN" ORDERS OF ARCHITECTURE, 

as examples of proportions of graceful curves and outlines, are useful as 
studies and manual practice for the draughtsman. 

The Tuscan, Doric, Ionic, Corinthian, and Composite orders are systems or 
assemblages of parts subject to certain uniform established proportions, regu- 
lated by the office each part has to perform, consisting of two essential parts, 
a column and entablature, subdivided into three parts each : the first into the 
base, the shaft, and the capital ; the second into the architrave, or chief beam, 
C (Fig. 1585), which stands immediately on the column ; the frieze, B, which 
lies on the architrave ; and the cornice. A, which is the crowning or uppermost 
member of an order. In the subdivisions certain horizontal members or mould- 
ings are used : thus, the ogee (a), the corona (b), the ovolo (c), the cavetto {d), 
with the fillets, compose the cornice; the fasciso (ff), the architrave; the 
abacus (^), the ovolo (c), the astragal (^^), and the neck {7i), are the capital of 
the column ; the torus (k) and the plinth (l) (Fig. 1587) are the base. The 
character of an order is displayed not only in its column, but in its general 
forms and details, whereof the column is, as it were, the regulator ; the expres- 
sion being of strength, grace, elegance, lightness, or richness. Though a build- 
ing be without columns, it is nevertheless said to be of an order, if its details be 
regulated according to the method prescribed for such order. 

In all the orders a similar unit of reference is adopted for the construction 
of their various parts. Thus, the lower diameter of the column is taken as 
the proportional measure for all other parts and members, for which purpose- 
it is subdivided into sixty parts, called minutes, or into two modules of thirty 
minutes each. Being proportional measures, modules and minutes are not fixed 
ones like feet and inches, but are variable as to the actual dimensions which 
they express — larger or smaller, according to the actual size of the diameter of 
the column. For instance, if the diametey be just five feet, a minute, being 
one sixtieth, will be exactly one inch. To draw an elevation of any one of the 
orders, determine the diameter of the column, and from that form, a scale of 
equal parts by sixty divisions, and then lay off the widths and heights of the 
different members according to the proportions of the required order, as marked 
in the body or on the sides of the figures. 

Figs. 1585 to 1589 are illustrations of the Tuscan order: e, in the frieze 
corresponding to the Doric triglyph, may or may not be introduced. Fig. 1585 
is an elevation of the capital and entablature ; Fig. 1587 of the base ; and Fig. 
1586 of another capital. 

A slightly convex curvature, or entasis^ is given in execution to the outline 
of the shaft of a column, by classic architects, to counteract a fancied appear- 
ance of concave curvature, which might cause the middle of the shaft to ap- 
pear thinner than it really is. 

Fig. 1588 represents the form of a half-column from the Pantheon at 
Rome. In Fig. 1589, another example, the lower third of the shaft is uni- 
formly cylindrical. The entasis of the two thirds is constructed by dividing 
the arc, a Z>, into equal parts, and the columns into the same number, and pro- 
jecting the divisions of the arc on to those of the column. The upper diame- 
ter of column or chord at h is 52 minutes. 



ARCHITECTURAL CONSTRUCTION. 



659 




660 ARCHITECTURAL CONSTRUCTION. 

Figs. 1590 to 1594 exhibit an example of the Doric order, from the Temple 
of Minerva, in the Island of Egina. Fig. 1590 is an elevation of the capital 
and the entablature ; Fig. 1591 of the base ; Fig. 1592 shows the forms of 
the flutes at the top of the shaft, and Fig. 1593 at the base ; Fig. 1594 the 
outline of the capital on an enlarged scale. 

The mutules, a at, the triglyphs, l Z*, the guttae or drops, d d^ of the entabla- 
ture, the echinus,/, and the annulets, g g, of the capital, may be considered 
characteristic of the Doric. The triglyph is placed over every column, and 
one or more intermediately over every mtercolumn (or span between two col- 
umns), at such a distance from each other that the metopes, c, or spaces between 
the triglyphs, are square. 

In the best Greek examples of the order there is only a single triglyph over 
each intercolumn. The end triglyphs are placed quite up to the edge or outer 
angle of the frieze. The mutules are thin plates attached to the under side or 
soffit of the corona, over each triglyph and each metope, with the former of 
which they correspond in breadth, and their soffits or under surfaces are 
wrought into three rows of guttae or drops, conical or otherwise shaped, each 
row consisting of six guttae, or the same number as those beneath each triglyph. 
The shaft of the Doric column was generally fluted ; the number of channels 
is either sixteen or twenty, afterward increased in the other orders to twenty- 
four, a centre flute on each side of the column. - 

Figs. 1595 to 1598 exhibit an example of the Ionic order, taken from the 
Temple of Minerva Polias, at Athens. Fig. 1595 is an elevation of the capital 
and entablature; Fig. 1596, of the base; Fig. 1597 is a sectional half of the- 
plan of the column at the base and the top ; Fig. 1598 an elevation of the bal- 
uster side of the capital. It differs from the Doric in the more slender pro- 
portions of its shaft, and the addition of a base ; but the capital is the indi- 
cial mark of the order. 

When a colonnade was continued in front and along the flanks of the 
building, this form of capital in the end column occasioned an offensive 
irregularity ; for while all the other columns on the flanks showed the volutes, 
the end one showed the baluster side. It was necessary that the end column 
should, therefore, have two adjoining volute faces, which was effected by plac- 
ing the volute at the angle diagonally. 

Figs. 1599 and 1600 represent an example of the Corinthian order, from 
the Arch of Hadrian, at Athens. This order is distinguished from the Ionic 
more by its deep and foliaged capital than by its proportions. The capital is 
considerably more than a diameter in height, varying in different examples 
from one to one and a half diameter, upon the average about a diameter and a 
quarter, and has two rows of leaves, eight in each row, so disposed that of the 
taller ones, composing the upper row, one comes in the middle, beneath each 
face of the abacus, and the lower leaves alternate with the upper ones, coming 
between the stems of the latter ; so that in the first or lower tier of leaves there 
is in the middle of each face a space between two leaves occupied by the stem 
of the central leaf above them. Over these tv/o rows is a third series of eight 
leaves, turned so as to support the small volutes which, in turn, support the 
angles of the abacus. Besides these outer volutes, invariably turned diagonalh^ 
there are* two other smaller ones, termed caulicoli, which meet each other be- 



ARCHITECTURAL CONSTRUCTION. 



661 




662 



ARCHITECTURAL CONSTRUCTION. 




ARCHITECTURAL CONSTRUCTION. 



663 




/ 



664: 



ARCHITECTURAL CONSTRUCTION. 




Fig. IBOl. 



neatli a flower on the face of the abacus. The sides of the abacus are concave 
in plan, being curved outward so as to produce a sharp point at each corner, 
which is usually cut off. 

Fig. 1601 represents one of the capitals of the Tower of the Winds, showing 
the earliest formation of the Corinthian capital. In this example the abacus 

is square, and the upper row of leaves, of the kind 
called IV at er -leaves^ are broad and flat, and merely 
carved upon the vase or body of the capital. 

The shaft is, in general, fluted, similarly to that 
of the Ionic column, but sometimes the flutes are 
cabled ; that is, the channels are hollowed out for 
only about two thirds of the upper part of the 
shaft, and the remainder cut so that each channel 
has the appearance of being partly filled up by a 
round staff or piece of rope. 

The cornice is very much larger than in the 
other orders, in height and in projection, consisting 
of a greater number of mouldings beneath the corona, for that and the cymati- 
um over it are invariably the crowning members. In Fig. 1599 square blocks 
or dentels are introduced, but often to the dentels is added a row of modillions 
(Fig. 1719), immediately beneath, and supporting: the corona; and between 
them and the dentels, and also below the latter, are other mouldings, some- 
times cut, at others left plain. 

The Composite Order is a union of the Ionic and Corinthian orders. Its 
capital consists of a Eoman Ionic one, superimposed upon a Corinthian foli- 
aged base, in which the leaves are without stalks, placed directly upon the body 
of the base. 

The spacing between the columns, or intercolumn, is from one to one and 
one half diameters, but modern architects have coupled the columns, making 
a wide intercolumn between every pair of columns, so that as regards the 
average proportion between solids and voids, that disposition does not differ 
from what it would be were the columns placed singly. Supercolumniation, 
or the system of piling up orders, or different 
stages of columns one above another, was em- 
ployed for such structures merely as were upon 
too large a scale to admit of the application of 
columns at all as their decoration, otherwise 
than by disposing them in tiers. 

The Creeks seldom employed human figures 
to support entablatures or beams ; the female 
figures, or Caryatides, are almost uniformly rep- 
resented in an erect attitude, without any ap- 
parent effort to sustain any load ; while the 
male figures, Telamones or Atlantes, display 
strength and muscular action. Besides entire 
figures, either Hermes pillars or Termini are 
occasionally used as substitutes for columns of the usual form, on a moderate 
scale. The first mentioned consist of a square shaft with a bust or human head 




ARCHITECTURAL CONSTRUCTION". 



665 




Fio. 1604. 



for its capital ; the latter of a half-length figure rising out of, or terminating 
in, a square shaft tapering downward. Hermes pillars are frequently employed 
by modern architects for the decoration of window architraves. 

The Romans introduced circular forms and curves, not only in elevation 
and section, but in plan. The true Roman order consists, not in any of the 
columnar ordinances, but in an arrangement of two pillars (Fig. 1602) placed 
at a distance from one an- 
other nearly equal to their 
own height, and having a 
very long entablature, 
which, in consequence, re- 
quired to be supported in 
the centre by an arch 
springing from piers. 

Figs. 1603, 1604, and 
1605, from the Palace of 
Diocletian at Spalatro, are 
illustrations of the differ- 
ent modes of treatment of 
the arch and entablature. 

Perhaps the most sat- 
isfactory works of the Ro- 
mans are those which we 
consider as belonging to 
civil engineering rather 
than to architecture — 
their aqueducts and via- 
ducts, all of which, admi- 
rably conceived and exe- 
cuted, have furnished 
practical examples for 
modern constructions, of 
which High Bridge across 
Harlem River may be tak- 
en as an illustration. 

The history of Roman 
architecture is that of a 
style in course of transi- 
tion, beginning with purely pagan or Grecian, and passing into a style almost 
wholly Christian. The first form of Christian art was the Romanesque, which 
afterward branched off into the Byzantine and the Gothic. 

The Romanesque and Byzantine, as far as regards the architectural features, 
are almost synonymous ; in the earlier centuries there is an ornamental distinc- 
tion. In its widest signification, the Romanesque is applied to all the earlier 
round-arch developments, in contradistinction to the Gothic or later pointed 
arch varieties of the North. In this view the Norman is included in the Ro- 
manesque. 

The general characteristics of the Gothic are its essentially pointed or ver- 




em 



ARCHITECTURAL CONSTRUCTION. 







Fig. 1606. 



Fig. 1607. 



Fig. 1608. 



Fig. 1609. 








B 



Fig. 1611. 



Fig. 1612. 



Fig. 1613. 




ARCHITECTURAL CONSTRUCTION. 



667 



tical tendency, its geometrical details, its window-tracery, its openings, its 
cluster of shafts and bases, its suits of mouldings, the universal absence of the 
dome, and the substitution of the pointed for the round arch. 

The Romanesque pillars are mostly round or square, and, if square, gener- 
ally set evenly, while the Gothic square pillar is set diagonally. 

Figs. 1606 to 1610 represent sections of Gothic pillars. Fig. 1611 is half 
of one of the great western piers of the Cathedral of Bourges, measuring 8 feet 
on each side. Figs. 1612 and 1613 are elevations of capitals and bases, and sec- 
tions of Gothic pillars ; one from Salisbury, the other from Lincoln Cathedral. 

Figs. 1614, 1615, and 1616 are examples of Byzantine capitals; Fig. 1617 
a Norman one, from Winchester Cathedral; and Fig. 1618 a Gothic capital 
and base, from Lincoln Cathedral. 

Arches are generally divided into the triangular-headed arch, the round- 
headed arch, and the pointed arch. Of the round-headed arch, there are 
semicircular, segmental, stilted (Fig. 1619), and horseshoe (Fig. 1620). Of 






Fig. 1619. 



Fig. 1620. 



Fig. 1621. 



the two-centred pointed, the equilateral (Fig. 1621), the lancet, and the ob- 
tuse. Of the first, the radii of the segments forming the arch are equal to the 
breadth of the arch, of those of the lancet longer, and of the obtuse shorter. 

Of the complex arches, there are the ogee (Fig. 1622) and the Tudor (Fig. 
1623). The Tudor arch is described from four centres, two on a level with the 
spring and two below it. 

Of foiled arches, there are the round-headed trefoil (Fig. 1624), the pointed 




Fig. 1622. 



Fig. 1623. 




Fig. 1624. 



Fig. 1625. 



Fig. 1626. 



trefoil (Fig. 1625), and the square-headed trefoil (Fig. 1626). The points c are 
termed cusps. 

The semicircular arch is the Roman Byzantine and Norman arch ; the ogee 
and horseshoe are the profiles of many Turkish and Moorish domes ; the pointed 
and foliated arches are Gothic. 

Domes and Vaults.— The Greek vaulting consisted wholly of spherical sur- 
faces, the Roman of cylindrical ones. Figs. 1627 and 1628 illustrate this dis- 
tinction. Fig. 1627 being the elevation of a Roman cylindrical cross- vault, and 
Fig. 1628 the elevation of the roof of the church of St. Sophia at Constantino- 
ple ; and the sprouting of domes out of domes continues to characterize the 



668 



ARCHITECTURAL CONSTRUCTION. 



Byzantine style. As a constructive expedient the cross- vault is to be preferred, 
as the whole pressure and thrust are collected in four definite resultants, ap- 





FiG. 1627. 



Fig. 1628. 



plied at the angles only, so that it might be supported by four flying buttresses, 
placed in the direction of the resultants, and strong enough to resist the 
pressure. 

Fig. 1629 represents a compartment of the simplest Gothic vaulting — a, «, 
groin ribs ; Z*, J, ^, side ribs. 

The Romans introduced side ribs, appearing on the inside as flat bands, and 
harmonizing with the similar form of pilasters in the walls, but they never used 
groin ribs ; the Gothic builders introduced these, and deepened the Roman 
ribs. The impenetration of vaults, either round or pointed, produces elliptical 
groin lines, or else lines of double curvature ; ye-t the early Gothic architects 
made their groin ribs usually simple pointed arches of circular curvature, 

thrown diagonally across the space to be groined, and 
the four side arches were equally simple, the only care 
being that all the arches should have their vertices at 
the same level. The strength depended on the ribs, 
and the shell was made quite light, often not more 
than six inches, while Roman vaults of the same 
span would have been three or four feet. The Ro- 
mans made their vault surfaces geometrically regu- 
lar, and left the groins to take their chance ; while the 
early Gothic architects made their groins geometri- 
cally regular, and let the intermediate surfaces take their chance. 

In the next step the groin rib? were elliptical, and when intermediate ribs 
or tiercerons were inserted, these ribs had also elliptical or cylindrical curva- 
tures, different from the groins, and the ribs were placed near each other, in 
order that the portion of the vault between each pair, might practically be 
almost cylindrical. In the formation of the compound circiilar ribs three con- 
ditions were to be observed : 1. That the two arcs should have a common tan- 
gent at the point of meeting. 2. That the feet of all the ribs should have the 
same radius, up to the level at which they completely separate from each other. 
3. That from this point upward their curvature should be so adjusted as to 
make them all meet their fellows on the same horizontal plane, so that all the 
ridges of the vaults may be on one level. 

The geometrical difficulty of such works led to what is called fan-tracery 
vaulting. If similar arches spring from each side of the pillars (Fig. 1629), 
the portion of vault springing from each pillar would have the form of an in- 
verted concave-sided pyramid, its horizontal section at every level being square. 




Fig. 1629. 



i 



ARCHITECTURAL CONSTRUCTION. 



669 




Fig. 1630. 



The later architects, by converting this section into a circle, the four-sided 

pyramid became a conoid, and all the ribs forming the conoidal surface became 

alike in curvature, so that they all might be made simple circular arcs ; these 

ribs are continued with unaltered curvature till they meet and form the ridge ; 

but in this case the ridges are not level, but 

gradually descend every way from the centre 

point (Fig. 1630). 

In the figure this is not fully carried out, 

for no rib is continued higher than those over 

the longer sides of the compartment, so that a 

small lozenge is still left, with a boss at its 

centre. When the span of the main arch h a 

was large in proportion to that of h c, the arch 

h c became a very acute lancet arch, scarcely 

admitting windows of an elegant or sufficient 

size. To obviate this, the compound curve 

was again introduced. 

The four-centred arch is not necessarily flat or depressed ; it can be made 

of any proportion, high or low, and always with a decided angle at the vertex. 

In general, the angular extent of the lower curve is not more than 65°, nor less 

than 45°. The radius of the upper curve varies from twice to more than six 

times the radius of the lower. The projecting points of the trefoil arch, or 

cusps, are often introduced for ornament merely, but serve constructively, both 
in vaults and arches, as a load for the sides, to prevent 
them rising from the pressure on the crown. 

As vaultings, in general, were contrived to collect the 
whole pressure of each compartment into four single re- 
sultants, at the points of springing, leaving the walls so 
completely unloaded that they are required only as in- 
closures or screens, they might be entirely omitted or re- 
placed by windows. Indeed, the real supporting walls 
are broken into narrow strips, placed at right angles to 
the outline of the building, and called buttresses, and 
the inclosing walls may be placed either at the outer or 
inner edge of the buttresses. The first, that adopted by 
the French architects, gave deep recesses to the interiors, 
while the other, or English method, served to produce 
external play of light and shade. 

The Norman buttress (Fig. 1631) resembles a flat 
pilaster, being a mass of masonry with a broad face, 
slightly projecting from the wall. They are, generally, 
of but one stage, rising no higher than the cornice, under 
which they often,- but not always, finished with a slope. 
Sometimes they are carried up to, and terminate in, the 
corbel table. 
Fig. 1632 represents a buttress in two stages, with slopes as set-offs. 
Fig. 1633 is a buttress of the early English style, having a plain triangular 

or pedimental head. The angles were sometimes chamfered off, and sometimes 




Fia. 1631. 



670 



ARCHITECTURAL CONSTRUCTION. 




ornamented with slender shafts. In buttresses of different 
stages, the triangular head or gable is used as a finish for the 
intermediate stages. 

In the Decorated style, the outer surfaces of the buttresses 
are ornamented with niches, as in Fig. 1634. In the Perpen- 
dicular style the outer surface is often partially or wholly cov- 
ered with panel- work tracery (Fig. 1635). 

The buttress was a constructive expedient to resist the 
thrust of vaulting; but to resist the thrust of the principal 
vault, or that over the nave or central part of the church, but- 
tresses of the requisite depth would have filled up the side 
aisles entirely. To obviate this, the system of flying but- 



Fig. 1632. 








Fig. 1633. 



Fig. 1634. 



Fig. 1635. 




Fig. 1636. 



Fig. 1637. 



tresses was adopted ; that is, the connection of the interior with 
the outer buttress, by an arch or system of arches, as shown in 
Fig. 1636. The outer piers were surmounted by pinnacles, to 
render them a sufficiently steady abutment to the flying arches. 
The earlier towers of the Romanesque style were con- 
structed without spires. All are square in plan, and extremely 
similar in design. Fig. 1637 is an elevation of the tower at- 
tached to the church of Sta. Maria, in Cosmedin, and is one of 
the best and most complete examples of this style. It is 15 feet 
broad and 110 feet high. These towers are the types of the 
later Italian campaniles, generally attached to some angle of 
churches; if detached, so placed that they still form a part of 
the church design. Sometimes they are but civic constructions, 
_as belfries, or towers of defence. The campanile is square, 
carried up without break or offset to two thirds, at least, of its 



ARCHITECTURAL CONSTRUCTION. 



671 



«^ 






intended height ; it is generally solid to a consid- 
erable height, or with only siich openings as serve 
to admit light to the staircases. Above this solid 
part one round window is introduced in each 
face ; in the next story, two ; in the one above 
this, three ; then four, and lastly five ; the lights 
being separated by slight piers, so that the upper 
story is virtually an open loggia. 

The Gothic towers have projecting buttresses, 
frequent offsets, lofty spires, and a general pyra- 
midal form. Fig. 1638 is the front elevation of 
a simple English Gothic tower; here the plain 
pyramidal roof, rising at an equal slope on each 
of the four sides, is intersected by an octagonal 
spire of steep pitch. The first spires were simple 
quadrangular pyramids ; afterward the angles 
were cut off, and they became octagonal, and this 




Fig. 1638. 



Fig. 1639. 

is the general Gothic form of spire. Often, in- 
stead of intersecting the square roof, as in the 
figure, the octagonal spire rests upon a square 
base, and the angles of the tower are carried up 
by pinnacles, or the sides by battlements, or by 
both, as in Fig. 1639, to soften the transition be- 
tween the perpendicular and sloping part. 

In general the spires of English churches are 
more lofty than those on the Continent, the an- 
gle at the apex in the former being about 10°, 
and in the latter about 15°. The apex angle of 
the spires of Chichester and Lichfield are from 
12° to 13°., or a mean between the two propor- 
tions, and, according to Ferguson, more pleasing 
than either. Although having more lofty spires, 
yet the English construction is much more mas- 
sive in appearance than the Continental ; the 
apertures are less numerous, and the surfaces are 



^72 ARCHITECTURAL CONSTRUCTION. 

Fig. 1642. Fig. 1640. Fig. 1643. Fig. 1641. 



Fig. 1645. 




Fig. 1646. Fig. 1647. 



Fig. 1644. 



Fig. 1648. 



ARCHITECTURAL CONSTRUCTION. 



673 



less cut up and covered with ornaments. The spires of Freiberg Church, and 
many others on the Continent, are open work. 

Figs. 1640 and 1G41 are bell-cots. Figs. 1642 to 1648 are spires. Fig. 1649 
is an apse, or circular end of a church, from German Gothic examples. 




Fig. 1652. 



Fig. 1653. 



Fig. 1654. 



Figs. 1650 and 1651 are examples of spire finials, with weather-cocks. 
Figs. 1652 and 1653 are examples of towers not connected with church 
edifices. 

Fig. 1654 is a tower of very recent construction, and is applied to the utili- 
44 



674 



ARCHITECTURAL CONSTRUCTION. 



tarian purpose of sustaining a water-tank for the highest service of the Croton 
in Xew York city. 

Fig. 1655 represents the upper portion of the tower of Ivan Yeliki, at Mos- 
cow. The Russian towers are generally constructed independent of their 
churches, and are intended for the reception of their massive bells. 

Windows. — Before the use of painted glass, as very 
I small apertures sufficed for the introduction of the re- 

I 1 |. quired quantity of light into a church, the windows of 

" ^ ^ the Romanesque churches were generally small, and de- 

void of tracery ; and as the Byzantine architects, adorn- 
ing the walls with paintings, could not use stained glass, 
they followed in general form the Romanesque window, 
apertures with circular heads, either single or in groups 
(Fig. 1656 or Fig. 1657). The Korman windows were 
also small, each consisting of a single light, semicircular 




1^ 


.jz7^_ \m 


m 







Fig. 1655, 



Fig. 1656. 



Fig. 1657. 



in the head, and placed as high as possible above the ground ; at first splayed 
on the inside only, afterward the windows began to be recessed with mould- 
ings and jamb-shafts in the angles, as in Fig. 1657. 

The Lancet, in general use in the early Gothic period, was of the simplest 
arrangement : in these windows the glass was brought within three or four 
inches of the outside of the wall, and the openings were widely splayed in the 
interior. The proportions of these windows vary considerably, in some the 
height being but five times the width, in others as much as eleven ; eight or 
nine times may be taken as the average. Lancet windows occur singly (Fig. 
1658), or in groups of two, three, five, and seven, rarely of four and six. The 
triplet (Fig. 1659) is the most beautiful arrangement of lancet windows. It 
was customary to mark with greater importance the central light, by giving it 
additional height, and in most cases increased width also. In some examples 
the windows of a lancet triplet are placed within one drip-stone forming a 
single arch, thus bearing a strong resemblance to a single three-light window. 
The first approximation to tracery appears to have been the piercing of the 
space over a double lancet window comprised within a single drip-stone (Fig. 
1660). 

A traceried window is a distinctive characteristic of Gothic architecture ; 
with the establishment of the principle of window tracery the mullions were 
recessed from the face of the wall in which the window arch was pierced, and 



ARCHITECTURAL CONSTRUCTIOX. 



675 



the fine effect thus produced was speedily enhanced by the introduction of dis- 
tinct orders of mullions, and by recessing certain portions of the tracery from 
the face of the primary mullions and their corresponding tracery bars. 





Fig. 1659. 




Fig. 1658. 



Fig. 1660. 



Examples of window tracery, showing its constructive centres and lines, are 
given on pages 81 and 82, illustrating the chief varieties. The following figures 
are more complete in position 
and with architraves, Geomet- 





Fig. 1661. 



Fig. 1662. 



rical and Flowing; the former consisting of geometrical figures, as circles, 
trefoils, quatrefoils, curvilinear triangles, lozenges, etc. ; while in flowing tracery 
these figures, though still existing, are gracefully blended together in one de- 
sign. 

Fig. 1661 represents an example of the earlier decorated tracery window- 
head, consisting of two foiled lancets, with a pointed quatrefoil in the spandrel 
between them. One half of the windows in this, as in some of the following 
figures, is drawn in skeleton, to explain their construction. Fig. 1662 is an- 
other example of Decorated tracery. 

Fig. 1663 is an example of the English leaf tracery; Fig. 1664, of the 
French flamboyant. The difference between the two styles is, that while the 
upper ends of the English loops or leaves are round, or simply pointed, the 
upper ends of the latter terminate, like their lower ones, in angles of contact, 
giving a flamelike form to the tracery bars and form pieces. 



676 



ARCHITECTURAL CONSTRUCTION. 



In England the Perpendicular style succeeded the Decorated ; the muUions, 
instead of diverging in flowing or curvilinear lines, are carried up straight 
through the head of the windows ; smaller 
mullions spring from the head of the prin- 




FiG. 1663. 



Fig. 1664. 



Fig. 1665. 



cipal lights, and thus the upper portion of the window is filled with panel-like 
compartments. The principal as well as the subordinate lights are foliated in 
their heads, and large windows are often divided horizontally by transoms. 
The forms of the window arches vary from simple pointed to the complex 
four-centred, more or less depressed. 

Fig. 1665 is an example of a Perpendicular window. 

Fig. 1666 is a square-headed window, such as were usual in the clear-stories 
of Perpendicular architecture. 

Figs. 1667 and 1668 are quadrants of circular window^s, used more espe- 




FiG. 1666. 



Fig. 1667. 



Fig. 1668. 




Fig. 1669. 



cially in France for the adornment of the west 
ends and transepts of the cathedrals. 

Besides the tracery characteristic of Gothic 
architecture, there is a tracery peculiar to the 
Saracenic and Moorish style, of which Fig. 
1669 may be taken as an example — it being a 
w^indow of one of the earliest mosques. The 
general form of the window and door-heads of 
this style is that of the horse-shoe, either cir- 
cular or pointed. 

Doorumys. — Fig. 1670 is the elevation of a 
circular-headed doorway, which may be con- 



ARCHITECTURAL CONSTRUCTION. 



077 



sidered the type of many entrances both in Romanesque, Gothic, and later 
styles. It consists of two or more recessed arches, with shafts or mouldings 
in the jambs. In the earlier styles the 
arches were circular, in the later Gothic, 1 1 , . J 





Fig. 1671. 




Fig. 1670. 



Fig. 1672. 



generally pointed, but sometimes circular ; in the earlier, the angles in which 
the shafts are placed are rectangular ; in the latter, the shaft is often moulded 
on a chamfer plane — that is, a plane inclined to the face of the wall, generally 
at an angle of 45° ; often the chamfer and rectangular plane are used in con- 
nection. 

Fig. 1671 is a simple head of a depressed four-centred or Tudor-arched 
doorway, with a hood moulding. 

Fig. 1672 represents the incorporation of a window and doorway. Some- 
times the doorway pierces a buttress; in that case, the buttress expands on 
either side, forming a sort of porch. The Gothic architects placed doors 
where they were necessary, and made them subservient to the beauty of the 
design. 

Fig. 1673 is an example of a gabled doorway with crockets and finial. 

Fig. 1674 is an example of a perpendicular doorway, with a label or hood 
moulding above, and ornamented spandrels. 

Fig. 1675 is an example of a Byzantine, and Fig. 1676 of a Saracenic 
doorway. 

The Renaissance style was, originally, but the revival or a fair rendering of 
the classical orders of architecture, with ornaments from the Byzantine and 
Saracenic styles. 

Garbett divides this style into three Italian schools, the Florentine, Vene- 
tian, and Roman. The Florentine admits of little apparent ornament, but 
any degree of real richness, preserving in its principal forms severe contrast ; 
powerful masses self-poised without corbeling, without arching ; breadth of 



678 



ARCHITECTURAL CONSTRUCTIOX, 



everything, of light, of shade, of ornament, of plain wall ; depth of recess in 
the openings, of perspective in the whole mass, of projection in the cornice. 




Fig. 1673. 




Fig. 1674. 



Absence of features useless to convenience or stability, admitting of great 
plainness, or of very florid enrichment. 

The aim of the Venetian school was splendonr, variety, show, and orna- 
ment; not so much real as effective ornament. Thus, it rarely contains as 




Fig. 1675. 




Fit,. 1676. 



much carving or minute enrichment as the Florentine admits ; but it has 
larger ornaments, constructed (or built) ornaments, great features useless 
except for ornament, such as inaccessible porticoes, detached columns, and 
architraves supporting no ceiling, towers built only for breaking an outline. 

The Roman school is intermediate in every respect between the two other 
schools. It is better adapted to churches than to any other class of buildings. 
This fitness arises from the grand, simple, and unitary effect of one tall order, 



ARCHITECTURAL CONSTRUCTION. 



679 



generally commenciug at or near the ground, obliterating the distinction of 
two or three stories, making a high building appear a single story. 

Mouldings. — "All classical and Eomanesque architecture is composed of 
bold independent shafts, plain or fluted, with bold detached capitals forming 
arcades or colonnades where they are needed, and of walls whose apertures are 
surrounded by courses of parallel lines called mouldings, and have neither 
shafts nor capitals. The shaft system and moulding system are entirely sepa- 
rate ; the Gothic architects confounded the two ; they clustered the shafts till 
they looked like a group of mouldings, they shod and capitalled the mouldings 
till they looked like a group of shafts." The mouldings appear in almost every 
conceivable position ; from the bases of piers and piers themselves, to the ribs 
of the fretted vaults which they sustain. 

In the earliest examples of Norman doorways the jambs are mostly simply 
squared back from the walls ; recessed jambs succeeded, and are common in 
both K"orman and Gothic architecture ; and when thus re- 
cessed, detached shafts were placed in each angle (Fig. 
1677). In the later styles the shafts were almost invariably 
attached to the structure. The angles themselves were 
often cut or chamfered off, and the mouldings attached to 
the chamfer-plane. The arrangement of window jambs, 
during the successive periods, was in close accordance with 
that of doorways. 

In the richer examples small shafts were introduced, 
which, rising up to the springing of the window, carried 
one or several of the arch mouldings. Yet mouldings are 
nevertheless not essential accessories; many windows of the richest tracery 
have their mullions and jambs composed of simple chamfers. 

Figs. 1678 to 1686 are examples of arch and architrave mouldings^ which. 




Fig. 1677. 



^fi 



^|rtiiiifc^^^^^^^^^ 




Fig. 1680. 



Fig. 1682. 



680 



ARCHITECTURAL CONSTRUCTION. 




Fig. 1683. 






Fig. 1684. 



Fig. 1685. 



Fig. 1686. 



even when not continuous, partook of the same general 
ari-angement as those in the jambs, with greater rich- 
ness of detail. When shafts were employed, they car- 
ried groups of mouldings more elaborate than those 
of the jambs, though still falling on the same planes. 

Capitals were either moulded or carved with foliage, 

animals, etc. ; they always consisted of three distinct 

parts (Fig. 1687)— the head mould (A), the bell (B), and the neck mould (C). 

In Norman examples the head mould was almost invariably square ; in the 

later styles it is circular, or corresponding to the form of the 

pillar. 

Bases consist of the plinth and the base mouldings. The 
plinth was square in the Norman style, afterward octagonal ; 
then, assuming the form of the base mouldings, it bent in 
and out with the outline of the pier. Base mouldings were 
also extensively used round the buttresses, towers, and walls 
of churches. 

String Courses, of which Figs. 1688 to 1693 are exam- 
ples, were horizontal courses in the face of a wall, the most 
usual position being under the windows. In the Nbrman styles they were usu- 
ally heavy in the outline ; in the later styles they were remarkably light and 
elegant ; free from restraint or horizon tali ty, they now rose close under the sill 




Fig. 168r. 




Fig. 1691. 



Fig. 1692. 



Fig. 1693. 



ARCHITECTURAL CONSTRUCTION". 



681 



In the Nor- 



of the window, and then suddenly dropping to accommodate themselves to the 
arch of a low doorway, and again rising to run immediately under the adjoin- 
ing window. In this way the string courses frequently served the purpose of a 
dripstone or hood moulding over doors ; occasionally the hood mould was con- 
tinued from one window to the other. 

Cornices are not an essential feature in Gothic architecture. 
man and early English styles the cornice was a sort of enlarged, 
projecting string course, forming a drip-stone beneath the roof, 
which, if supported on brackets or corbels^ was termed the corbel 
table. 

The earliest moulding in Norman work is a circular bead 
strip, worked out of the edges of a recessed arch, called a circu- 
lar hoivtel(¥ig. 1694). From a circular form the bowtel soon be- 
came pointed, and, by an easy transition, into the bowtel of one, two, or three 
fillets. 

Figs. 1695 to 1700 are sections of Romanesque drip- or cap-stones, adapted 
to different pitches of roof. 

Fig. 1701 is the scroll moulding ; a simple filleted bowtel, with the fillet 




Fig. 1694. 



Fig. ie99. 




Fig. 1700. 



682 



ARCHITECTURAL CONSTRUCTION. 



undeveloped on one side, as shown by the dotted lines. If this moulding be 
cut in half, through the centre of the fillet, we have on the developed side the 
moulding now termed by carpenters the 
rule joint, which, by rounding off the 
corners by reverse curves, becomes the 
wave moulding. 





FfG. 1702. 



Fig. 11 



Fig. 1702 is a Gothic example of the 
filleted bowtel with prominent alternate 
hollows. 

rig. 1703 is an example of the perpendicular style, an insignificant hollow 
separating groups of mouldings. 

Figs. 1704 to 1709 are examples of moulded timbers, used largely in open- 
timbered roofs and for exposed beams. It is still the custom, when the fram- 
ing is not covered in with plastering or ceiling, to corner the edges of the joists 
and beams, at an angle of 45°, for about 1" on each face, but not extending 
close to the joint or wall ; this is called stop-chamfering. 




Fig. 1704. 



Fig. 1705. 



Fig. 1706. 



Fig. 1707. 



f. o,llS:~» 




Fig. 1708. 



**-. 





Fig. 1709. 



Ornameiit. — Architectural ornament is of two kinds, constructive and deco- 
rative. By the former is meant all those contrivances, such as capitals, brack- 
ets, vaulting-shafts, and the like, which serve to explain or give expression to 
the construction ; by the latter, such as mouldings, frets, foliage, etc., which 
give grace and life, either to the actual constructive form, or to the construe- 



ARCHITECTURAL CONSTRUCTION. 



683 



tive decoration. Mouldings of the different styles have been already treated of ; 
it is proposed to give now what are even more purely decorations of a style. 

In the Grecian orders the Doric (Fig. 1590) has the triglyph mutules and 
guttoe; the Ionic (Fig. 1596) has various mouldings of the cornice, frieze, 
abacus, and neck of the column enriched. The principal ornament of the 
neck of the column is the anthemion, commonly known, in its most simple 
form, as the honeysuckle or palmetto ; in the anthemion, as represented in the 
figure, the palmetto alternates with the lily or some analogous form. The 
ornament of the abacus is the egg and dart (Fig. 1710) ; the ornament of the 



J 


M 


k 




Fig. iriO. 



Fig. 1711. 



frieze and cornice (Fig. 1711). The fret (Fig. 1712) and the guilloche (Fig. 
1713) are also common Greek ornaments, used to adorn the soffits of beams 
and ceilings. The acanthus is the distinctive ornament of the Corinthian, of 
which a leaf is represented in front and side view (Figs. 1714 and 1715). 




Fig. 1714. 



Fig. 1715. 



Figs. 1716, 1717, and 1718 are the side elevation, front elevation, and sec- 
tion of a Greek bracket, the principal ornaments of which are taken from the 
anthemion and acanthus. 

Fig. 1719 is an elevation of a portion of an enriched cornice from the 
temple of Jupiter Stator, at Eome, of the Corinthian order of architecture. 
Fig. 1720 is the under side of the modillion, on a larger scale. 

The chief characteristic of Roman ornament is its uniform magnificence, an 
enrichment of the Greek. The most used elements of the Roman decorations 
are the scroll and the acanthus. The acanthus of the Greeks is the narrow 
prickly acanthus ; that of the Roman, the soft acanthus. For capitals the 
Roman acanthus is commonly composed of conventional clusters of olive-leaves. 
Fig. 1721 represents a Roman acanthus scroll. 



68-i 



ARCHITECTURAL CONSTRUCTION. 



The free introduction of monsters and animals is likewise a characteristic 
of Greek and Roman ornament, as the sphinx, the triton, the griffin, and 
others ; they occur, however, more abundantly in the Roman. 



O5OOOOOO0(^ 




Fig. 1717. 




Symbols are the foundation of decorations in the Byzantine and Romanesque. 
The early symbols were the monogram of Christ, the lily, the cross, the ser- 
pent, the fish, the aureole, or vesica piscis, and the circle or nimbus, the trefoil 
and quatrefoil, the first having reference to the Trinity, the second to the 

four Evangelists. Occasionally the 

symbolic images of the Evangelists, the 
angel, the lion, the ox, and the eagle, 







Fig. 1719. 



Fig. 1720. 



i 



ARCHITECTURAL CONSTRUCTIOX. 



685 



are represented within these circles. The hand in the attitude of benediction, 
and the lily (the fleur-de-lis), the emblem of the virgin and purity, are com- 




FiG. 1721. 



mon ; also a peculiarly formed leaf, somewhat resembling the leaf of the ordi- 
nary thistle. The serpent figures largely in Byzantine art as the instrument of 
the fall, and one type of the redemption. 




Fig. 1722. 

Pagan ornaments, under certain symbolic modifications, were admitted into 
Christian decorations. Thus the foliations of the scroll were terminated by 
lilies, or by leaves of three, four, and five blades, the number of blades being 
significant; and in a similar way the anthemion and every other ancient orna- 
ment. In the Byzantine, all their imitations of natural forms were invariably 
conventional ; it is the same even with animals and the human figure ; every 
saint had his prescribed colours, proportions, and symbols. 

The Saracenic was the period of gorgeous diapers (Figs. 1722 and 1723), for 
their habit of decorating the entire surfaces of their apartments was highly 
favourable to the development of this class of design. The Alhambra displays 
almost endless specimens, and all are in relief and enriched with gold and colour, 
chiefly blue and red. The religious cycles and symbolic figures of the By- 
zantine are excluded. Mere curves and angles or interlacings were now to bear 
the chief burden of a design, but distinguished by a variety of colour. The 
curves, however, very naturally fell into standard forms and floral shapes, and 



6S6 



ARCHITECTURAL CONSTRUCTION. 



the lines and angles were soon developed into a very characteristic species of 
tracer}^, or interlaid strap-work, very agreeably diversified by the ornamental 




Fig. 1723. 

introduction of the inscriptions, which last custom of elaborating inscriptions 
with their designs was peculiarly Saracenic. Although flowers were not palpa- 
bly admitted, yet the great mass of the minor details of Saracenic designs are 
composed of flower forms disguised — the very inscriptions are sometimes thus 
grouped as flowers ; still, no actual flow^er ever occurs, as the exclusion of all 
natural images is fundamental to the style in its purity. 

All the symbolic elements of the Byzantine are continued in the Gothic. 
Ornamentally, the Gothic is the geometrical and pointed element elaborated to 
the utmost ; its only peculiarities are its combinations of details ; at first the 
conventional and geometrical prevailing, and afterward these combined with 
the elaboration of natural objects in its decoration. The most striking feature 
of all Gothic work is the wonderful elaboration of its geometric tracery ; vesi- 
cas, trefoils, quatrefoils, cinquefoils, and an infinity of geometric varieties be- 
sides. The tracery is so paramount a characteristic that the three English 
varieties, the early English, the decorated, and the perpendicular, and the 
French flamboyant, are distinguished almost exclusively by this feature. (See 
Figs. 1661 to 1665.) 

The ornamental mouldings used in the decorative details are numerous, 
among which the more common is the chevron or zigzag (Fig. 1724), simple 
as the indented, or duplicated, triplicated, or quadrupled ; the billet, the pris- 
matic billet, the square billet, and the alternate billet (Fig. 1725) ; the star 
(Fig. 1726), the fir-cone; the cable (Fig. 1727); the embattled (Fig. 1728); 
the nail-head (Fig. 1729) ; the dog-tooth (Fig. 1730) ; the ball-flower (Fig. 
1731) ; and the serpentine vine-scroll. 




Fig. 1724 



Fig. 1725. 



Fig. V, 



The crocket, in its earliest form, was the simple arrow-head of the episco- 
pal pastoral staff ; subsequently flnished with a trefoil, and afterward still fur- 
ther enriched. Figs. 1732 and 1733 are early English crockets; Fig. 1734 a 
decorated one. Fig. 1735 is a flnial of the same style. Both finials and crock- 
ets in detail display a variety of forms. 



ARCHITECTURAL CONSTRUCTION. 



687 



The parapets of the early English style are often a simple horizontal course, 
supported by a corbel table, sometimes relieved by a series of sunk blank trefoil- 




FiG. 1728. 




Fig. 1730. 





Fig. 1729. 

headed panels ; sometimes 
a low embattled parapet 
crowns the wall. In the 
decorated style the hori- 
zontal parapet is some- 
times pierced with trefoils, sometimes with wavy, flowing tracery (Fig. 1736). 
Grotesque spouts or gargoyles discharge the water from the gutters. The para- 



FiG. 1731. 




Fig. 1734. 




Fig. 1733. 




Fig. 1735. 



pets of the perpendicular style are frequently embattled (Fig. 1737), covered 
with sunk or pierced panelling, and ornamented with quatrefoil, or small tre- 





FiG. 1737. 



Fig. 1736. 

foil-headed arches ; sometimes not em- 
battled but covered with sunk or 
pierced quatrefoils in circles, or with 
trefoils in triangular spaces, as in Fig. 
1738. 

Among the varieties of ornamental ^^°- ^^^• 

w^ork, the mode of covering small plain surfaces with diapering (Fig. 1739) 
was sometimes need, the design being in exact accordance with the architec- 




688 



ARCHITECTURAL CONSTRUCTION. 



tural features and details of the style. The rose (Fig. 1740), the badge of the 
houses of York and Lancaster, is often met with in the perpendicular style ; 




Fig. 1739. 




and tendrils, leaves, and fruit of the vine are carved in great profusion in the 
hollows of rich cornice mouldings, especially on screen-work in the interior of 
a church. Fig. 1741, in its original type a Byzantine ornament, an alternate 
lily and cross, is a common finish to the cornice of rich screen-work in the lat- 
est Gothic, and is known under the name of the Tudor flower. 

Sculptured foliage (Figs. 1742 to 1747) 
is much used in capitals, brackets, corbels, 
bosses, and crockets. Among the forms of 
foliage the trefoil is most predouiinant. 

The Ornaments of the Renaissance. — The 
term Eenaissance is used in a double sense ; 
in a general sense implying the revival of 
art, and specially signifying a peculiar style 
of ornament. It is also sometimes, in a very confined sense, applied in refer- 
ence to ornament of the style of Benvenuto Cellini ; or, as it is sometimes des- 
ignated, the Henry II (of France) style. 

The mixture of various elements is one of the essentials of this style. These 




Fig. 1741. 





Fio. 1742. 



Fig. 1743. 



Fig. 1744. 




Fig. 1745. 



Fig. 1746. 



Fig. 1747. 



^ARCHITECTURAL CONSTRUCTION. 



689 



elements are the classical ornaments 
age ; men and animals, natural and 



unnatural and natural flowers and foli- 
grotesque ; cartouches, or pierced and 
scrolled shields, in great promi- 
nence ; tracery independent, and 
developed from the scrolls of the 
cartouches , and jewel forms (Figs. 
1748 and 1749). 

The Elizabethan is a partial 
elaboration of the same style ; the 
present Elizabethan exhibits a very 
striking preponderance of strap and 
shield work ; but the earlier is 
much nearer allied to the Continen- 
tal styles of the time, classical orna- 
ments but rude in detail, occasional 
scroll and arabesque work, and strap- 
work, holding a much more promi- 
nent place than the pierced or 
scrolled shields. Fig. 1750 is an ex- 
ample of the style from the old 
guard chamber, Westminster. 

Of the earliest and transition 
styles of Renaissance ornament are the Tricento and the Quatrecento. The 
great features of the first are its intricate tracery and delicate scroll-work of 
conventional foliage, the style being but a slight remove from the Byzantine 
and Saracenic ; of the second, elaborate natural imitations of fruit, flowers, 
birds, or animals (Fig. 1751), all disposed simply with a view to the ornamen- 
tal ; also occasional cartouches, or scrolled shield-work. 




Fig. 174S. 




Fig. 1749. 

The Renaissance is something more approximative to a combination of pre- 
vious styles than a revival of any in particular, developed solely on esthetic 
principles, from a love of the forms and harmonies themselves, as varieties of 
effect and arrangements of beauty, not because they had any particular signi- 
fication, or from any superstitious attachment to them as heirlooms. 

Fig. 1752 is an example of ornament in the Cinquecento style. The ara- 
besque scroll-work is the most prominent feature of the Cinquecento, and with 
this in its elements, it combines every other feature of classical art, with the 
unlimited choice of natural and conventional imitations from the entire animal 
45 



690 



ARCHITECTURAL CONSTRUCTION. 



and vegetable kingdom, both arbitrarily disposed and combined. .Absolute 
works of art, such as vases and implements, and instruments of all kinds^ are 
prominent elements of 
the Cinquecento ara- 
besque, but cartouches 
and strap-work wholly 






Fig; 1750. 



Fig. 1751. 



Fig. 1752. 



disappear from the best examples. Another chief feature of the Cinquecento 
is the admirable play of colour in its arabesques and scrolls ; and it is worthy 

of note that the three secondary colours — 
orange, green, and purple — perform the chief 
parts in all the coloured decorations. 

Fig. 1753 is an example of the Louis 
Quatorze style of ornament. The great medi- 
um of this style was gilt stucco-work, and 
this absence of colour seems to have led to its 
most striking characteristic, infinite play of 
light, of shade ; colour, or mere beauty of form 
in detail, having no part in it whatever. Flat 
surfaces are not admitted ; all are concave or 
convex : this constant varying of the surface 
gives every point of view its high lights and 
brilliant contrasts. 

The Louis Quinze style differs from that 
of Louis Quatorze chiefly in its absence of 
p, ^ j^gg symmetry ; in many of its examples it is an 

almost random dispersion of the scroll and 
shell, mixed only with that peculiar crimping of shell-work, the coquillage. 




ARCHITECTURAL CONSTRUCTION. 691 

The ornaments of which we have thus given examples are, in general, 
applied to interior decorations, to friezes, pilasters, panels, architraves, the 
faces and soffits of arches, ceilings, etc., to furniture, and to art-manufactures 
in general. For exteriors these ornaments are sparingly applied ; shield and 
scroll-work, of the later Elizabethan or Renaissance style, is sometimes used, 
but very seldom tracery. 

Principles of Design. — Professedly treating of architecture only in its most 
mechanical phase of drawing, the history of it as an art, and the distinctions 
of styles, have been but briefly treated. To one anxious to acquire knowledge 
in this department we refer, as the very best compendium within our knowl- 
edge, to Ferguson's " Hand-Book of Architecture." The study of this work 
will give direction to a person's observation, but, without referring to actual 
examples, mere reading will be of little use. Drawings give general ideas of 
the character of buildings, but no idea of size or of the surroundings of a 
building. Many a weak design, especially in cast-iron buildings, acquires a 
sort of strength by the number of its repetitions, giving an idea of extent ; and 
many a beautiful design on paper has failed in its execution, being dwarfed by 
its surroundings. With regard to the style of a building, there are none of the 
ancient styles in their purity adapted to present requirements ; our churches 
and theatres are more for the gratification of the ear than the eye, and the 
comforts of our domestic architecture, and the requirements of our stores and 
warehouses, are almost the growth of the present century. For a design, look 
first to the requirements of the structure, the purposes to which it is to be 
applied ; sketch the plan first, arrange the divisions of rooms, the openings for 
doors and windows, construct the sections, and then the elevations, first in 
plain outline ; modify each by the exigencies of construction. 

" Construction, including in the term the disposition of a building in ref- 
erence to its uses, is by some supposed to be the common part of the art of 
architecture, but it is really the bone, muscle, and nerve of architecture, and 
the arts of construction are those to which the true architect will look, rather 
than to rules and examples, for the means of producing two at least of the 
three essential conditions of building well, commodity, firmness^ 3,ndi delight, 
which conditions have been aptly said to be the end of architecture as of all 
creative arts. 

" The two great principles of the art are : First, that there should be no 
features about a building which are not necessary for convenience, construc- 
tion, or propriety ; second, that all ornament should consist of enrichment of 
the essential construction of the building. 

" The neglect of these two rules is the cause of all the bad architecture of 
the present time. Architectural features are continually tacked on buildings 
with which they have no connection, merely for the sake of what is termed 
effect, and ornaments are continually constructed instead of forming the deco- 
ration of construction to which in good taste they should always be subservient. 
The taste of the artist ought to be held merely ancillary to truthful disposition 
for structure and service. The soundest construction is the most apt in the 
production, or the reproduction, it may be, of real art. The Eddystone Light- 
house is well adapted to its uses ; it is commodious, firm and stable almost to a 
miracle, and its form is as beautiful in outline to the delight of the eye as it is 



692 ARCHITECTURAL CONSTRUCTION. 

well adapted to break and mitigate the force of the sea in defence of its own 
structure. The English Exhibition Building of 1851 was most commodious for 
the purposes of an exhibition, firm enough for the temporary purpose required 
of it, and there was delight in the simplicity and truth of its combinations ; and 
all this may be said to have grown out of propriety of construction, as applied 
to the material, cast-iron. The use of unfitting material, or fitting material 
inappropriately, leads almost entirely to incommodiousness, infirmity, and 
offence, or some of them. 

" Out of truth in structure, and that structure of a very inartificial sort, 
grow the beautiful forms of the admirable proportions found in the works of 
the Greeks ; and out of truth in structure, with the strictest regard to the ne- 
cessities of the composition and of the material employed, and that structure 
as full of artifice as the artifice employed is of truth and simplicity, grew the 
classical works vulgarly called Gothic, but now characteristically designated as 
Pointed, from the arch which is the basis of the style. Structural untruth is 
not to be justified by authority ; neither Sir Christopher Wren, nor the Athe- 
nian exemplars of Doric or Ionic in the Propylaeum and in the Minerva Polias, 
with their irregular and inordinately wide intercolumniation, can persuade 
even the untutored eye to accept weakness for strength, or what is false for 
truth. 

" The Greek examples offer th« most beautiful forms for mouldings, and 
the Grecian mode of enriching them is unsurpassed. It should be borne in 
mind that the object in architectural enrichment is not to show ornament, but 
to enrich the surface by producing an effective and pleasing variety of light and 
shade ; but still, although ornament should be a secondary consideration, it 
will develop itself, and therefore should be of elegant form and composition." 

We have quoted thus at some length from the article "Architecture," 
"Encyclopaedia Britannica," because with many authority is necessary, and 
they distrust their own powers of observation and analysis ; all must feel the 
truth of the above, but in practice it is very little appreciated or carried out. 
The present taste in architecture, as in the theatre, is for the spectacular; 
breadth or dignity of effect is not popular ; edifices are not only covered with, 
but built up in ornament ; and construction is but secondary. The French, 
having a building-stone that is very easily worked, cut merely the joints, leav- 
ing the rough outer surface to be worked after it is laid ; chopping out mould- 
ings and ornaments almost as readily as though it were in plaster, and the sur- 
face when finished is covered with enrichments in low relief. The fashion thus 
set is imitated in this country at immense cost, in the most unfitting materials, 
marble and granite. Our architectural buildings express fitly our condition — 
a rich country, recent and easily acquired wealth, and a desire and rivalry to 
exhibit it, or a display as a means of advertising, and in this truth of expression 
will have an archaeological interest ; although it does not contribute much to 
present excellence in construction, it still has this value : that the architect or 
constructor need be governed by no rules or principles — he can make experi- 
ments on a pretty extensive scale, and out of much bad construction even forms 
and ornament may spring up which will stand the test of time, and form a 
nucleus of a new style adapted to the present wants. 

Cast-iron as a building material, with the exception of exhibition buildings, 



ARCHITECTURAL CONSTRUCTION. 693 

has seldom been treated distinctively; buildings erected with it have been 
copies of those in stone, and have been even imitated in colour. For the first 
story of stores, where space is necessary for light and the exhibition of wares, 
cast-iron columns are almost invariably used, but are objected to architecturally, 
that they look too weak for the support of the piles of brick and stone above 
them. The objection should not be to the use, but that the truth of the ade- 
quate strength of the cast-iron is not conveyed by the form or colour. No 
one objects that the ankles of Atlas look too light to support the massive figure 
and globe, or wishes him seated to give the idea of stability; so if the columns 
and lintels were some other form than Greek or Roman with immense inter- 
columniations, and coloured fitly, the appearance of weakness would be entirely 
lost sight of. 

Improvements in the manufacture of iron and steel have led up to the 
skeleton construction (page 565) — frames of cast or rolled iron and steel framed 
and set before any of the masonry except that of the foundations is laid. All 
the columns, girders, and beams are bolted together, built into, and covered 
wuth masonry to add to the rigidity of the structure and for protection against 
fire. The framing is square, but, for variety and design, arches, soffits, and orna- 
mental clothing is made in masonry. Little in exterior form can be considered 
a necessity of construction, and there is as yet no standard of finish. The 
function of the metal, like the bone in the animal structure, is to give strength 
to sustain it ; the masonry is the muscle to stiffen, protect, and ornament it. 
Constructive expedients, like roofs, reduce the appearance of height, and are 
objectionable from the necessity of gutters and leaders. 

In conclusion, the draughtsman should be conversant with classic and later 
styles ; still, as he must design to suit the necessities of the times, and the 
requirements of present tastes and fashions of buildings, he should keep him- 
self posted on what is being done, and he will find it very convenient to have a 
scrap-book of cuts from which to draw parts of a design, and afford him ready 
means of combinations. He will find much in illustrated magazines and news- 
papers, many cuts unpromising as a whole, yet fruitful in suggestions of parts ; 
many an agreeable outline unsatisfactorily filled up ; many that are only valuable 
as showing dimensions requisite for certain uses. But the larger the collection 
the better for the draughtsman ; it will save time to know, as far as possible, 
what has been done, that he may judge what forms and proportions it will be 
best for him to use, and what to avoid. 

It has been our practice to select, from papers and magazines, cuts w^hich 
we considered of value, and arrange them in scrap-books with appropriate 
headings. In the Appendix a few pages of " scraps " are given as illustrations. 



ISOMETRICAL DRAWING. 



Peofessor Farish, of Cambridge, has given the term Isometrical Per- 
spective to a particular projection which represents a cube, as in Fig. 1754. 
The words imply that the measure of the representations of the lines forming 
the sides of each face are equal. 

The principle of isometric representation consists in selecting, for the plane 
of the projection, one equally inclined to three principal axes, at right angles 
to each other, so that all straight lines 

coincident with or parallel to these ^ 

axes are drawn in projection to the 





Fig. 1754. 

same scale. The axes are called iso- 
metric axes, and all lines parallel to 
them are called isometric lines. The 

planes containing the isometric axes are isometric planes ; the point in the 
object projected, assumed as the origin of the axes, is called the regulating- 
point. 

To draw the isometrical projection of a cube (Fig. 1755); draw the horizontal 
line A B indefinitely ; at the point D erect the perpendicular D F, equal to one 
side of the cube required; through D draw the lines D h and D/to the right 
and left, making /D B and ^ D A each equal an angle of 30°. Consequeutly, 
the angles F D/ and FDJ are each equal to 60°. Make D J and D/each 
equal to the side of the cube, and at h and /erect perpendiculars, making ha 
and/e each equal to the side of the cube ; connect F a and F e, and draw eg 
parallel to a F, and a g parallel to F e, and we obtain the projection of the 
cube. 

If from the point F, with a radius F D, a circle be described, and com- 
mencing at the point D, radii be laid off around the circumference, forming a 



ISOMETRICAL DRAWING. 



695 



regular inscribed hexagon, and the points J) aehe connected with the centre 
of the circle F, we have an isometrical representation of a cube. The point D 
is called the regulating -point. 

On page VZ'd, Fig. 255, is shown the 
orthographic projection of a parallelo- 
pipedon on the several planes, and Fig. 
254 the revolution of these planes and 
their cubical representation. Fig. 1756 is 
the representation of the same solid in iso- 
metric perspective, producing nearly the 
same effect. Measures are transferred di- 
rectly from plans and elevations in or- 
thographic projections to those in isom- 
etry. The isometric scale adopted ap- 
plies only to isometric lines, as F D, F a^ 
and F e (Fig. 1755), or lines parallel 
thereto ; the diagonals which are equal to 
each other, and longer than the sides of 
the cube, are the one less, the other greater. 

Understanding the isometrical projec- 
tion of a cube, any surface or solid may be 
similarly constructed, since it is easy to 
suppose a cube sufficiently large to con- 
tain within it the whole of the model in- 
tended to be represented, and, as hereafter 
will be further illustrated, the position of 

any point on or within the cube, the direction of any line, or the inclination of 
any plane to which it may be cut, can be easily ascertained and represented. 

In Figs. 1754 and 1755 one face of the cube appears horizontal, and the 
other two faces appear vertical. If now the figures be inverted, that which 




Fig. 1756. 





Fig. 1757. 



Fig. 1759. 



696 



ISOMETRIC AL DRAWING. 



before appeared to be the top of the object will now appear to be its under 
side. 

The angle of the cube formed by the three radii meeting in the centre of 
the hexagon may be made to appear either an internal or external angle, in 
the one case the faces representing the interior, and in the other the exterior of 
a cube. 

Figs. 1757, 1758, and 1759 illustrate the application of isometrical drawing 
to simple combinations of the cube and parallelopipedon. The mode of con- 
struction of these figures will be easily understood by inspection, as they con- 
tain no lines except isometrical ones. 

To draw Angles to the Boundary Lines of an Isometrical Cube. — Draw a 
square (Fig. 1760) whose sides are equal to those of the isometrical cube A 




40 30 20 /o 
Fig. 1760. 



(Fig. 1761), and from any of its angles describe a quadrant, which divide 
into 90°, and draw radii through the divisions meeting the sides of the square. 
These will then form a scale to be applied to the faces of the cube; thus, on 
D E, or any other, by making the same divisions along their respective edges. 

As the figure is bounded by twelve isometrical lines, and the scale of tan- 
gents may be applied two ways to each, it can be applied therefore twenty-four 
ways in all, affording a simple means of drawing, on the isometrical faces of 
the cube, lines at any angles with their boundaries. 

Figs. 1762 to 1767 show the section of the cube by single planes, at various 
inclinations to the faces of the cubes. Figs. 1768 and 1769 are the same cube, 
but turned round, with pieces cut out of it. Fig. 1770 is a cube cut by two 
planes forming the projection of a roof. Fig. 1771 is a cube with all of the 
angles cut off by planes, so as to leave each face an octagon. Fig. 1772 repre- 
sents the angles cut off by planes perpendicular to the base of the cube, form- 
ing thereby a regular octagonal prism. By drawing lines from each of the 
angles of an octagonal base to the centre point of the upper face of the cube, 
we have the isometrical representation of an octagonal pyramid. 

As the lines of construction have all been retained in these figures, they will 
be easily understood and copied, and are sufficient illustrations of the method 
of representing any solid by inclosing it in a cube. 



ISOMETRICAL DRAWING. 



697 




Fig. 176-^ 



Fig. 1763. 



Fig. 1761. 




Fig. 1765, 



Fig. 17C6. 



Fig. 1767. 




Fig. r, 



Fig. 1769. 



Fig. 1770. 




V 




Fig. 1771. 



Fig. 1772. 



698 



ISOMETRICAL DRAWING. 



In the application of this species of projection to curved lines, let A B 
(Fig. 1773) be the side of a cube with a circle inscribed ; and all the faces of a 
cube are to have similarly inscribed circles. Draw the diagonals A B, C D, and 
at their intersection with the circumference, lines parallel to A 0, B D. Now 



A 






D 


f 




^^-x. 




\ 
/ 


/ 




/ 

\ 




Fig. 1773. 



Fig. 1774. 

draw the isometrical projection of the cube (Fig. 1774), and lay out on the 
several faces the diagonals and the parallels ; the projection of the circle will 
be an ellipse, of which the diagonals being the axes, their extremities are de- 
fined by their intersections /6, e 5, « 2, ^ 1, 6^ 3, c 4, with the parallels ; having 
thus the major and minor axes, construct the ellipse bj the trammel, or, since 
the curve is tangent at the centre of the sides, we have eight points in the 
curve ; it may be put in by curves or by the hand. 

To divide the Circumference of a Circle. — First method : On the centre of 
the line A B (Fig. 1775) erect a perpendicular, D, making it equal to A or 
B ; then from D, with any radius, describe an arc and divide it in the ratio 




Fig. 1775. 



ISOMETRICAL DRAWING. 



699 



required, and draw through the divisions radii from D meeting A B ; then 
from the isometric centre of the circle draw radii from the divisions on A B, 
cutting the circumference in the points required. 

Second method : On the major axis of the ellipse describe a semicircle, and 
divide it in the manner required. Through the points of division draw lines 




Fio. 1777. 



perpendicular to A E, which will divide the circumference of the ellipse in the 
same ratio. On the right hand of the figure both methods are shown in com- 
bination, and the intersections of the lines give the points in the ellipse. 

Fig. 1776 is an isometrical projection of a bevel-wheel, with a half -plan 
(Fig. 1777) beneath, and projected lines explanatory of the method to be 
adopted in drawing the teeth, and of which only half are shown as cut. It 
will be seen, by reference to the second method given above for the division of 
the circumference of a circle, that the semicircle is described directly on the 
major axis of the ellipse. In practice it will be found more convenient, when 
a full drawing is to be made, to draw the semicircle on a line parallel to the 
major axis, and entirely without the lines of the main drawing; and also, as in 
the example of the bevel-gear, complete on the semicircle, or half-plan, the 
drawings of all lines, the intersections of which with circles it will be necessary 
to project on the isometrical drawing. 

Fig. 1778 is an isometrical projection of a complete pillow-block, with its 
hold-down bolts. By reference to Fig. 700 and Figs. 563 and 564, it will be 



700 



ISOMETRICAL DRAWING. 




seen how graphically these forms of gearing are given by isometry. Fig. 1779 
is an isometrical projection of a water-closet cistern with a standard waste. 




Fig. 1779 



ISOMETRICAL DRAWING. 



YOl 




702 



ISOMETRICAL DRAWING. 



Fig. 1780 is an isometrical projection of a culvert, such as were built be- 
neath the Oroton Aqueduct. 

Fig. 1016 is an isometrical view of the overflow and outlet of the Victoria 
and Regent Street sewers in the Thames embankment. 

Fig. 1781 is an isometrical elevation of the roof-truss (Fig. 1151). 

Figs. 1782 and 1783 are the elevation and section in isometry of the district 
school-house given in Figs. 1495 and 1496. To bring the drawing within the 
limits of the page, the scale has been necessarily reduced, but it is given in 
the figure as it should always be, either drawn or written, on all drawings 
to a scale, not intended for mere pictures or illustrations. The section is 
drawn at the height of 8 feet above the base course, and higher than is usual 
in such sections, but it was necessary on account of the extra height of the 
window-sill above the floor, desirable in all school-rooms. Fig. 1783 is more 




Fig. 1781. 



graphic than the plan (Fig. 1496), especially when more detail is to be shown, 
but there is nothing in the present drawing that can not be nearly as well 
shown by the plan; and to a mechanic, for the purposes of construction, the 
plan is the simpler. 

By comparing the elevation (Fig. 1782) with the perspective (Fig. 1799), 
the former appears distorted and out of drawing, but it is much more readily 



ISOMETRICAL DRAWING. 



703 




Fig. 1783. 



T04 



ISOMETRICAL DRAWING. 



drawn, and has this great convenience, that it is drawn to and can be measured 
by a scale on the isometric lines. 

Fig. 1784 is the isometrical projection, of the wave-line principle, of ship 



^ 






S\ 



Fig. 1784. 



construction, from Russell's "Naval Architecture" — as explained and illus- 
trated on pages 545, 546, and 547. 



ISOMETRICAL DRAWING. 



705 










46 



PERSPECTIVE DRAWING. 








The science of Perspective is the representation by geometrical rules, upon 
a plane surface, of objects as they appear to the eye, from any point of view. 

All the points of the surface of a body are visible by means of luminous 
rays proceeding from these points to the eye. Thus, let the line A B (Fig. 
1785) be placed before the eye, C, the lines drawn from the different points 1, 
2, 3, 4, etc., represent the visual rays emanating from each of these points. If 
in the place of a line a surface is substituted, the result will be a pyramid of 
rays. 

The greatest angle under which one or more objects can be distinctly seen 
is one of 90°. If between the object and the eye there be interposed a trans- 
parent plane, the intersections of this plane with the visual rays are termed 

perspectives of the points from which the 
B rays emanate. In the operations of projec- 
tion, several important planes are employed 
in perspective, as : 

1. The horizontal plane A B (Fig. 1786), 
on which the spectator and the object viewed 
are supposed to stand, for convenience sup- 
posed perfectly level, is termed the ground 
plane. 

2. The plane G N, which has been con- 
sidered as a transparent plane placed in front 
of the spectator, on which the objects are 

delineated., is called the plane of perspective or the plane of the picture. The 
intersection G L of the first and second planes is called the line of projection, 
the ground., or base line of the picture. 

3. The plane E F passing horizontally through the eye of the spectator, and 
cutting the plane of the picture at right angles, is called the horizontal plane, 
and its intersection at D D with the plane of the picture is called the horizon 
line., the horizon of the picture, or simply the horizon. 

706 




Fig. 1785 



PERSPECTIVE DRAWING. 



TOY 



4. The piano S T passing vertically through the eye of the spectator, and 
cutting each of the other planes at a right angle, is calleel the central plane. 

Point of vie?v, or point of sight, is the point where the eye is supposed to 
be placed to view the object, as at C, and is the vertex of the optical pyramid. 
Its projection on the ground plane at S is termed the station point. 









^ 






T 


r ( 


x^ 




D 






,. — 




V, .--''' 




^ 


^^ 




^ 




^y- 


^^^ 


D 








B 


,.--' 




,.' '' 


^ 




^'^ ^^ 



Fig. 178 



The projection of auy point on the ground plane is called the seat of that 
point. 

Centre of vieic, or centre of, picture (commonly, though erroneously, called 
the point of sight), is the point V where the central vertical line intersects the 
horizon line ; a line drawn from this point to the eye would be in every way 
perpendicular to the plane of the picture. 

Points of distance are points on the horizon as remote from the centre of 
view as the eye. 

Vanishing points are points in a picture to which the perspective of all 
lines converge that in the original object are parallel to each other. 

The vanishing point of any line or system of parallel lines is found by pass- 
ing a line through the point of sight parallel to the given line, or system of 
lines. Its intersection with the plane of the picture will be the vanishing 
point desired. Therefore the vanishing points of all horizontal lines lie on the 
horizon, and the vanishing points of horizontal lines making an angle of 45° 
with the ground line are at the points of distance. 

Parallel Perspective. — An object is said to be seen in parallel perspective 
when one of its sides is parallel to the plane of the picture. 

Angular Perspective. — An object is said to be seen in angular perspective 
when none of its sides are parallel to the picture. 

The vanishing points of all lines parallel to the plane of perspective are at 
infinity, or, in other words, such lines have no vanishing points. 

The perspectives of lines paralld to the perspective plane are parallel to 
their projections on that plane. 

The process of finding the perspective of lines, plane figures, and solids 
consists merely in finding the perspectives of established points and connecting 
them. 

To find the Perspective of Two Squares i?i the Ground Plane whose Sides 



708 



PERSPECTIVE DRAWING. 



are Parallel and Perpendicular to the Perspective Plane (Fig. 1787). — Let G L 
be the ground line, ah d c and e f h g the horizontal projections of the two 
squares; S' is the horizontal, and S the vertical projection of the point of 
sight \ ab in the ground line is the vertical projection of the two squares. 




Fig. 1787. 



Fig. 1788. 



Draw a S and h S ; these will be the indefinite perspectives of the sides of 
the squares perpendicular to the perspective plane. Draw h S' ; where this 
line intersects the ground line, project it vertically to h^, on b S, which is the 
perspective of h ; the line g h^ being parallel to the perspective plane, is parallel 
to the ground line, and is shown at g^ h^- In the same way e^ /i and Cj di are 
found. The perspectives of the diagonals are the lines connecting the corners. 

The line ab \^ in the perspective plane, and is its own perspective. All 
lines or plane figures lying in the perspective plane appear in perspective in 
their true form and size. 

To find the Perspectives of Two Cubes whose Sides are Parallel and Perpen- 
dicular to the Perspective Plane (Fig. 1788). — a b c d is the vertical, and a' b' 
o' n' and/' e' h' g' the horizontal, projections of the cubes. Draw a S, Z> S, c S, 
and d S. These will be the indefinite perspectives of the edges of the cubes 
perpendicular .to the perspective plane. Draw S' g' ; where this strikes the 
ground line, project to r^ and ^^ on S « and S d^ which will be the perspectives 
of the two corners horizontally projected at g' and vertically projected at a and 
^) di ^hi drawn parallel to the ground line and limited by S c and S a, is the 
perspective of g' h'. In a similar manner the perspectives of all other points 
and edges are found. 

From the drawing of a square in parallel perspective, we deduce rules for 
the construction of a scale in perspective. Let D G L D (Fig. 1789) be the 



PERSPECTIVE DRAWING. 



709 



plane of the picture. From S' lay off the distance o S' equal to some unit of 
measure, as may be most convenient ; from o draw the diagonal to D the point 




o s" 

Fig. 1789. 



of distance ; now draw 1 1' parallel to the ground line G L, again draw from 1' 
the diagonal 1' D, and lay off the parallel 2 2', proceed in the same way with 
the diagonal 2' D and the parallel 3 3', and extend the construction as far as 
may be necessary. It is evident o S' 1 1', 1' 1 2 2', 2' 2 3 3' are the perspective 
projections of equal squares, and therefore o S', 1 1', 2 2' 3 3', etc., and S' 1, 
1 2, 2 3, etc., are equal to each other, and that if o S' is set off to represent any 
unit of measure, as one foot, one yard, or ten feet, etc., each of these lines 
represents the same distance, the one being measured parallel to the base line, 
the others perpendicular to it. In making a perspective drawing a scale thus 
placed will be found convenient ; which in the centre of the picture might 
interfere with the construction lines of the object to be put in perspective, is 
better transferred to the side of the picture « G o, the diagonals to be laid off 
to a point to the right of D equal to the point of distance. 

The scales thus projected are for lines in the base or ground plane ; for lines 
perpendicular to this plane the following construction is to be adopted : Upon 
any point of the base line removed from S', as «, for instance, erect a perpen- 
dicular, a d; on this line, lay off as many of the units o S' as may be necessary ; 
in this example three have been laid off, that is, a d = 3 o S'. From a and d 
draw lines to the centre of view, and extend the parallels 1 1', 2 2', 3 3'; at the 
intersection of these lines with a V erect perpendiculars. The portions com- 
prehended between the lines a V and d V will be the perspective representa- 
tions of the line a d, in planes at distances of 1, 2, 3, o S' from the base line, 
and as b, c, d are laid off at intervals equal to o S', by drawing the lines c V 
and b V nine equal squares are constructed, of which the sides correspond to 
the unit of measure o S'. 

7'ojind the Scale for the Perspective of any Line Obliqite to the Perspective 
Plane (Fig. 1790). — Let A B be the perspective of any line oblique to the 
perspective plane and V its vanishing point ; through the extremity A draw any 
line A 7 ; divide it into as many parts as is desired to divide the perspective 
line A B, here seven. Draw 7 B. Connect the remaining points 6, 5, 4, etc., 
withV; where these lines intersect the line 7 B they are projected on A B, par- 
allel to A 7. The divisions A 6*, 6" b"^ etc., are the perspectives of the seven 



no 



PERSPECTIVE DRAWING. 



,^v: 



X. 



equal divisions of A B. If the line A B is fourteen feet long, the divisions 
A e'\ 6'[ b% 5" 4:" are each equal to two feet. 

To find the Perspective of a Hexagonal Prism with a Pyramidal Top (Fig. 

1791). — The perspective plane 
\ in the original position is a pro- 

file plane; ah fie is the verti- 
cal and c' y Cq dd e' d' the hori- 
zontal projection of the figure. 
M N is the profile perspective 
plane in which the edge of the 
prism e i lies. S is the vertical 
and S' the horizontal projection 
of the point of sight. Draw rays 
of light at S a; and S' a', S c, 
S' c', S d, S' d', etc. These rays 
pierce the profile perspective plane at points a^ c^ di, etc. 

All the points in sight being thus fixed, the profile perspective plane is then 
transferred to the position Mj Nj and revolved about its vertical trace into the 
plane of the paper. Thus, the point projected at a" and a', the perspective of the 
point originally projected at a and a' is transferred to a'" and revolved to a'^, which 



4C 



Fig. 1790. 





Fig. 1791. 



is its final position. All other points are treated in the same way. The edge e i 
lying in the perspective plane is the same length in perspective as in projection. 

The transposition of the profile plane from M IST to Mi Nj is only necessary 
to avoid complicating the perspective with the projections. 

Method of Perpendiculars and Diagonals^ to find the Perspective of a Pave- 
ment in Parallel Perspective (Fig. 1792). — a b d c is the pavement, the square 
blocks running diagonally across it. 



PERSPECTIVE DRAWING. 



ni 



The projection of the pavement being revolved so as to appear below the 
ground line, diagonals drawn through points of it to the right will vanish in 
the point of distance to the left and vice versa. 



s 



D. 



r---^- 






G ^r < - 





f Y 



Fig. 1792. 



Fig. 1793. 



The sides of the pavement, being perpendicular to the perspective plane, are 
their own perpendiculars. Thus S a and S l are their perspectives. The lines of 
division of the blocks, being at 45°, are their own diagonals and vanish at D and D^. 

To find the Perspective of a Cube in Parallel Perspective (Fig. 1793), aide 
is the horizontal projection of the cube. The face a b f e being in the plane 
of perspective, appears in full size. From the point c the diagonal c x disap- 
pears at Di, and the perpendicular at S. Their intersection C2 is the perspective 
of the lower corner ; c?2 is found in the same way ; c and d are found by pro- 
jecting up vertically from Cg and dz and intersecting S e and S /, or they could 
be found by constructing diagonals in the plane Y Y of the top. 

To find the Perspective of the Frustrum of a Right Square Pyramid by Per- 




s 

Fig. 1794. 



712 



PERSPECTIVE DRAWING. 



pendiculars and Diagonals (Fig. 1794). — a h c d\^ the horizontal projection of 
the base and efgh of the top of the pyramid. The point of sight is projected 
at S' and S ; D and Dj are the points of distance. 

The perspective of each point is found by drawing its perpendicular and 
diagonal and fixing the intersection of their perspectives. The perpendiculars 
and diagonals must lie in their proper plane. Thus those at the top of the 
pyramid must be projected up to the plane s t. 

To find tlie Perspective of a Horizontal Circle (Fig. 1795). — To find the per- 
spective of any curve it is merely necessary to find the perspectives of enough 




Fig. 1795. 



Fig. 1796. 



points on it to enable the perspective curve to be traced through them \ a g e c 
is the horizontal circle. Take any number of equidistant points on it, as a h c^ 
etc. Their perspectives are found by the usual method of perpendiculars and 
diagonals at a^ h^ Ci, etc. The curve traced through these perspective points is 
the perspective of the circle. This curve is an ellipse. 

To find the Perspective of a Circle in a Profile Plane (Fig. 1796). — a' h' is the 
horizontal and e d the vertical projection of the circle. As before, a number of 
points are taken on the circle, the location of these points on the horizontal 
and vertical projections of the circumference are found by revolving the cir- 
cle about its horizontal diameter parallel to the horizontal plane of projection. 
The vertical distance of all points on the circumference from the diameter a' li* 
are thus ascertained and set oif on the vertical projection of the circle. 

M M, N N, 0, P P, and Q Q are the vertical traces of the horizontal 
planes in which the points taken lie. Perpendiculars and diagonals drawn 
from these points and carried up to get the points in the correct planes give 
ax Cx dx ^1, etc., as the perspective of the circle. 

The projection of the circle is only necessary to give the height above the 
ground line of the planes M M, N N, etc., in which lie the points taken on the 



PERSPECTIVE DRAWING. 



713 



circle. Had the circle been in any vertical plane other than a profile plane, the 
mode of proceeding would have been the same. 

To find the Perspective of a Cylinder whose Axis is Horizontal and at an 
Angle of 4J)° with the Perspective Plane (Fig. 1797). — a ejfis the horizontal 







Fig. 1797. 



S^ 



Fig. 1798. 



projection of the cylinder. The base/y is revolved parallel to the horizontal 
plane and shown at s f h" j and equidistant points taken on it. Set off above 
the ground line the heights s t,s h,s ti, and s h" and draw horizontal lines 
through them. These lines will be traces on the perspective plane of horizontal 
planes passing through the assumed points and corresponding points on the other 
base. Then finding the perspectives of diagonal and perpendicular lines passing 
through these points, the perspectives of corresponding points on the bases 
through which the perspective curves can be drawm. 

To find the Perspective of an Octagonal Prism with its Axis Horizontal and 
making an A?igle of Jf5° with the Perspective Plane (Fig. 1798). — a d h e is the 
horizontal projection of the prism. M M, N N, and are the traces on the 
perspective plane of the horizontal planes containing the edges of the prism. 
The perspectives of the points abed, etc., from the perspectives of the edges 
yanishing at D^ and of the perpendiculars vanishing at S. The intersections 
/of these perspectives give the points desired. 

To draiu the Elevation of a Building in Angular Perspective (Fig. 1799). — 
The plan of the two sides which 'are to appear in perspective are drawn, all 
openings, projections, and roof plan being indicated. This plan, c, «, 5, is 
placed at the top and about the centre of the drawing board in any desired 
position ; a line P P', known as the picture plane or plane of measures, is drawn 
of indefinite length. For convenience in measuring heights it is usual, though 
not necessary, to draw P P' through the point a of the building. 



(/ Th 



714 PERSPECTIVE DRAWING. 

The station point S is selected, largely a matter of judgment, and lines 
drawn through S parallel to the sides of the building and intersecting the pic- 
ture plane at P P' ; from P and P' perpendiculars are dropped of indefiiiite 
length ; the ground line G L, parallel to P P', is drawn at any convenient place^ 
and the horizon drawn parallel and about six feet above, and intersecting the 
perpendiculars at V V, the vanishing points, all lines parallel to a c vanishing 
at V and those parallel to a b a,t Y' ; lines are drawn from all points in the 
plan which are to appear in the perspective to S intersecting P P' and then 
transferred by vertical lines to the portion of the paper reserved for the per- 
spective drawing ; the horizontal measures are thus obtained. For the vertical 
ones the sides of the plan a c and a b are extended till they cut P P' ; at d and e 
perpendiculars are dropped from these points which are lines of heights. Ele- 
vations drawn to the same scales as the plan are placed to the right and left 
of space reserved for the perspective on G L ; heights are transferred from the 
elevation on the left to line of heights e e' and vanish at V, heights on the 
right to d d' and vanish at V. The remaining lines and filling in of details 
will be understood from the drawing. 

Fig. 1800, the building sketched on page 592, is shown in angular perspec- 
tive. The general construction will be understood from the description of Fig. 
1799, the same letters being used to describe similar lines. Additional lines of 
measures must be taken where there are recesses, projections, chimneys, etc., to 
locate. Thus, take the chimney/; the line of heights for this is obtained by 
continuing the line of chimney till it intersects P P' at /', a perpendicular is 
dropped from this point, and the height transferred to this line from the eleva- 
tion ; a vanishing point drawn from this intersection to V intersects the hori- 
zontal limits of the chimney and gives the height; the bay window similarly. 

At page 906 is a general diagram showing the principal constructive lines 
necessary in rendering a building in perspective. 

Fig. 1800 A illustrates a method whereby the orthographic plan is dispensed 
with and a perspective plan substituted, from which the vertical lines and hori- 
zontal measures may be taken directly. 

The horizon, vanishing points, and point of sight are determined as in the 
previous examples. Describe arcs from the vanishing points through the point 
of sight. The intersection of these arcs with the horizon are the points of dis- 
tance. A line of measures is taken parallel to and at any convenient distance 
above or below the horizon, and a point, indicating the corner of the building, 
located where desired on it ; to the right and left of this point the horizontal 
measures of the two sides of the building are laid off to scale ; from the corner 
of the building to each vanishing point lines are .drawn representing the sides 
of the plan. The extreme limits of the building laid off on the line of meas- 
ures vanish at the points of distance ; that to the left of the corner to the point 
of distance to the right, and vice versa. Where these lines intersect the sides 
of the building are the limits of the perspective plan. These lines may then be 
transferred by perpendiculars to the perspective elevation. 

The perspective plan described above is shown on a larger scale in Fig- 
1800 B, the dimensions of the doors and windows of the plan being laid off on 
the line of measures and carried to their respective points of distance as de- 
scribed in obtaining the perspective limits of the building. 



PERSPECTIVE DRAWING. 



715 



;-= ':q 




^ ' -^ -' ^ 




I 
I 





716 



PERSPECTIVE DRAWING. 



To draw in Parallel Perspective tlie Interior of a Room. (Fig. 1801). — Let a 
h c d\)Q the plan of the room. A line P P', known as the picture plane of meas- 




oint of Si^ht 



Fig. 1800.— a. 




Fig. 1800.— B. 

• 

ures, is drawn far enough forward to include all that is desired to be shown in 
perspective and usually parallel to the rear of the room. S is taken outside the 
room and as far away from the plan as the size of the board will admit of. In 
this example S has been taken to the right of the centre of the room ; if taken 
in the centre, the perspective would be symmetrical. The points a and d of the 
plan subtend the greatest angle, which should never be over 60°. The same 
may be said of the vertical angle, a greater angle causing distortion. Dotted 
lines show rays from various points intersecting P P' and establishing the posi- 
tion of the vertical lines. The ground line G L is drawn parallel to P P', and 
the horizon drawn at a suitable elevation. A perpendicular erected at S and 
intersecting the horizon at V gives the vanishing point for all lines parallel to 
a h and d c. Vertical heights are laid off on either a a' or d d\ and transferred 
to their proper position in the perspective. 

To draio an Arched Bridge in Angular Perspective. — Let A and B (Fig. 
1802) be the plans of the piers ; on the line a p, one of the sides of the bridge, 
lay down the curve of the arch as it would appear in elevation, in this example 
an ellipse. Divide the width of the arch as at § c 6? e/^ A, carry up lines per- 
pendicnlar io h h until they intersect the curve of the arch, and through these 
points draw lines parallel to ^ ^ as y^ / and m ; let o r be the height of the para- 



PERSPECTIVE DRAWING. 



717 




T18 



PEBSPECTIYB i DRAWING. 



pet of the bridge above the spring of the arch. Through the station point 
draw lines parallel to the side a h and end a aoi the bridge, till they intersect 




Fig. 1801. 



the assumed base line M M ; project these intersections to the horizon line of 
the picture for the vanishing points D, D' of perspective lines parallel io a h 
and a a. Let fall a perpendicular from a to a\ and on this perpendicular set 
off from a' the heights s k, s I, s m, and s r ; from a' and r' draw lines to D and 
D', and from the points m\ I', Jc' to D'. Draw rays from the points ah cdef ff 
h to the station point S, and project their intersection with the base lines to the 
perspective line a' D' as in previous examples ; the intersection of the lines ¥ 
D', /' D', m! D' by the perpendiculars thus projected will establish the points 



PERSPECTIVE DRAWING. 



719 



of the curve of the arch on the side nearest the spectator. To determine the 
position of the opposite side of the arch, from a!\ the perspective of the corner 
of the pier a" draw a" D', and from It' draw lines to D ; the line li' p' will be 




Fig. 1802. 



the perspective width of the pier ; draw k^ D ; and from ^", h" D' ; from ^" 
the intersection of the curve of the arch by the perpendicular to g\ draw g' D, 
the intersection with k" D' will be one point in the curve of the arch on the 
opposite side of the bridge ; in the same way, from any point in the nearer 
arc draw lines to D, and the intersection with lines in the same planes on the 
opposite side of the bridge will furnish points for the further arch ; all below 
the first only will be visible to the spectator. 

To draw in Perspective a Flight of Stairs (Fig. 1803). — Lay off the base 
line, horizon, centre of view, and point of distance of the picture ; construct 
the solid a h c d^ e f g h^ containing the stairs, and in the required position in 
the plane of the picture ; divide the rise a c into equal parts according to the 
number of stairs, nine, for instance ; divide perspectively the line a h into one 
less (eight) number of parts ; at the points of division of this latter erect per- 
pendiculars, and through the former draw lines to the centre of view ; one will 
form the rise and the other the tread of the steps. From the top of the first 
step to the top of the upper continue a line a d^ till it meets the perpendicular 
S' V prolonged in v ; this line will be the inclination or pitch of the stairs ; if 
through the top of the step at the other extremity a similar line be drawn, it 



720 



PERSPECTIVE DRAWING. 



will meet the central perpendicular at the same point v^ and will define the 
length of the lines of nosing of the steps, and the other lines may be completed. 




Fig. 1803. 

As the pitch lines of both sides of the stairs meet the central vertical in the 
same point, in like manner v will be the vanishing point of all lines having a 
similar inclination to the plane of the picture. The projection of the other 
flight of stairs will be easily understood from the lines of construction perpen- 
dicular to the base line or parallel thereto, lying in planes. 

To find the Rsfiection of Objects in the Water. — Let B (Fig. 1804) be a cube 
suspended above the water ; find the reflection of the point a by letting fall 
a perpendicular from it, and setting off the distance a' lo below the plane of 
the water equal to the line a lu above this line ; the line lu f will also be equal 



D 

....... 


s^ 












Fig. 1804. 



PERSPECTIVE DRAWING. . 721 

to the line w/; find in the same way the points h' and e\ through these points 
construct perspectively a cube in this lower plane, for the reflection of the cube 
above. 

To find the reflection of the square pillar D removed from the shore : sup- 
pose the plane of the water extended beneath the pillar, and proceed as in the 
previous example. 

The lines of an object which meet in the centre of view Y, in the original, 
have their corresponding reflected lines converging to the same point. If the 
originals converge to the points of distance, the reflected ones will do the same. 
To find the reflection of any inclined line, find the reflection of the rectangle 
of which it is the diagonal, if the plane of the rectangle is perpendicular to 
the plane of the picture. If the line is inclined in both directions inclose it in 
a parallelepiped and project the reflection of the solid. 

To find the Perspective Projection of Shadoius (Fig. 1805). — Let the con- 
struction points and lines of the picture be plotted. Let A be the perspective 
projection of a cube placed against another block, of which the face is parallel 
to the plane of the picture : to find the shadow upon the block and upon the 
ground plane, supposing the light to come at such an angle as to cause the 
projections of it (both vertical and horizontal) to make an angle of 15° with 
the ground line. Since the angle of light is the diagonal of a cube, construct 
another cube similar to A, and adjacent to the face leg; draw the diagonal 
b ^, it will be the direction of the ray of light, and k will be the shadow of b ; 
connect/^ and ck^fk must be the shadow of the line bf^ and ck oi b c\ the 
one upon the horizontal plane and the other in a vertical one : the former will 
have its direction, being a diagonal, toward the point of distance D', the other 
being a diagonal in a plane parallel to that of the picture, will be always pro- 
jected upon this plane in a parallel direction. 

Let B be a cube similar to A ; to find its projection upon a horizontal plane, 
the shadow of the point V may be determ^'-'^ed as in the preceding example, but 
the shadow of the point c\ instead of falling upon a plane parallel to the pic- 
ture, falls upon a horizontal one; its position must be determined as before 
by b. Construct the cube and draw the diagonal r' / ; in the same way deter- 
mine the point m the shadow of d' ; connect c k' I m /?, and for the shadow of 
the cube in perspective on a horizontal plane. 

On examination of these projected shadows, it will be found that as the 
rays of light fall in a parallel direction to the diagonal of the cube, the vanish- 
ing point of these rays will be in one point V on the line D' L, prolonged, at 
a distance below D' equal V D' ; and since the shadows of vertical lines upon a 
horizontal plane are always directed toward the point of distance, the extent of 
the shadow of a vertical line may be determined by the intersection of the 
shadow of the ground point of the line by the line of light, from the other ex- 
tremity. Thus, the point k, cube A, is the intersection of /'D' by b\' ; the 
points k\ Z, m are the intersections of c D', o D', nJ)' by b' \\ c'Y' d'\'. 
Similarly on planes parallel to that of the picture, ^', cube A is intersection of 
the diagonal c k, by the ray of light b V. 

Applying this rule to the frame C, from ;•, 5, jt?, draw lines to D' ; from r\ 
s\ p\ draw rays to V ; their intersections define the outline of the shadow of 
the post. To draw the shadow of the projection, the shadow upon the post 



722 



PERSPECTIVE DRAWING. 




PEKSPECTIVE DRAWING. 



723 




724 



PERSPECTIVE DRAWING. 



from t will follow the direction of the diagonal c Ic. Project u and v upon the 
ground plane at u' and v' ; from t u' v' and j9 draw lines to D' ; from i\ u^ v, lu^ 
and X draw rays to V, and the intersection of these lines with their corre- 
sponding lines from their bases will give the outline required ; as v and w are 
on the same perpendicular, their rays will intersect the same line v' V. 

With reference to the intensity of " shade and shadow," and the necessary 
manipulation to produce the required effect, the reader is referred to the article 
on this subject. 

In treating of Perspective it has been considered not from an artistic point, 
as enabling a person to draw from Nature, but rather as a useful art to assist 
the architect or engineer to complete his designs, by exhibiting them in a 
view such as they would have to the eye of a spectator when constructed. Our 
examples, owing to size of the page, have been limited in the scale of the 
figures, and in the distance of the point of view, or distance of the eye from 
the plane of the picture, unimportant to the mathematical demonstration. It 
is unnecessary in these particular points that the examples should be copied. 
The most agreeable perspective representations are generally considered to be 
produced by fixing the angle of vision at from 45° to 50°, and the distance of 
the horizon above the ground-line at about one third the height of the picture. 

In the early edition of this work there were illustrations of machinery on 




Fig. 180r. 

sale in a kind of perspective, of which two, Figs. 1806 and 1807, specimens of 
ship work, a windlass and centreboard winch, are reproduced. They are 
graphic and natural in appearance, and similar illustrations will be found in 
the collection of " Scraps." 

With the introduction of photography and the ready transfer of the nega- 
tives to the positive and permanent condition of prints and plates, one is 
enabled to judge of sizes and dimensions from their surroundings, or by the 
introduction into the view of appropriate marks or bounds of known distance 



PERSPECTIVE DRAWING. 



T25 



affording lines for measures. In fact, photography has been applied to surveys 
with records of angles and topographical views of lines. Views of buildings, 
circulars of machinery, and objects on sale or of interest are illustrated by the 
aid of photography. The figure below represents the office of the publishers 
of this work taken by photography, printed on plain salted paper. The pen- 
work is done in water-proof ink on the photograph ; the print is then washed 
in a chemical solution, removing the photographed lines and leaving those in 
ink. (See Free-Hand Drawing.) 




FREE-HAND DRAWING. 

A DRAUGHTSMAN^, who has made himself conversant with the rules of pro- 
jection as laid down in the preceding pages, and has applied these rules to prac- 
tice, will be capable of representing correctly such objects as have been illus- 
trated, or make up similar combinations of his own invention and design for 
the comprehension of others. But natural objects, as animals, trees, rocks, 
clouds, etc., can not be imitated on paper with the aid of drawing instruments ; 
outlines so varied can not be copied in this mechanical way ; it can only be done 
by hand drawing, an educated eye that can recognise proportion and position, and 
an educated hand that can execute and portray naturally things recognised by 
the eye, with the aid of pencil, pen, crayon, bruslvor the various tools-that now 
obtain with draughtsmen. But it is by education that one acquires the facili- 
ties of such an eye and hand. As the writer acquires facilities by the copying 
of pothooks, letters, and flourishes which may develop into a valuable distinct- 
ive hand, so the draughtsman by the study of examples, first of drawings and 
copying, the learning of proportions, comparison of the works of different art- 
ists, observations of effect in drawing and nature, will commence an education 
which will produce pleasant and successful pictures distinctive of the educated 
artist, appreciated by the public and of mercantile value. 

An educated free hand adds largely to the effect on most drawings, where 
close measures are not requisite, giving grace and beauty to mechanical designs, 
and is especially applicable to architectural ornaments and accessories. It will 
be found impossible to draw many of these in any other way, and there are few 
drawings that do not require some patching by hand — short curves, which can 
be thus done much more readily, and connections of lines, which can not be 
done by drawing instruments. 

The pencil or pen should be held by the thumb and first finger, and sup- 
ported and guided by the second. The two fingers touching the pencil should 
be placed firmly on it, and be perfectly straight, the end of the middle finger 
at least one inch above the point of the pencil. In drawing, it is well to com- 
mence, as in writing, with straight lines. Lines vertical, horizontal, and in- 
clined, parallel to each other and at angles, light and strong — short and long 
lines, straight and curved, with pen, pencil, or crayon on paper, or chalk on 
a board. Dot points, and draw lines between them, at a single movement, 
without going over them a second time, and without patching. Besides 
direction, lines have a definite length, and the draughtsman must practise 
himself in drawing lines of equal lengths, or in certain proportions to each 
other. 

726 



FREE-HAND DRAWING. Y27 

Lines equal to each other : 



Lines twice another line : 



Divide a line into any number of equal jiarts : 

I I I i I 



The accuracy of these divisions may be tested by a strip of paper applied 
along the line, marking off the divisions upon it, and then slipping it along 
one division, and noting if the divisions on the paper and line still agree. By 
practice, the eye will be able to make these divisions almost accurately. Having 
acquired this skill, apply it to the construction of the Geometrical Problems, in 
the earlier part of the book, in their proper proportions, both in straight and 
curved lines. The construction should be dependent entirely on eye and hand ; 
but it will be found, whether the draughtsman draws from copy or nature, that it 
is almost impossible to get along well without defining positions by some points 
in the pictures, and sketching in some defined lines which may serve as guides. 

Following this practice of guide lines, it will be well to copy the outlines of 
architectural mouldings, of which most of the ornaments are conventional rep- 
resentations of natural objects. 

At page 60 will be found an application to the drawing of acanthus leaves 
within the guiding lines of squares and the designing for calicoes and woven 
goods, oilcloths, ceiling, and wall ornamentation based on geometrical figures. 

In such designs " a true artistic end has been accomplished when w^ell-ob- 
served features of natural objects have been chronicled within the convention- 
alized limits of a few geometric rules that include proportion, symmetry, and 
a proper subordination of one part to another." 

To acquire still further readiness in free hand, extend the practice to " let- 
tering. " 

Material. 

Pcqnr. — The different papers manufactured by Whatman are excellent for 
sketching purposes, and can be purchased either in sheets or in pads of various 
sizes. Any toothed paper answers the purpose very well, such as common new^s- 
paper ; a sketching paper with either a rough grain or a canvas grain may be 
made by pinning a sheet of thin typewriting paper over a piece of sandpaper 
or a canvas book in the same manner. 

For pen-and-ink work a hard, unyielding surface is needed ; nothing an- 
swers the purpose as well as the best quality of Bristol board, although excel- 
lent results are obtained on Whatman's H. P. (Hot Pressed) paper. 

Pencils. — Faber's or Dixon's pencils of medium hardness are best for sketch- 
ing, but for drawing on Bristol board the harder grades are better. 

Lithographic chalks are now coming into use ; they are much superior to 
the ordinary chalks, crayons, and charcoal in their not being readily smeared. 
They find their best medium in .Whatman's paper, either H. P. or "not," and 
in grained scratch-out cardboards they give greater intensity than lead pencil, 
and reproduce with more certainty. Of course they can not be used where 
much detail is required, but for generalities they are excellent. 

Pens. — The use and selection of pens must be left largely to the draughts- 
man's own judgment. The ordinary school pen is excellent ; Gillott's 303, or 



728 FREE-HAND DRAWING. 

the same maker's mapping pens, are also good. The amateur is cautioned 
against the diminutive crow quill and lithographic pens; the pen is merely a 
secondary matter, some illustrators doing excellent work with a brush used as 
a pen, a reed pen, a toothpick, or, indeed, with anything that happens to be 
at hand. 

Jnh. — The best ink for reproductive purposes is India ink ; that which has 
a dull appearance when dry is the best for this purpose ; India ink can be pur- 
chased in the stick and ground down with water or ready prepared in bottles, 
either waterproof or otherwise. 

The first step in free-hand drawing is its application to simple objects, of 
which one must learn to determine the relative proportion of their parts and to 
lay them down on paper in their proper position and this entirely by eye. Hav- 
ing thus drawn one object, one proceeds to increase the group of objects. As 
has been shown in " Perspective," objects appear smaller as they are more re- 
mote from the spectator, who must know how much the relative scale is changed, 
not only in objects remote from each other, but also as to what parts of objects 
can be seen and how they are seen. The rules of perspective give an idea of 
what can be seen and the proportions, and serve to make the eye intelligent in 
its observations to be confirmed and strengthened by practice. 

In drawings of the human frame there are numerous charts and rules which 
may be said to be established which may assist the learner in fixing the form 
and proportions of parts within certain classical or'normal limits. Outlines 
from these charts may be traced for a brief time by the learner to acquire ideas 
of the forms, proportions, and positions when at rest ; but when in action limbs 
are moved, muscles increase under action, and the parts present different lines 
of sight which must be studied by themselves. Although the length of limbs 
is not increased, it may be more or less foreshortened. 

" Proidortions of the Human Frame.'''' By Joseph Bonomi. 

The following, with the illustrations, are taken from the above work : 

" The human frame is (Figs. 1808 and 1809) divided into four equal 
measures, by very distinctly marked divisions on its structure and outward 
form : 

" 1. From the crown of the head to a line drawn across the nipples. 

" 2. From the nipples to the pubes. 

" 3. From the pubes to the bottom of the patella (knee-pan). 

" 4. From the bottom of the patella to the sole of the foot. 

" Again, four measures, equal in themselves, and equal to those just de- 
scribed, and as well marked in the structure of the human body, are seen when 
the arms are extended horizontally. They are the following : 

" From the tip of the middle or longest finger to the bend of the arm is 
one fourth of the height of the person. 

" From the bend of the arm to the pit of the neck is another fourth. 

" These two measures, taken together, make the half of the man's height, 
and with those of the opposite side equal the entire height. 

" In the figures, the differences in width between the male and female figures 
are given from the tables of the Count de Clarac of the Apollino and the Venus 
de Medici. The male figure is in thicker line than the female, and the measure- 



FREE-HAND DRAWING. 



729 



ments referring to it are on your right hand, and those referring to the female 
on your left. 

" The measurements of length, according to Vitruvius and Leonardo da 
Vinci, are the same in both sexes, and expressed in long horizontal lines run- 
ning through both the front and profile figures. 




"Almost innumerable are the varieties of character to be obtained by the 
alterations of widths, without making any change in the measurements of 
length ; nevertheless, some ancient statues differ slightly in these measurements 
of length. 

" No measurement is given in the figure of the width of the foot ; its normal 



'30 



FREE-HAND DRAWING. 



proportion should be one sixteenth of the height. The views of the foot are 
those of the female. 

" The. scale, V, used is 8 heads to the height ; parts, ^ of a head ; and min- 
utes, ^2 ^^ ^ part. 




" The whole height is usually taken at 8 heads, but there are slight differ- 
ences in the classic statues ; the height of the Venus de Medici is equal to 7 



FREE-HAND DRAWING. fj^i 

heads, 3 parts, 10 minutes, that of the Apollino of Florence, 7 heads, 3 parts, G 
minutes. 

" When the student is acquainted with the forms of the body and limbs in 
two aspects — viz., the front and side views — and the normal pro^^ortions they 
bear to each other, then will follow the study of the characteristic features of 
childhood, youth, and mature age, and those niceties of character that the 
ancients invariably observed in the statues of their divinities, so that in most 
cases a mere fragment of a statue could be identified as belonging to this or 
that divinity — as, for instance, the almost feminine roundness of the limbs of 
the youthful Bacchus, the less round and distinctly marked muscles of the 
Mercury, and of the statues of the Athletse." 

Fig. 1811 is a half-tone reproduction of a photograph showing three views 
of a plaster model, ecorche — i. e., the body with the skin removed, showing the 
muscles. In the half-tone process a ruled screen of glass is interposed between 
the drawing or object to be photographed and the negative. The screen of 
glass is closely ruled with lines crossing at right angles and etched with hy- 
drofluoric acid ; into the grooves thus produced printing ink is rubbed. It is 
these lines which produce the crisscross appearance seen in the resulting pic- 
ture. This process is commonly used in reproducing wash drawings and pho- 
tographs. 

Figs. 1812, 1813, and 1814 are three views of the above figure drawn in line. 
A large negative was taken and the print made on " plain salted paper " — that 
is, paper prepared without albumen, which gives to the ordinary print its glossy 
appearance. This paper is made by being soaked in a solution of 

Chlorate of ammonia 100 grains ; 

Gelatin , 10 " 

Water 10 ounces. 

The figures thus made may now be drawn in with pen and water-proof India 
ink. The pen work should not attempt the fulness of detail given in the pho- 
tograph. When the drawing has been finished it may be immersed in a solution 
composed of 1 ounce of bichloride of mercury dissolved in 8 ounces of water, 
which removes all trace of the photograph, leaving the drawing uninjured on 
white paper. Omissions may now be supplied, but if there are any conspicuous, 
the photograph may again be brought out by immersing in a solution of hypo- 
sulphite of soda in water. 

A readier way is to draw with water-proof ink upon photographs printed on 
ferro-prussiate paper or blue print paper, the directions for making which will 
be found on page 52, or it can be purchased. It can then be sent for reproduc- 
tion as it is, as the blue will not photograph, or the blue may be bleached by 
immersing the print in a dish of water in which a small piece of washing soda 
has been dissolved; then wash the 'print in clean water. 

Both pen drawing and oj)aque water colour can be used on the ordinary 2)ho- 
tograph by mixing a small j)iece of ox gall with the liquid. 

Figs. 1815 and 1816 are two views of Sandow taken from his photographs, 
the pen work being executed as above and the photograph washed out. 

In the " Dictionnaire Kaisonne de I'Architecture " of M. Viollet-le-Duc 



732 



FREE-HAND DRAWING. 



are given drawings from an album of the middle of the thirteenth century. Cer- 
tain mechanical processes are given to facilitate the composition and design of 
figures. According to these sketches, geometry is the generator of movements 




of the human body, and that of animals, and serves to establish certain relative 
proportions of the figures. The pen sketch (Fig. 1817) is an example of this 
practical process. In comparing this mode of drawing with figures in the vi- 
gnettes of manuscripts, with designs on glass, and even with statues and bas-reliefs, 
we must recognise the general employment in the thirteenth and fourteenth 
centuries of these geometrical means, suited to give figures not only their pro- 
portions but also the justness of their movement and bearing. Rectifying 



FREE-HAND DRAWING. 



733 



tlie canon of Villard in its proportions by comparison witli the best statues, 
notably those in the interior of the western fa9ade of the Cathedral of Reims, 
we obtain the Fig. 1818. The line A B, the height of the human figure, is di- 




FiG. 1815. 



734 



FREE-HAND DRAWING. 




Fig. 1816. 



vided into seven equal parts. The upper division is from the top of the head 
to the shoulders. Let C D be the axis of the figure, the line at the breadth of 
the shoulders is f of the whole height A B. The point E is the centre of the 



FREE-HAND DRAWING. 



735 



line C D ; draw through this point two lines, af and h e, and from the point g 
two other lines, g e and gf. The line b h is the length of the humerus, and 





Fig. 1817. 

the line of the knee-pan is on i h. The length of the foot is -| of a division, A 1. 
Having established these proportions, it will be seen by the following cuts how 
the artisan gave movements to these figures when the movements were not in 
absolute profile. 

Suppose the weight of the figure to be borne upon one leg (Fig. 1819), the 
line g e becomes perpendicular, and the axis op of the figure is inclined. The 
movement of the shoulders and trunk follow this inflection ; the axis of the 
head and the right heel are in the same vertical line. 

In stepping up (Fig. 1820), the axis of the figure is vertical, and the right 
heel raised is on the inclined line s t^ while the line of the neck is on the line 
/ ?7i, and the trunk is vertical, 

In Fig. 1821 it will be seen how a figure can be submitted to a violent move- 
ment and yet preserve the same geometrical trace. The figure is fallen, sup- 
ported on one knee and one arm, while the other wards off a blow ; the head 
is vertical. 

In Fig. 1822, the left thigh being in the line a/, to determine the position 
of the heel c on the ground, supposed to be level, an arc is to be described from 
the knee-pan ; the line ef is horizontal. 

It is clear that, in adopting these practical methods, all the limbs can be 
developed geometrically without shortening. The above will supply to many a 



736 



FREE-HAND DRAWING. 



ready means of sketching the human figure in various attitudes, naked, or in 
the close-fitting dresses of the present fashion ; but in the arrangement of 





Fig. 1819. 



Fig. 1820. 



drapery upon a figure, care must be taken that the drapery should fall in grace- 
ful folds. " It is necessary to give the body certain inflections which would be 
ridiculous in a person walking naked. The walk should be from the hips, with 




Fig. 1821. 



FREE-HAND DRxVWING. 



Y3T 



wide-spread legs, and, by the movements of the trunk, make the drapery cling 
on certain parts and float on others." 

In figures in repose, their centres of gravity must fall within the points of 
support, but the body can be sustained by muscular exertion, and this should 
be expressed in such cases by the tension of the muscles on which the position 
depends. In the act of running, the body inclines forward, its weight assists 
the movement, and the motions prevent its falling. 

In drawing figures it will be understood that the part that lies behind an- 
other can not be seen, and that one side of a limb or of the body can not be 
turned toward you without turning the other from you, and that the length of 
a body or limb can only be shown in its full length and proportion when it is 




Fig. 1822. 



perpendicular to the line of sight — that is, if the arm, for instance, is directed 
toward the eye, the hand will be the prominent object in view, that the arm will 
only be shown by the portions prominent beyond the outlines of the hand, that 
limbs or portions more or less inclined to the line of sight will be more or less 
foreshortened or show less than their natural length. 

It is very common in the drawing of figures to indicate merely the centre 
lines of the various portions and then clothe them as shown in several of -the 
figures. 

It is very common with modern draughtsmen to adopt a somewhat similar 
form of sketching as given in the " Dictionnaire Raisonne de I'Architecture " — 
a framework of bones in positions of action — and then clothing them with fiesh 
or drapery ; or manikins and lay figures in which the limbs can be set or fixed 
as desired, and then drawn from as models. Figs. 1823 and 1824 are illustra- 
tions from Dr. Rimmer's " Elements of Design " of skeleton lines and of manikins. 

Fig. 1825 is taken from photographs of a manikin in our office, which, al- 
though maimed as to its hands, is one of the best forms of these jointed figures, 
of which the limbs and body can be set in any required position ; but the sug- 
gestion is obvious that by the salted-paper or blue-print process, nude figures 
can be used instead of manikins, and photographs promptly secured without 
fatigue to the model and in positions of motion impossible in sketching. As a 
further illustration of this process, a pen drawing is given of the Venus de Milo 
(Figs. 182G-1827) from two points of view, taken from a plaster model, and a 
j)ortrait of Alexandre Dumas (Fig. 1858) from a photograph. 
48 



738 



FREE-HAND DRAWING. 




Fig. 1823. 




-v<.Sj^- 



Fig. 1824. 





Fig. 1825. 



FREE-HAND DRAWING. 



Y39 



Artists object that photography is too exact a reproduction, but it is well 
that they should understand what is an exact reproduction. Tint and colour 
may produce pleasant impressions without conformity to laws of perspective, but 
if the picture is to be taken as whole it should be natural, and with the present 
processes of photography it is well to throw the mechanical drudgery on it. 





Fig. 1826. 



Fig. 1827. 



Figs. 1828-1831 are drawings of male hands. Figs. 1832-1838 of legs and 
feet, with guide-lines to assist the draughtsman. 

Figs. 1839-1841 are drawings of female hands and arms. 

Figs. 1842-1845 -are hands and feet of children. 

Figs. 1846 and 1847 are illustrations of the human head and face. 




Fig. 1828. 



Fig. 1829. 



Fig. laso. 



Fig. 1831. 



740 



FREE-HAND DRAWING. 




Fig. 1837. 



Fig. 1838. 




Fig. 1839. 



Fig. 1840. 



Fig. 1841. 



FREE-HAND DRAWING. 



741 




Fig. 1844. 



Fig. 1845. 








Fig. 1846. 



Fig. 1817. 



742 



FREE-HAND DRAWING. 




Electioneer. 



The Forms of Ani7nals. — The bodies of most quadrupeds can be included 
in rectangles as guide-lines, which may be drawn around the illustration of the 
cow and horse (Figs. 1848 and 1849). The action of the limbs of quadrupeds is 
chiefly directly forward or directly backward, the power of lateral motion being 
limited. The hinder limbs always commence progressive motion, as in the first 
position of the walk, the fore foot of the same side advances next, then the 
hind foot of the opposite side, and lastly the fore foot on that side, and so on. 
In the trot, the hinder leg of one side and the fore leg of the other are raised 
together. In the canter or gallop, both fore legs and one hind leg are raised 
together ; when rapidly moving, the two fore legs and two hind legs appear to 
advance together. In fact, all the movements are rather resultants, as they 
appear to us, but when instantaneously photographed the legs are wonderfully 
mixed. 




i '/^,>/'C,l 






Fig. 1848. 



FREE-HAND DRAWING. 



743 




Fig. 1849. 




. ^^^M^^>^- 



Fig. 1850. 



Fig. 1850 is one of Landseer's sketches. 

The forms of feet range under two great divisions — hoofs (Fig. 1851) and 
paws (Fig. 1852). All hoofs, whether whole or cloven, approximate to a right- 
angled triangle, and all paws to a rhomboid. 



Y44 



FREE-HAND DRAWING. 



The Noses of Animals. — Fig. 1853 represents that of the horse ; Fig. 1854, 
that of the ox and deer tribe ; Fig. 1855, those of the carnivori ; Fig. 1856, 
those of the camel, sheep, and goat tribes ; and Fig. 1857, those of the hog 
tribes. The muzzles of nearly all quadrupeds will be found to range under 
one or other of these classes, with minute variations to characterize the differ- 
ent species and individuals. 







Fia. 1853. 



Fig. 1854. 



Fig. 1857 



In looking over the many sketches and engravings of Landseer which have 
been published, it will be noticed in how varied a manner they were executed. 
Sometimes in mere outline with lead-pencil, sometimes with a camel's-hair 
pencil charged with India ink or sepia for the outlines, giving effect to the 
subject by slight tints or washes of the same colour ; in others, pen and ink 
have been alone employed ; some are in oils, others in water-colours ; fre- 
quently chalks, both black and coloured. " As we look at some of these, we are 
tempted to believe that, of all the instruments that can be used by the artist, 
there is none quite so wonderful as the pen. A simple sketch with a pen or 
lead-pencil is naked, unadorned truth, bearing witness to the skill or its oppo- 
site of the hand which produced it." 

Strength and boldness in outline are acquired by large scale in drawing ; 
and in copying, if suitable originals can be obtained, copy them, but if you are 
confined to the illustration of books and periodicals, recollect that they have 
usually been reproduced on a reduced scale, and make your drawings two or 
three times their lineal dimensions. 

The directions and illustrations already given may be considered copying, 
which is absolutely necessary as an introduction to free-hand drawing, and ex- 
amples have been selected from figure drawing to give the draughtsman a 
strong bold hand and an education in proportions. 



FREE-HAND DRAWING. 



745 




y. - 



Sketching from Nature. — It is useless to give detailed rules for sketching, 
as each has his own way and perhaps equally good though dissimilar. If one is 
inside the house, what one sees through a window is a picture, and it may be 
transferred to paper if the eye is kept in a single position by a sight fastened 
to the sash at a convenient distance ; and if the pane of glass be prepared in 
squares, as described on page 60, the location of different points can be readily 
established. A simple plan to begin with is to set out carefully the most con- 
spicuous outline and draw the others with reference to it. If doubtful as to 
the distances and length of lines, stretch out your arm, holding )^our pencil 
vertically, horizontally, or aslant, as the case may be, and shutting one eye, 
mark off the measure from the end of the pencil by placing your thumb on the 
spot ; then compare that line or space with any other needed. By noting the 
relative position of one object with reference to another, all will fall into place 
almost without thought. Thus you have sketched a house, notice the next ob- 
ject and observe where it is projected against the building, as at such a window 
or door, and draw it in. Every artist has his own method of handling the 
sketch, of using his pen or pencil, charcoal or brush ; the aim of each should 
be to express what he sees by cross-lines and hatching if the pen is used, or by 
scribbling if the work is in pencil or charcoal. A general role is to adapt your 
strokes as far as possible to the modelling of the subjects you are drawing. 
Thus if you are representing water, it is natural to do it with horizontal lines. 
If the water is in motion, the lines, though still horizontal, will be broken and 
irregular. The reflections which in still water will be represented by vertical 
lines, in running water are indicated by horizontal lines with closer shading to 
give depth of tone. 

In drawing the trunk of a tree the characteristics of the bark must be ob- 
served. The trunk of an oak is rough and broken, while that of the bircli 
requires curved lines across the thickness of the tree. Xature sufficiently indi- 
cates the treatment. In many cases one must not be content with an exact 
reproduction. The scene must be interpreted. 



746 



FREE-HAXD DRAWING. 




FREP]-HAND DRAWING. 



747 



In all sketching from Nature the lines must be crisply and unhesitatingly 
drawn, the forms clearly defined, and the masses decisively indicated. In rapid 
work a mere outline must suffice, but it must be clearly and cleanly pencilled 
in. "When an elaborate drawing is required, begin by indicating the general 
arrangement, and then fill in as much detail as may be necessary ; but it is to 
be remembered that the simplest expression is the best and at the same time 
the most difficult, the effort being to concentrate the effect on the object to be 
emphasized, all others being subordinate to it. 

When a sketch has been faithfully made from Nature, as a general rule it is 
better not to try to improve it afterward, as one is apt to lose the crispness and 
vigour of the original. It is better to modify or amplify the first notes on an- 
other sheet of paper. Neither should there be many erasures, as they impart 
to the paper a dingy appearance and the sketch loses its sharpness. 

The depth of tone of shaded portions, as clouds, in some hasty sketches is 
indicated by numerals or letters, 1 or A representing the lightest; but it is 
better if time is afforded to put the shading in the sketch. In sketches of 
landscapes not intended for reproduction the addition of colour often adds very 
much to the effect and value of the sketch, but the colour must be light and 
transparent. 

The foregoing applies chiefly to landscape sketching. If you desire to 




Fig. 1861. 



FREE-HAND DRAWING. 



sketch figures or animals, the character of the individual is what you must try 
to seize ; if an animal in motion, one must work quickly and await the repeti- 
tion of the action or particular movement you are sketching. Meanwhile em- 




ploy your pencil on those portions that remain longer in one position, except- 
ing to work on the moving limb the instant it has regained the required 
position. The sketching of animals in rapid motion is still more difficult and 
is to a great extent a matter of careful observation and memory, for the limbs 
are not the only parts that change their position ; the whole attitude of the 
body is changed. In addition to memorizing all possible of the movement. 



FREE-HAND DRAWING. 



'i9 



considerable aid may be obtained in observing the animal at rest, which will 
enable you to understand the details of the structure. 

All sketches made should be preserved for future use, as they furnish the 
best material for original work that one can have. Sketches made in pencil or 
other materials which smear may be fixed with a solution composed of one part 
of gum mastic and seven parts of methylated spirits of wine, and is best applied 
with an atomizer. 

In transferring your sketches to the paper on which the pen drawing is to 
be made, commence by making a careful drawing with a hard pencil in outlines, 
confining yourself to those of shadows as much as possible, to save the surface 
of the paper, as rubbing spoils it and grays the ink ; or make the drawing on 
another sheet of paper and transfer it by means of graphite paper to the fair 
sheet, then ink in. 

If you want a clean, sharp line, the ink must be perfectly black and must 
stand out alone on the paper. If you want a gray line, it will not be obtained 
by using light ink, but by making thin lines. A single thin line will come out 
in the reproduction much blacker than is the intention, for though a number 
of lines will stand together, a single one will have to be thickened in the type 
metal by the photo-engraver. 





Fig. 1859. 



Fig. 1858. 



Fig. 1858, portrait of Alexander Dumas. For description of process see 
page 738. 

Fig. 1859 is a portrait of Erik Werenskiold, the artist, drawn by himself on 
Whatman's paper. 

Wash drawings are made with a brush on either Bristol board or water-colour 
paper, the wash consisting of India'ink and water, of various degrees of inten- 
sity. A number of illustrations are given of this method on page 750, by Paul 
de Longpre, and reproduced in half toa^. 

Fig. 1860 is a design for a small jiumping station, drawn witli India ink 
and a toothpick, after W. R. Emerson, in the 
view." 



Technology Architectural Re- 



750 



FREE-HAND DRAWING. 



T^.- ■: 





sy 




FUEE-HAXD DRAWING. 75I 

There are many devices which ma}' be used with effect in pen-and-ink draw- 
ing, such as sphitter work, wdiich is done by using a small stiff bristle brush (a 
toothbrush answers the purpose very w^ell), inking it, and holding the bristles 
downward and inclining toward the drawing and stroking the bristles toward 
one with a match stick. All parts not intended to be splattered should be cov- 
ered with paper masks, and even then a waterproof ink must be used in case it 
is necessary to pamt out some portions with Chinese white. The lower poi'fcion 
of Fig. 1860 is in splatter. An inked thumb is also a novel and effective means 
of representing a background or an imitation of velvet, the lines on the skin 
being marked on the paper and reproduced excellently. 

An invention of recent years is knowni among artists as stipple paj^er or 
clay board. The surfaces of these cardboards are of various kinds, but are all 
prepared with a surface of china cla}'. The simplest variety is that prepared 
with a plain white surface, upon which the drawing is executed with pen and 
ink or brush ; the lights are taken out with a sharp ink eraser. It is usual to 
work upon these boards wdth a pigmental ink, such as lampblack, ivory black, 
or India ink. More liquid inks have a tendency to soak through the prepared 
surface rather than rest upon it, rendering the board useless for scratch-out 
purposes ; other kinds of boards are impressed with a grain or with plain in- 
dented lines, which are used similar to the above. Scratch-out boards are diffi- 
cult of manipulation and are not to be recommended to the amateur. 

Fig. 1861, a portrait of Salvini, is an example of the use of stipple paper. 
The background or middle tone shows the board in its natural state. The 
high lights and shadows are obtained respectively by erasing and adding India 
ink. 

Fio-. 1862, " A Venetian Fete on the Seine," is another specimen of work on 
clay board. In this case the board was entirely black, the various tones being 
obtained by various degrees of erasing. 

The appearance a drawing will present when reduced may be approximate- 
ly judged by the use of a " diminishing glass " — that is, a concave glass. 

To remove blots or make erasures, use an ink eraser or simply paste a piece 
of paper over and join the lines at the edges; or a neater way, cut out the 
blotted part and paste a piece of paper underneath. 

To clean pen-and-ink drawings use bread one or two days old and not rubber. 

Aerial perspective, or the tones of lights and shadows according to their 
distance from the observer and the sources of the light, will be acquired by 
studies of pictures and observations of Nature. The rule in drawing from 
Nature is to draw only what you see and express it in the most truthful form. 



752. 



FREE-HAND DRAWIXG. 




After a Pen-and-ink Design, hy Portuny. 



FREE-HAND DRAWING. 



753 




G. L. Seymulk. 



49 



'54: 



FREE-HAND DRAWING. 






FREE-HAND DRAWING. 



765 




-.^•^^^^-^^ 



Y56 



FREE-HAND DRAWING. 




Study of Oak-Trees. E. Landseer. 



FREE-HAND DRAWING. 



757 




Morning. H. W. Robbins. 



T58 



FREE-HAND DRAWING. 




Cattle going Home. James M. Hart. 



FREE-HAND DRAWING. 



759 



ISfMSSS* ,«fW'R.-W-'v ■ 1 i&H;i|ii|IM*.s«s«,iii iii'i" 




TOO 



FREE-HAND DHAWINa. 




The Lady of the Woods. 



FREE-HAND DRAWIxXG. 



761 




^. 



762 



FREE-HAND DRAWING. 







■ -MMm 






Sketch in Chalk. 



FREE-HAND DRAWING. 



763 




764 



FREE-HAND DRAWING. 




PL.T. 



Fiq. 4. 
.3 4- a b 1 2 c/ 



3 4 d e 1 2 

FigJ. 



3 Oi 



I) i 2 g 



^ 3 d C 1 2 

Fig. 2. 



bj__a 



Fig.l. 



B 




Fig.l2. 



Fig.ll 



Fig.lO. 



Fig 



Fig.8. 



Fig. 7. 



Fig. 6. 





I 



a c 



9 I Fio.5. h d 




FL.H. 



Fig. 4^. 



^^9-^:,-> 



f c ni 




Viii i!/ 



9 



Fig. 3. 




Fig. 2 



d 



Fig.l. 

y. a — _c 




Fig.d 




rj — ^9' 



trK 



PL.m. 




PL.K 




PL.Y 




nff. 




Jl 




STATE N ISLAND 

CONTOURS 20 FT. APART. 



4r 



.TX. 



^ 




iF 




VIX. 

GEOLOGICAL MAP OF 

A^EW JERSEY 

geotige.h.cooe;staie geologist. 





Q. 

2 



PL, XII. 




Topographical Map of Massachusetts " 



PL.XIII. 




PLXV 




PL.XVI. 





PL.XYII. 




APPENDIX. 



PATENT-OFFICE DRAWINGS 

must be made upon pure white jDaper, of a thickness corresponding to three-sheet Bristol 
board, with surface calendered and smooth. India ink alone must be used. 

The size of the sheet must be exactly 10 by 15 inches. 1" from its edges single mar- 
ginal lines are to be drawn, leaving the " sight " precisely 8" by 13". Within this mar- 
gin all work must be included. Measuring downward from the marginal line of one of 
the shorter sides, a space of not less than IJ inch is to be left blank for the heading of 
title, name, number, and date. 

All drawings must be made with the pen only. All lines and letters must be abso- 
lutely black, clean, sharp, and solid, and' not too fine or crowded. Surface shading 
should be open, and used only on convex and concave surfaces sparingly. Sectional 
shading should be made by oblique parallel lines, w^hich may be about ^^ ' apart. 

Drawings should be made with the few^est lines possible consistent w^ith clearness. 
The plane upon sectional views should be indicated on the general view^ by broken or 
dotted lines. Heavy lines on the shade sides of objects should be used, except where 
they tend to thicken the work and obscure letters of reference : light to come from the 
upper left-hand corner, at an angle of 45°. 

The scale of the drawing to be large enough to show the mechanism without crowd- 
ing; but the number of sheets must never be increased unless it is absolutely necessary. 

Letters and figures of reference must be carefully formed, and, if possible, measure at 
least i" in height, and so placed as not to interfere with a thorough comprehension of the 
drawing, and therefore should rarely cross the lines. Upon shaded surfaces a blank space 
must be left in the shading for the letter. The same part of an invention must always, 
be represented by the same character, and the same character must never be used to 
designate different parts. 

The signature of the inventor, by himself or by his attorney, is to be placed at the 
lower right-hand corner of the sheet,' and the signature of two witnesses at the lower left- 
hand corner, all within the marginal line. The title is to be written with pencil on the 
back of the sheet. The permanent names and title will be supplied subsequently by the 
office in uniform style. 

Drawings should not be folded for transmission to the office. 



REGISTRATION OF PRINTS AND LABELS. 

A label is a device or representation borne by an article of manufacture or vendible 
commodity. A print is a device or representation not borne by an article of manufac- 
ture or vendible commodity, but in some fashion pertaining thereto. A label can not 
be registered if it bear a device capable of sequestration as a trade-mark until after such 
device is registered as a trade-mark. Both labels and prints, in order to be entitled to 
registry, must be intellectual productions in the degree required by the coj^yrigbt law. 

765 



"IQQ APPENDIX. 

MENSURATION. 

The principles of measurement have been quite fully explained under the heads of the 
Construction of Geometrical Problems and Plotting, but for ready reference there are 
many rules which are of general application and very necessary in designing and calcula- 
tion, and are given briefly as follows : 
To find 

The area of a parallelogram. Multiply the length by the height or perpendicular by 
the breadth. Multiply the product of two contiguous sides by the natural sine of the 
included angle. (See Appendix, Table of Natural Sines.) 

The area of a triangle. Multiply the base by the perpendicular height and take half 
the product. Multiply half the product of two contiguous sides by the natural sine of 
the included angle. 

The area of a trapezoid. Multiply half the sum of the parallel sides by the perpen- 
dicular distance between them. 

The area of any quadrilateral figure. Divide the quadrilateral into two triangles; the 
sum of the areas of the triangles is the area. 

The area of any polygon. Divide the polygon into triangles and take the sum of their 
areas. 

The circumference of a circle. Multiply the diameter by 3 '1416 = n. 

The diameter of a circle. Multiply the circumference by the reciprocal of n. 

The area of a circle. Multiply the square of the diameter by '7854, or the circumfer- 
ence by one fourth of the diameter. 

The length of an arc of a circle. Multiply the number of degrees in the arc by the 
radius, and by -01745. 

Note. — The length of an arc of one degree = radius x •017453. 

'' " " " " minuter " x -000291. 

" " " " " " " second = " x -000005. 

The area of a sector of a circle. Multiply the length of the arc of the sector by half 
the radius. 

The area of a segment of a circle. From the area of a sector subtract the area of the 
triangle formed by the radial sides of the sector and its chord. The area of this triangle 
is the product of the natural sine and cosine by the square of the radial side. 

The area of regular polygons. Find the area of one triangle, and multiply by the 
number of triangles composing the polygon : 

Or, multiply the total of cosines for the periphery by one half the sine, by the square 
of the radius for the area. 

No. of Verti- 
i Chord. Sides. cal. Product. 

Pentagon ." -5878 x 5 x -8090 = 2-3776 

Hexagon -5000 x 6 x -8660 = 2'5980 

Heptagon -4357 x 7 x •9032 = 2-7478 

Octagon -3827 x 8 x -9238 = 2-8284 

Nonagon ' -3420 x 9 x -9396 = 2-8925 

Decagon -3090 x 10 x -9510 = 2^9389 

Undecagon -2817 x 11 x -9594 = 2-9739 

Dodecagon -2588 x 12 x -9660 = 3-0000 

Circle = tt = 3-1416 

To find 

The area of the cycloid. Multiply the area of the generating circle by 3. 
To find 

The area of tlie parabola. Multiply the base by the height; two thirds of the product 
is the area. 



APPENDIX. 767 

The circumference of an ellipse. Multiply the square root of half the sum of the 
squares of the two axes by 3-1416. 

The area of an ellipse. Multiply the product of the two axes by -7854 = I n. 

XoTE. — The area of an ellipse is equal to the area of a circle of which the diameter is a 
mean proportional between the two axes. 

To find the area of any curvilineal figure, bounded at the ends by parallel straight 
lines (Fig. 198). Divide the length of the figure into any number of equal parts and draw 
ordinates through the points of division, to touch the boundary lines. Or, add together 
the first and last ordinates, making the sum A ; and add together all the intermediate 
ordinates, making the sum B. Let L = the length of the figure, and n = the number of 
divisions, then 

A + 2B 



2n 



X L = area of fiofure. 



That is to say, twice the sum of the intermediate ordinates, plus the first and last ordi- 
nates, divided by tw^ice the number of divisions, and multiplied hj the length, is equal 
to the area of the figure. This method is sufiiciently exact for most purj^oses. 
To find 

The surface of a prism or cylinder. To the product of the perimeter of the end by 
the height, add twice the area of an end. 

The cubic contents of a prism or a cylinder. Multiply the area of the base by the 
height. 

The surface of a f)yramid or cone. Multiply the perimeter of the base by half the 
slant height, and add the area of the base. 

The cubic contents of a pyramid or a cone. Multiply the area of the base by one third 
of the perpendicular height. 

The surface of a frustum of a p^'ramid or a cone. jVIultiiily the sum of the perime- 
ters of the ends by half the slant height, and add the areas of the ends. 

The cubic contents of the frustum of a pyramid or a cone. Add together the areas 
of the two ends and the mean proportional between them (that is, the square root of their 
product) and multiply the sum by one third of the perpendicular height. 

The cubic contents of a wedge. To twice the length of the base add the length of 
the edge ; multiply the sum by the breadth of the base, and by one sixth of the height. 

The cubic contents of a jnismoid (a solid of w^hich the two ends are unequal but par- 
allel plane figures of the same number of sides). To the sum of the area of the two ends 
add four times the area of a section parallel to and equally distant from both ends; and 
multiply ihe sum by one sixth of the length. 

The surface of a sphere. Multiply the square of the diameter by 3*1416. 

The surface of a sphere is equal to four times the area of one of its great circles. 

The surface of a sphere is equal to the convex surface of its circumscribing cylinder. 

The surfaces of spheres are to one another as the squares of their diameters. 

The curve surface of any segment or zone of a sphere. Multiply the diameter of the 
sphere by the height of the zone or segment, and by 3*1416. 

The cubic contents of a sphere. Multijily the cube of the diameter by *o236 = | n. 

The cubic contents of the segment of a sphere. From three times the diameter of the 
sphere subtract twice the height of the segment ; multiply the diiierence by the square of 
the height, and by *o236. 

The cubic contents of a frustum or zone df a sphere. To the sum of the squares of 
the radii of the ends add i of the square of the height; multiply the sum by the height 
and by 1 *5708 = |- tt. 

The cubic contents of a spheroid. (A solid body generated by the revolution of an 
ellipse around one of its axes.) Multiply the square of the revolving axis by the fixed 
axis and by *5236. 



'68 



APPENDIX. 



LINEAL MEASUEE. 



Inches. 


Feet. 


Yards. 


Fath- 
oms. 


Links. 


Rods. 


Chains. 


Furlongs 


Statute 
miles. 

•000016 


Nautical 
miles. 


Metres. 


1 = 


-08333 


-02778 


-0139 


-126 


-005 


•00126 


•000126 




•0254 


12 = 


1 


•333 


•1667 


1-515 


•0606 


•0151 


•00151 


•00019 


. 






©•3048 


36^ 


3 


1 


-5 


4-545 


•182 


•0454 


•00454 


•00057 


. 






0^9144 


72 = 


6 


2 


1 


9-1 


•364 


•091 


•0091 


•00114 








r8289 


7-92 = 


0-66 


•22 


•11 


1 


•04 


•01 


•001 


-000125 








•2012 


198 = 


16.i 


5^ 


2f 


25 


1 


•25 


•025 


•003125 








5-0294 


792 = 


66 


22 


11 


100 


4 


1 


•10 


•0125 








20^118 


7920 = 


660 


220 


110 


1000 


40 


10 


1 


•125 








20M8 


63360 = 


5280 
6086-07 


1760 
2028-69 


880 


8000 


320 


80 


8 


1 
M527 


0-86755 
1 


1609^41 
1855-11 


39-3685 = 


3-2807 


1-0936 


•5468 









*■ 


0-000621 




1 



Latin prefixes, as milli-, centi-, deci-, to the French units of length (metre), surface (are), weight 
(gramme), or volume (litre), signify Yiooo, Vioo, or Yio of the unit; as, millimetre, Yiooo of a metre, 
decigramme, Vio of a gramme. Greek prefixes, as kilo, hekto, deka, multiples of the unit by 1,000, 
100, or 10, as kilometre = 1000 metres, 

MEASUEES OF SUEFACE. 



Sq. inches. 


Sq. feet. 


Sq. yards. 


Sq. rods. 


Eoods." 


Acres. 


Sq. miles. 


Sq. metres. 


Ares. 


1 = 


-00394 













.... 




144 = 


1 


-Ill 


-0037 




.... 




-0929 


•0009 


1296 = 


9 


1 


-033 








•8361 


-0084 


.... 


2721 


30J 


1 


-025 


-00625 




25-293 


0-253 




10890 


1210 


40 


1 


•25 




. ., . 







43560 


4840 


160 


4 


1 


•00156 


4046-86 


40-47 


.... 


27878400 


3097600 




.... 


640 


1 




25899 


1549-8 = 


10-763 


1-196 


-0395 


-0009 


-000247 





1 


-01 


' 


1076-31 


119-60 


.... 




-02471 


.... 


100 


1 



BOARD AND TIMBER MEASURE. 



In board measure boards are assumed at one inch in thickness. To obtain the num- 
ber of feet, board measure (B. M.), of a board or stick of square timber, multiply to- 
gether the length in feet, the breadth in feet, and the thickness in inches. 

To Compute the Volume of Round Tim,der. —When all dimensions are in feet, multiply 
the length by one quarter of the product of the mean girth and diameter, and the prod- 
uct will give the measurement in cubic feet. 

For Square Timter. — When all dimensions are in feet, multiply together the length, 
breadth, and depth : the product will be the volume in cubic feet. When one dimen- 
sion is given in inches, divide by 13 ; when two dimensions are given in inches, divide 
by 144; when all three dimensions are given in inches, divide by 1728. 



APPENDIX. 



769 



MEASURES OF CAPACITY. 
LIQUID MEASURE. 



Gills. 


Pints. 


Quarts. 


Gallons. 


Imp. gallons. 


Litres. 


Cubic feet. 


Cubic in. 


Lbs. water 
at 62". 


1^ 


0-25 


0-125 


•03125 


•026 


•1183 


•0042 


7-219 


•26 


4 = 


1 


0-5 


0125 


-1041 


•4731 


•01671 


28^875 


r0412 


8 = 


2 


1 


0-25 


•2083 


0^9463 


•03342 


57-75 


2-0825 


32 = 


8 


4 


1 


0-8331 


3^7852 


01337 


231 


8-33 


38^4096 = 


9-6024 


4-8012 


1-2003 


1 


4-5435 


0-1605 


277-27 


10-00 


8-4534 = 


2-1133 


1^0567 


0-26417 


0-2201 


1 


0-0353 


61-0279 


2-2007 


239-36 = 


59-84 


29-92 


7-48 


6-232 


28-320 


1 


1728 


62-321 


"138528 = 


-034632 


-017316 


•004329 


•0036 


0-01639 


0-000579 
•01604 


1 

27-727 


-03606 

1 



1 barrel = 31i gallons. Reciprocal = -03175. 



DRY MEASURE. 



Pints. 


Quarts. 


Gallons. 


Pecks. 


Bushels. 


1 = 


0-50 


0^125 


-0625 


0-01562 


2 = 


1 


0-25 


0-125 


00312 


8 = 


4 


1 


0-50 


0-125 


16 = 


8 


2 


1 


0-^5 


64 = 


32 


8 


4 


1 



The standard bushel contains 2150-42 cubic inches. 



WEIGHTS. 



APOTHECARIES' 



Grains. 


Scruples. 


Drachms. 


Ounces. 


Pounds. 
-00018 


1 = 


•05 


•0167 


•0021 


20 = 


1 


•333 


•042 


-0035 


60 = 


3 


1 


-125 


-0104 


480 = 


24 


8 


1 


-083 


5760 = 


288 


96 


12 


1 





TROY. 




Grains. 


Pennyweights. 


Ounces. 


Pounds. 


1 = 


-042 


-0021 


-00018 


24 = 


1 


•05 


-0042 


480 = 


20 


1 


-083 


5760 = 


240 


12 


1 



AVOIRDUPOIS. 



Drachms. 


Ounces. 


Poimds. 


Hundred-weights. 


Tons. 


French grammes. 


16 = 

256 = 

28672 = 

573440 = 


•0625 

1 

16 

1792 

35840 


•0039 

•0625 

1 

112 

2240 


•000035 

•000558 

•00893 

1 

20 


•00000174 

•000028 

-000446 

•05 

1 


1-771836 

28-34938 

453-59 

50802- 

1016041-6 



It is common usage here to omit hundred-weights (cwt.) and rate tons at 2,000 pounds 
net, and 2240 lbs. as gross ; 7,000 troy or apothecaries' weight equal 1 pound avoirdupois. 
50 



770 






APPENDIX. 








COMPAEISON 


OF WEIGHT. 






DYNAMIC 


TABLE. 




Pounds 
apothecaries'. 


Pounds 
Troy. 


Pounds 
avoirdupois. 


Kilo- 
gramme. 




Pounds, 
feet. 


Kilogramme- 
metre. 


Horse- 
power. 


French 
horse-power. 


1 = 


1 


0-8229 


0-37324 


1 = 


0-13825 


-00003 


-000031 


1 = 


1 


0-8229 


0-37324 




7-2331 = 


1 


-000219 


•000222 


1-2153 = 

2-6792 = 


1-2153 
2-6792 


1 
2-2046 


0-4536 

1 




Per min. 

33-000 = 

32548-9 = 


4562-3 
4500 


1 
0-98633 


1-01386 

1 



CUBIC OE SOLID MEASUEE. 



Cubic inches. 


Cubic feet. 


Cubic yards. 


Cubic metres. 


United States gallon. 


1- 

1728 = 

46656 = 

61016 = 

231 = 


•00058 

1 

27 

35-31 

0-1337 


•000021 

0-037 

1 

1-3078 

•00495 


•000016 

0^0283 

0-7646 

1 

-00379 


•004329 

7-48 

201-9; 

264-141 

1 



SHIPPING MEASURE. 



Register Ton. — For register tonnage or for measurement of the entire internal capacity 



of a vessel : 

100 cubic feet = 1 register ton. 
Shipping Ton. — For the measurement of cargo : 

( 1 U. S. shipping ton. 
40 cubic feet = ■< 31*16 Imp. bushels. 42 cubic feet = 

32*143 U. S. " 



1 British shipping ton. 
32-719 Imp. bushels. 
33-75 U. S. 



Carpenter'^ s Rule. — Weight a vessel will carry = length of keel x breadth at main 
beam x depth of hold in feet -f- 95 (the cu. ft. per ton). The result will be the tonnage. 
For a double-decker, instead of the depth of the hold take half the breadth of the beam. 

TABLE OF INCHES AND SIXTEENTHS IN DECIMALS OF A FOOT. 



Inches. 




A 


A 


A 


A 


-h 


A 


iV 


1^ 


A 


« 


H 


« 


•068 


•073 


H 


0.... 


-000 


-005 


-010 


•016 


•021 


•026 


•031 


-036 


-042 


-047- 


-052 


-057 


-062 


•078 


1 


-083 


•089 


-094 


-099 


-104 


•109 


-115 


-120 


•125 


-130 


-135 


-141 


•146 


•151 


•156 


•161 


2 


•167 


•172 


•177 


-182 


•187 


-193 


•198 


-203- 


•208 


-214 


-219 


•224 


•229 


•234 


•240 


•245 


3.... 


•250 


•255 


-260 


-266 


•271 


-276 


•281 


•286 


•292 


•297 


•302 


•307 


•312 


•318 


-323 


•328 


4 


-333 


-339 


•344 


-349 


•354 


•359 


•365 


•370 


•375 


•380 


•385 


•391 


•396 


•401 


•406 


•411 


5.... 


-417 


-422 


•427 


•432 


•437 


-443 


•448 


•453 


•458 


•464 


•469 


•474 


•479 


•484 


•490 


•495 


6.... 


•500 


•505 


-510 


•516 


•521 


•526 


•531 


•536 


•542 


•547 


•552 


-557 


•562 


•568 


•573 


•578 


7.... 


•583 


-589 


-594 


-599 


-604 


•609 


•615 


•620 


•625 


•630 


•635 


-641 


•646 


•651 


•656 


•661 


8.... 


-667 


•672 


-677 


-682 


-687 


•693 


•698 


•703 


•708 


•714 


•719 


•724 


•729 


•734 


•740 


•745 


9.... 


-750 


•755 


-760 


-766 


•771 


-776 


•781 


-786 


-792 


•797 


-802 


•807 


•812 


•818 


•823 


•828 


10 ... . 


•833 


•839 


-844 


-849 


-854 


-859 


•865 


•870 


•875 


•880 


-885 


•891 


•896 


•901 


•906 


•911 


11.... 


•917 


-922 


•927 


-932 


-937 


•943 


•948 


-953 


958 


•964 


•969 


-974 


•979 


•984 


■990 


•995 



APPENDIX. 7Y1 



ELECTRICAL UNITS. 

C. G. S. 

Unit of space, 1 centimetre, C. ; of mass, 1 gramme, G. ; of time, 1 second, S. 

The definitions of units as adopted at the International Electrical Congress at Chicago 
in 1893, established by Act of Congress of the United States, July 13, 1894, are as follows : 

The ohm (the unit of resistance, represented by R) is equal to 10^ (or 1,000,000,000) 
units of resistance of the C. G. S. system, and is represented by the resistance offered to 
an unvarying electrical current by a column of mercury at 32° Fahr. (14*4521 grammes 
in mass) of a constant cross-sectional area, and of the length of 106*3 centimetres. 

The ampere (tlie unit of current strength, or rate of flow, represented by C) is one tenth 
of the unit of current of the C. G. S. system, and is the equivalent of the unvarying cur- 
rent which, when passed through a solution of nitrate of silver in water in accordance 
with standard specifications, deposits silver at the rate of *001118 gramme per second. 

The volt (the unit of electro-motive force, or difference of potential, represented by E) 
is the electro -motive force that, steadily applied to a conductor whose resistance is 1 
ohm, will produce a current of one ampere, and is equivalent to y^%^ (or *6974) of the 
electro-motive force between the poles or electrodes of a Clark's cell at a temperature 
of 15° C, and prepared in the manner described in the standard specifications. 

The coulomb (or ampere-second, the unit of quantity, Q) is the quantity of electricity 
transferred by a current of one ampere in one second. 

The farad (the unit of capacity represented by K) is the capacity of a condenser 
charged to a potential of one volt by one coulomb of electricity. 

The joule (volt-coulomb, the unit of energy or work, W) is equal to 10,000,000 units 
of work in the C. G. S. system, and is practically equivalent to the energy expended in 
one second by an ampere in one ohm. 

The watt, or ampere-volt (the unit of power, P), is equal to 10,000,000 units of power 
in the C. G. S. system, and is practically equivalent to the work done at the rate of one 
joule per second; 746 watts = 1 H. P. 

The lienry (the unit of induction) is the induction in a circuit when the electro-motive 
force induced in this circuit is one volt, while the inducing current varies at the rate of 
one ampere per second. 

The ohm. volt, etc., as above defined, are called the " international " ohm, volt, etc.,, 
to distinguish them from the " legal " ohm, B. A. unit, etc. 

The value of the ohm, determined by a committee of the British Association in 1863, 
called the B. A. unit, was the resistance of a certain piece of copper wire preserved in 
London. The so-called "legal " ohm as adopted by the International Congress of Elec- 
tricians in Paris in 1884, was a correction of the B. A. unit, and was defined as the re- 
sistance of a column of mercury 1 square millimetre in section and 106 centimetres long, 
at a temperature of 32° F. 

1 legal ohm = 1*0112 B. A. units, 1 B. A. unit = 0*9889 legal ohm. 

1 international ohm = 1*0136 " " 1 " " = 0*9866 int. " 
1 " " =1*0023 legal ohm, 1 legal ohm = 0*9977 " 

UNIT OF HEAT. 

The British Thermal Unit (B, T. U.) is that quantity of heat required to raise the 
temp, of 1 pound of pure water 1° F. at or near 39*1° F., the maximum density of water. 

The French thermal unit, or calorie, is that quantity of heat which is required to raise 
the temperature of 1 kilogramme of pure water 1° C, at or about 4° C, which is 
equivalent to 39*1° F. 

1 French calorie = 3*968 British thermal units, 1 B. T. U. = *252 calorie. 



772 



APPENDIX. 



FIFTH POWERS, TABLE OF. 





Fifth Power. 




Fifth Power. 


j 


Fifth Power. 




Fifth Power. 


11 


1 61051 


33 


391 35393 


1 55 


5032 84375 


77 


27067 84157 


12 


2 48832 


34 


454 35424 


! 56 


5507 31776 


78 


28871 74368 


13 


3 71293 


35 


525 21875 


: 57 


6016 92057 


79 


30770 56399 


14 


5 37824 


36 


604 66176 


58 


6563 56768 


80 


32768 00000 


15 


7 59375 


37 


693 43957 


! 59 


7149 24299 


81 


34867 84401 


16 


10 48576 


38 


792 35168 


60 


7776 00000 


^ 82 


37073 98439 


17 


14 19857 


39 


902 24199 


61 


8445 96301 


83 


39390 40643 


18 


18 89568 


40 


1024 00000 


1 62 


9161 32832 


84 


41821 19424 


19 


24 76099 


41 


1158 56201 


i 63 


9924 36543 


85 


44370 53125 


20 


32 00000 


42 


1306 91232 


1 64 


10737 41824 


86 


47042 70176 


21 


40 84101 


43 


1470 08443 


' 65 


11602 90625 


87 


49842 09207 


22 


51 53632 


44 


1649 16224 


' 66 


12523 32576 


88 


52773 19168 


23 


64 36343 


45 


1845 28125 


67 


13501 25107 


89 


55840 59449 


24 


79 62624 


46 


2059 62976 


: 68 


14539 33568 


90 


59049 00000 


25 


97 65625 


47 


2293 45007 


69 


15640 31349 


91 


62403 21451 


26 


118 81376 


48 


2548 03968 


' 70 


16807 00000 


92 


65908 15232 


27 


143 48907 


49 


2824 75249 


1 '^1 


18042 29351 


93 


69568 83693 


28 


172 10368 


50 


3125 00000 


72 


19349 17632 


94 


73390 40224 


29 


205 11149 


51 


3450 25251 


' 73 


20730 71593 


95 


. 77378 09375 


30 


243 00000 


52 


3802 04032 


1 74 


22190 06624 


96 


81537 26976 


31 


286 29151 


53 


4181 95493 


i 75 


23730 46875 


97 


85873 40257 


32 


335 54432 


54 


4591 65024 


i 76 


25355 25376 


99 


95099 00499 





CAST-IRON BALLS, 


VOLUME 


AND WEIGHT 


OF. 




Diameter. 


Volume. 


Weight. 


Diameter. 


Volume. 


Weight. 


Diameter. 


Volume, 


Weight. 


Inches. 


Cu. inches. 


Pounds. 


Inches. 


Cu. inches. 


Pounds. 


Inches. 


Cu. inches. 


Pounds. 


2 


4-19 


1-09 


H 


87-1 


22-7 


9 


381-7 


99-4 


H 


8-18 


2-13 


6 


113-1 


29-5 


n 


448 9 


116-9 


3 


14-1 


3-68 


H 


143-8 


37-5 


10 


523-6 


136-4 


3i 


22-5 


5-85 


7 


179-6 


46-8 


11 


696-9 


181-8 


4 


33-5 


8-73 


n 


220-9 


57-5 


12 


904-8 


235-9 


U 


47-7 


12-4 


8 i 


.268-1 


69-8 


13 


1150-3 


299-6 


5 


65-5 


17-0 


8i \ 


321-5 


83-7 

1 


14 


1436-8 


374-6 



Weight for other metals vary as their specific gravities and for diameters as their cubes. 
CAST-IRON PIPES, STANDARD WEIGHTS OF. 



1 

o 


il 

•ga 

EH 


.2-S 

!i 

o 


0) o o 


5i 

SI- 


Itimate strength 
of Pipe, made 
of 18 000 lb. 
iron. 


i 
11 


^ 


m 




^ 


^ 


^ 


^ 


o 


o 


Inches. 


Inches. 


Pounds. 


Pounds. 


Pounds. 


Pounds. 


Pounds. 


U. S. gal. 


4 


0-40 


17-27 


18-75 


225 


3600 


720 


•6528 


6 


0-42 


26-46 


28-92 


347 


2515 


503 


1-469 


8 


0-45 


37-33 


40-50 


486 


2025 


405 


2-611 


10 


0-50 


51-54 


56-17 


673 


1800 


360 


4-081 


12 


0-55 


67-76 


73-75 


885 


1650 


330 


5-876 


14 


0-58 


83-02 


90-67 


1088 


1490 


298 


7-997 


16 


0-60 


97-78 


106-75 


1281 


1350 


270 


10-440 


18 


0-64 


117-11 


126-67 


1520 


1280 


256 


13-22 


20 


0-70 


142-25 


153-43 


1841 


1260 


252 


16-32 


24 


0-80 


194-77 


210-33 


2524 


1200 


240 


23-50 


30 


0-90 


273-00 


285-33 


3524 


1080 


216 


36-72 


36 


1-00 


363-22 


390-50 


4686 


1000 


200 


52-88 



Water Works," by Howland and Ellis. 



APPENDIX. 



1 

s 

i 

1 


<M 
















s 

1 


1 




O 


ill 


Ci 
















r?" 


00 
















OXMCO 


t- 














i-li-iO* 




«© 












f' 
S 




§Sg 


^ 












00 

0^ 






»o 














sis 














§ 

g 






Ksooo 


^ 










si 






^§3 


S 










S2^ 






Hi 


? 








to 


s^§ 


s^^ 


ggs 


SBgiS 


^^s 


gs? 


SS| 


^§^ 


S 


















« 










s^^ 
^li^ 




»-Q0OS 

^8l 


S2§ 


s< 






^ 
^ 












.^ 






§:2 












^- 












5^§ 


§3§ 


^^1 


. 






sss 


Si§ 


§gs 


SS9 


^sg 


§iSg 


ifteoao 


§S§3 


^§g 


§§s;^ 


^Sg 


5^g 


^ 




ss 


to-* — 


Si^S 


;=Sg 


^^S 


^l::§ 


Sfg?2 


Oi-i 


co«boo 

^22 22 


i::sa 


ssss 


^^^ 


^^i?? 


gS^ 


--i 




2S2 

b-doo 


S^2 




OOOt- 
<MI~-CO 


eo-*-* 




^ 


1^ 








»C«>do 




s§i 

'i-OOlM 
«OipO 


2g§ 

<Mec OS 
(Nt-eo 


- 1 


t-i-i 

00-^ 




t-aoo» 


00— c 




^ 1 


<N(NCO 




«bt-ao 


00C5O 


-^ 1 






000 


b-OOOO 




^ 1 


So S^w 


WW-* 




coGoeo 


b-a0 3» 




^000 


^ 1 


Sgs ^s=: 


S^fe 


^SS 


§^S 


(M-<J< 00 

TO 1-0 


^g2 


^,-1 ^T-ce^ 


<M(MCO 


eo^-* 


000 


«c<o t- 


000s s 


— 50O 


22s 


"^ 1 


^ S?i§ 2§S 


5S1O 


S2^ 


sz:=; 


?:§S 


^gs 


^2§ 


S§2 


^^-r 


r-<<MOsI 


(Mcceo 


CO-*-* 


-*oo 


toeot- 


ac Ot-< 


(MCCO 


^ 1 


^« ^SS ?2.^§ 


§9:2 








-*-*o 


10 ib- 


IM'OO 
Q0C5O 


^ 1 


§2S S^S p^S 


??? 


9?r 


^w-* 


2Sg 




(yiwio 


S3g 


•TiOJi pano^j 


|t:5 gf^ gg2 

oio Oi^.^ <Niii4j< 


OQOO 


22S 


00 C5^ 




2gS 

i8g 


Hi 


gsg 

-*o 


-nwip JO 




^^-. '*■*•*• «„:!• 


:?2r« 


5!r5r?r 


ccwco 


ot-^-^ 


o?«> 


h-aoo» 


— « 



774 APPENDIX. 

WEIGHTS OF WROCGHT-IEON AND BRASS PLATES AND WIRE, SOFT ROLLED. 



BIRMINGHAM GAUGE. 


No. of 




AMEKICAN GAUGE (BEOWN 


& 8HAEPE). 










PLATES PEE SQUARE FOOT. | 


WIEE PEE LINEAL FOOT. 




Thickness of 
each number. 


gauge. 


Thickness 










Plate iron. 


of each 
number. 


Wrought 


Brass. 


Wrought 


Brass. 










iron. 




iron. 




Lbs. 


Inch. 




Inch. 


Lbs. 


Lbs. 


Lbs. 


Lbs. 


17-025 


-454 


0000 


•46 


17-25 


19-68 


•5607 


•6051 


15-9375 


•425 


000 


-4096 


15^361 


17-53 


•4447 


•4799 


14-25 


•38 


00 


•3648 


13-68 


15-61 


•3527 


•3806 


12-75 


-34 





-3248 


12-182 


13-90 


•2797 


•3018 


11-25 


-3 


1 


•2893 


10-848 


12-38 


•2218 


•2393 


10-65 


-284 


2 


•2576 


9-661 


1102 


•1759 


•1898 


9-7125 


•259 


3 


-2294 


8-603 


9-81 


•1395 


•1505 


8-925 


•238 


4 


•2043 


7-661 


8-74 


•1106 


•1193 


8-25 


•22 


5 


•1819 


6-822 


7-78 


•0877 


•0946 


7-6125 


•203 


6 


-1620 


6-075 


6-93 


•0695 


•0750 


6-75 


-18 


7 


-1442 


5-410 


6-17 


•0551 


•0595 


6-1875 


-165 


8 


-1284 


4-818 


5-49 


•0437 


•0472 


5-55 


-148 


9 


-1144 


4-291 


4-89 


•0347 


•0374 


5-025 


•134 


10 


-1018 


3-820 


4-36 


-0275 


•0296 


4-5 


•12 


11 


-0907 


3-402 


3-88 


-0218 


•0235 


4-0875 


•109 


12 


•0808 


3-030 "^ 


3-45 


•0173 


•0186 


3-5625 


•095 


13 


•0719 


2-698 


3-07 


•0137 


•0148 


3-1125 


•083 


14 


-0640 


2-403 


2-74 


•0109 


•0117 


2-7 


•072 


15 


-0570 


2-140 


2-44 


•00863 


•00931 - 


2-4375 


•065 


16 


-0508 


1-905 


2-17 


•00684 


•00758 


2-175 


•058 


17 


•0452 


1-697 


1-93 


•00542 


•00585 


1-8375 


•049 


18 


-0403 


1-511 


1-72 


-00430 


•00464 


1-575 


•042 


19 


-0358 


1-345 


1-53 


•00341 


•00368 


1-3125 


-035 


20 


-(319 


1-198 


1-36 


•00271 


•00292 


1-2 


-032 


21 


•0284 


1-067 


1-21 


-00215 


•00231 


1-05 


•028 


22 


•0253 


•9505 


1-08 


-00170 


•00183 


•9375 


•025 


23 


•0225 


•8464 


-9660 


-00135 


•00145 


-825 


•022 


24 


•0201 


•7537 


•8602 


-00107 


•00115 


•75 


•02 


25 


•0179 


•6712 


•7661 


•00085 


•000916 


•675 


•018 


26 


•0159 


•5977 


•6822 


-000673 


•000726 


•6 


-016 


27 


•0141 


•5323 


•6075 


-000534 


•000576 


•525 


•014 


28 


•0126 


•4740 


•5410 


•000423 


•000457 


•4875 


-013 


29 


•0112 


•4221 


•4818 


•000336 


•000362 


•45 


•012 


30 


•0100 


•3759 


•4290 


•000266 


•000287 


-375 


-01 


31 


•0089 


•3348 


•3821 


-000211 


•000228 


-3375 


-009 


32 


-0079 


•2981 


•3402 


•000167 


•000180 


•3 


•008 


33 


•00708 


•2655 


•3030 


•000132 


•000143 


•2625 


-007 


34 


•00630 


•2364 


•2698 


•000105 


•000113 


•1875 


-005 


35 


•00561 


•2105 


•2402 


•0000836 


-00009015 


•15 


-004 


36 


•005 


•1875 


•214 


•0000662 


•0000715 






37 


•00445 


-1669 


•1905 


•0000525 


•00005671 






38 


•00396 


•1486 


•1697 


•0000416 


•00004496 






39 


•00353 


•1324 


•1511 


•0000330 


•00003566 






40 


•00314 

1 


•1179 


•1345 


-0000262 


•00002827 



Copper is about 5 per cent heavier than brass. Lead is about 47 per cent heavier than wrought 
iron. Zinc is about 7 per cent lighter than wrought iron. Sheet copper is rated by weight at so 
many ounces per square foot, and sheet lead at so many pounds per square foot. 



APPENDIX. 



775 



TABLE OF 


DIMENSIONS AND WEIGHT OF WROUGHT-IEON WELDED TUBES. 


Nominal 
diameter. 


External 
diameter. 


Thick- 
ness. 


Internal 
diameter. 


Internal 
circum- 
ference 


External 
circum- 
ference. 


Length of 
pipe per 
square 
toot of 
internal 
surface. 


Length of 
pipe per 
square 
foot of 
external 
surface. 


Internal 
area. 


Weight 
per foot. 


No. of 
threads 

per 
inch of 
screw. 


Inches. 


Inches. 
•40 


Inches. 
•068 


Inches. 

•27 


Inches. 

•86 


Inches. 

r27 


Feet. 
14-15 


Feet. 
9 44 


Inches. 
-057 


Lbs, 
•24 


27 


V4 


•54 


•088 


•36 


M4 


1-7 


10-5 


7^075 


•104 


•42 


18 


Vs 


•67 


•091 


•49 


1-55 


2-12 


7-67 


5^667 


192 


•56 


18 


V2 


•84 


.109 


•62 


1-96 


2^65 


6-13 


4-502 


•305 


• ^84 


14 


V4 


ro5 


.113 


•82 


2^59 


3^3 


4-64 


3-637 


•533 


M3 


14 


1 


1-31 


•134 


1-05 


3-29 


413 


3-66 


2-903 


-863 


1-61 


iiV. 


IV4 


r66 


•14 


V38 


4-33 


5^21 


2-77 


2-301 


1-496 


2-26 


iiV. 


IV2 


1^9 


•145 


1-61 


5^06 


5-97 


2-37 


2-01 


2-038 


2-69 


11V2 


2 


2-31 


•154 


2^07 


649 


7-46 


1-85 


1-611 


3-355 


3-67 


iiV. 


2/. 


2-87 


•204 


2-47 


7^75 


9-03 


155 


1-328 


4-783 


5-77 


8 


3 


3-5 


•217 


3-07 


9-64 


11- 


1-24 


1-091 


7-388 


7-55 


8 


3V2 


4- 


•226 


3^55 


1115 


12^57 


1-08 


0-955 


9-887 


9-05 


8 


4 


4-5 


•237 


4-07 


12-69 


14^14 


•95 


0-849 


12^73 


10-73 


8 


4V2 


5- 


•247 


4-51 


1415 


15-71 


•85 


0-765 


15^939 


12-49 


8 


6 


6^56 


•259 


5-04 


15^85 


17-47 


•78 


0-629 


19^99 


14^56 


8 


6 


6^62 


•28 


6-06 


19^05 


20-81 


•63 


0-577 


28^889 


18^77 


8 


7 


1-62 


•301 


7-02 


22^06 


23-95 


•54 


0-505 


38^737 


23^41 


8 


8 


8^62 


•322 


7^98 


25^08 


27-1 


•48 


0-444 


50^039 


28^35 


8 


9 


9-69 


•344 


9^ 


28^28 


30-43 


•42 


0-394 


63^633 


34-08 


8 


10 


10^75 


•366 


10-02 


3r47 


33^77 


•38 


0-355 


78^838 


40^64 


8 



Nominal 
diameter. 


Thickness, 
extra strong. 


Thickness, double 
extra strong. 


Actual inside diameter. 
Extra strong. 


Actual inside diameter. 
Double extra strong. 


Inches. 


Inches. 


Inches. 


Inches. 


Inches. 


Vs 


0-100 





0^205 





v* 


0-123 





0-294 





Vs 


0^127 




0-421 


... . 


V2 


0^149 


0-298 


0-542 


0^244 


'U 


0^157 


0-314 


0^736 


0^422 


1 


0^182 


0-364 


0-951 


0-587 


1V4 


0^194 


0-388 


1-272 


0-884 


1V2 


0-203 


0-406 


1-494 


1-088 


2 


0-221 


0-442 


r933 


1-491 


2V2 


0-280 


0-560 


2^315 


1-755 


3 


0-304 


0-608 


2^892 


2-284 


37, 


0-321 


0-642 


3^358 


2-716 


4 


0-341 


0^682 


3^818 


3-136 



BOILEK TUBES. 



External 
diameter. 


Thickness, 
wire gauge. 


Average 
weight. 


External 
diameter. 


Thickness, 
wire gauge. 


Average 
Weight. 


Inches. 


No. 


Lbs. per foot. 


Inches. 


No. 


Lbs. per foot. 


IV4 


16 


1- 


3 


11 


3-5 


IV2 


15 


M6 


374 


11 


4- 


IV4 


14 


r63 ' 


4 


8 


6^4 


2 


13 


2- 


5 


7 


9^1 


27* 


12 


2-U 


6 


6 


123 


272 


12 


2-56 


7 


6 


15^2 


2^Vl6 


11 


2-2 


8 


6 


16^ 



776 



APPENDIX. 



HEAVY PIPE FOE DEIVEN WELLS. 

Tested at 1200 pounds hydraulic pressure. Furnished in five-foot lengths. 



Size (inches). 



Weight per foot, lbs . 



3-62 


H 


2 


2^ 


3 


H 


2-75 


3-75 


6-00 


7-75 


9-25 



11-00 



HEAVY WROUGHT GALVANIZED lEON SPIRAL RIVETED PIPES, 

With Flanged Connections. 

Tested at 150 pounds hydraulic pressure. Eegalvanized after riveting. 



Inside diameter (inches ) 


3 


4 


5 


6 


7 


8 


9 


10 


11 


12 


Wire ffauffe, Nos 


20 


20 
4 


20 
5 


18 
6 


18 

7 


18 
8 


18 
9 


16 
12 


16 
13 


16 


Nominal weight per foot, lbs. . . 


14 



Manufactured lengths, 20 feet or less. Elbows and other fittings, cast iron. 



Light Pipe, suitable foe House Leaders, Ventilating, Aie, and Blower Pipes, etc. 



Inside diameter (inches). 



Nominal weight per foot, lbs 



2 


2i 


3 


f 


f 


i 



H 



n 



H 



If ! H 



H 



If 



If 



TABLE OF COPPEE AND BE ASS EODS ONE FOOT IN LENGTH. 

To find the weight of copper or brass pipe, take the weight of the exterior diameter from the 
table, and subtract from it the weight of a rod equal to that of the interior diameter, or bore. 



Diamet'r 






Diamet'r 






DiametT 






in 


Copper. 


Brass. 


in 


Copper. 


Brass. 


in 


Copper. 


Brass. 


inches. 






inches. 






inches. 






Vb 


•047 


-045 


IV. 


7-993 


7-593 


4V4 


55-62 


62^27 


7- 


•106 


•101 


1"A6 


8^630 


8^198 


4V8 


58-94 


5539 


v. 


•189 


•179 


1V4 


9^270 


8^806 


4V2 


62-36 


58-60 


Vie 


•296 


•281 


VVie 


9^950 


9^452 


4V8 


65^87 


61-90 


Vs 


•426 


•405 


iVs 


10^642 


10^110 


4V4 


69-48 


6 


Vl6 


•579 


•550 


i^V- 


11-370 


10^801 


4V8 


73-19 


68-77 


v= 


•757 


•719 


2 


12-108 


1P503 


5 


77-43 


72^76 


Vaa 


•958 


•910 


2V8 


13^668 


12^985 


5V8 


80-89 


76^00 


Ve 


1^182 


M23 


2V4 


15^325 


14^559 


5V4 


84-88 


79-76 


"A. 


1-431 


1^360 


27e 


17^075 


16^221 


5V8 


88-97 


83-60 


^4 


1-703 


P618 


2V» 


18^916 


17^970 


5V, 


93^15 


87-58 


'Vae 


1-998 


1-898 


2V8 


20-856 


19^808 


5V8 


97^44 


91-66 


Vs 


2-318 


2^202 


2V4 


22-891 


21^746 


5V4 


101-81 


95^68 


^V.6 


2^660 


2^527 


2V8 


25-019 


23^768 


•578 


106-29 


99^88 


1 


3-027 


2^876 


3 


27-243 


25^881 


6 


110-85 


104^15 


iVie 


3^417 


3-246 


3V8 


29-559 


28^081 


6V4 


120 30 


113-04 


IV. 


3-831 


3-639 


3V4 


31-972 


30-373 


6V. 


130-10 


122-26 


iViB 


4-269 


4-056 


3Vb 


34-481 


32-757 


6V4 


140-32 


131-85 


1V4 


4-723 


4-487 


3V. 


37-081 


35-227 


7 


150-86 


141-76 


lVl6 


5-214 


4^953 


3V8 


39-777 


37^788 


^V4 


161-87 


152-10 


iVs 


6^723 


5^437 


3V4 


42-568 


40^440 


VV^ 


173^22 


162^77 


lVl6 


6^255 


5^943 


3V8 


45^455 


43-182 


774 


184^97 


173-81 


IV. 


6-811 


6^470 


4 


48^433 


46-000 


8 


197^03 


185^14 


17:6 


7^390 


7^020 


4Vb 


52^40 


49-24 









APPENDIX. 



777 



NUMBER OF BURDEN'S RIVETS IN ONE HUNDRED POUNDS. 







DlAUETEB. 








Lengths, 








Lengths. 


^S.B. 




i 


1 


if 


1 




f 1 


,09S 


J 665 


.... 




5 


90 


i 1 


,02^ 


r 597 






H 


85 


1 


94C 


) 538 


450 


.... 


6 


80 


n 


84C 


) 512 


415 


.... 


6^ 


75 


H 


79" 


r 487 


389 


356 


7 


70 


If 


76C 


) 460 


370 


329 


n 


67 


H 


73C 


) 440 


357 


280 


8 


65 


If 


711 


420 


340 


271 


8^ 


61 


If 


69S 


390 


325 


262 


9 


57 


H 


64^ 


375 


312 


257 


H 


54 


2 


60^ 


360 


297 


243 


10 


51 


H 


572 


354 


.... 


.... 


m 


47 


2i 


55^ 


347 


280 


232 






H 


52c 


335 


260 


220 






2i 


50C 


) 312 


242 


208 






3 


46C 


) 290 


224 


197 






H 


43? 


267 


212 


180 






H 


4U 


1 248 


201 


169 






3| 


S9t 


) 241 


192 


160 






4 




230 


184 


158 






4i 


. . 


220 


177 


150 






H 


. . 


210 


171 


146 






4f 


. . 


200 


166 


138 






5 




190 


161 


135 






5i 




180 


156 


130 






5i 


. . 


172 


151 


124 






5f 


. . 


164 


145 


120 






6 




157 


140 


115 






H 




150 


138 


111 






H 




146 


134 


107 






6f 


. . 


143 


129 


104 






7 


•• 


140 


125 


100 







WROUGHT SPIKES — NUMBER TO A KEG OF ONE HUNDRED AND FIFTY POUNDS. 



Lbngth. 


i" 


^" 


1" 


tV 


i" 


Inches 
3 


2,250 
1,890 
1,650 
1,464 
1,380 
1,292 
1,161 


1,208 
1,135 
1,064 
930 
868 
662 
635 
573 


742 
570 
482 
455 
424 
391 


445 
384 
300 
270 
249 
236 




H 

4 


.... 


44 




5 




6 




7 


306 


8 


256 


9 


240 


10 


222 


11 


203 


12 


180 







778 



APPENDIX. 



LENGTHS OF CUT NAILS AND SPIKES, AND NUMBEE IN A POUND. 



Size. 


Length. 


No. 

420 


Size. 


Length. 


No. 


Size. 


Length. 


No. 


M. 


Inches. 


M. 


, Inches. 

2i 


100 


30o?. 


Inches. 
4 


24 


4 


U 


270 


10 


3 


65 


40 


4i 


20 


5 


If 


220 


12 


H 


52 


60 






6 


2 


175 


20 , 


H 


28 









APPROXIMATE NUMBER OF WIRE NAILS PER POUND. 



Wire 














Length 


Inches. 
















Gauge. 
B. W. G. 


M 


X 


H 


% 


% 


1 


1^ 


^H 


1% 


2 


2^ 


3 


3>^ 


4 


4X 


5 


6 


7 


00 














33 

34 

45 

52 

60 

72 

85 

99 

120 

137 

165 

198 

251 

329 

429 

568 

701 

913 

1246 

1655 

2133 

3000 


27 

29 

38 

44 

50 

60 

71 

82 

100 

115 

138 

165 

209 

274 

357 

473 

584 

761 

1038 

1379 

1778 


23 

25 

32 

37 

43 

51 

60 

71 

85 

98 

118 

142 

179 

235 

306 

406 

500 

653 

890 

1182 


20 

21 

28 

32 

38 

45 

53 

62 

75 

86 

103 

124 

157 

204 

268 

350 

438 

571 

779 


16 

17 

23 

26 

30 

36 

42 

50 

60 

69 

82 

99 

125 

164 

214 

284 

350 


14 

15 

19 

22 

25 

30 

35 

41 

50 

57 

69 

83 

105 

137 

178 

236 


12 
13 
16 
19 
22 
26 
30 
35 
43 
49 
59 
71 
90 
117 
153 


10 
11 

14 
16 
19 
23 
26 
31 
37 
43 
52 
62 
79 
103 


9 
10 
13 
14 
17 
20 
24 
28 
33 
39 
46 
55 
70 


8 
9 
11 
13 
15 
18 
21 
25 
30 
35 
41 
50 


7 
8 
10 
11 
13 
15 
18 
21 
25 
29 


6 



















1 . . . . 












57 

65 

76 

90 

106 

123 

149 

172 

207 

248 

314 

411 

536 

710 

876 

1143 

1.5.58 

2069 

2667 

3750 

4444 


8 


2 












9 


3 










100 
120 
141 
164 
200 
229 
276 
333 
418 
548 
714 
947 
1168 
1523 
2077 
2758 
.3556 
5000 
5926 
7618 


11 


4 










13 


5 






211 

247 

299 

345 

414 

496 

628 

822 

1072 

1420 

1752 

2280 

3116 

4138 

5334 

7500 

8888 

11428 


169 

197 

239 

275 

331 

397 

502 

658 

857 

1136 

1402 

1828 

2495 

3310 

4267 

6000 

7111 

9143 


15 


6 






18 


7 








8 








9 








10 




663 

837 

1096 

1429 

1893 

2336 

3048 

4156 

5517 

7112 

10000 

11850 

15237 




11 






12 






1,3 






14 


2840 
3504 
4571 
62.33 
8276 
10668 
15000 
17777 
22856 




15 

16 . 


B. \ 


Y.G. 


8 


9 


10 


11 


12 


17 





5 

7 
8 
10 
11 


6 

7 
8 
10 


4 

4>^ 


3M 
4 
5 
6 


3M 

4X 
5^ 


18 

19 


1 

2 


20 


3 


21 


4 


22 


5 









TESTS OP TELEGRAPH WIRE. 

The following data are taken from a table given by Mr. Prescott relating to tests of E. B. 
B. galvanized wire furnished the Western L^nion Telegraph Company : 







Weight. 




Resistance. 
Temp., 75-8° Fahr. 


Ratio of 


Size 


Diameter 
Parts of 






Length, 
Feet per 




Breaking 
Weight to 


of 










Wire. 


One Inch. 


Grains, per 


Pounds per 


Pound. 


Feet per 


Ohms per 


Weight per 






Foot. 


Mile. 




Ohm. 


Mile. 


Mile. 


4 


•238 


1043^2 


886-6 


6-00 


958 


5^51 




5 


•220 


891-3 


673^0 


7-85 


727 


7^26 




6 


•203 


758-9 


572^2 


9-20 


618 


8^54 


3-05 


7 


•180 


596-7 


449-9 


11-70 


578 • 


10^86 


3^40 


8 


•165 


501-4 


378-1 


14-00 


409 


12-92 


3-07 


9 


•148 


403-4 


304-2 


17-4 . 


328 


16-10 


3-38 


10 


•134 


330-7 


249-4 


21^2 


269 


19-l/G 


3^37 


11 


•120 


265^2 


200^0 


26^4 


216 


24-42 


2-97 


12 


•109 


218-8 


165^0 


32^0 


179 


29-60 


3^43 


14 


•083 


126-9 


95^7 


55^2 


104 


51-00 


3^05 



SIZES OF GALVANIZED WIRE USED IN TELEGRAPH AND TELEPHONE 

LINES. 

No. 4. Now used on important lines where the multiplex systems are applied. No. 
5. Little used. No. 6. Used for important circuits between cities. No. 8. Medium size 
for circuits of 400 miles or less. No. 9. For similar locations to No. 8, but on somewhat 



APPENDIX. 



70 



shorter circuits ; until lately was the size most largely used in this country. Nos. 10, 11. 
For shorter circuits, railway telegraphs, private lines, police and fire-alarm lines, etc. 
No. 13. For telephone lines, police and fire-alarm lines, etc. Nos. 13, 14. For telephone 
lines and short private lines : steel wire is used most generally in these sizes. 

The grades of line wire are generally known to the trade as "Extra Best Best " (E. 
B. B.), "Best Best" (B. B.), and "Steel." 





STANDARD I BEAMS. 



Depth 


Min. wt. 
foot. 


Min. 
b. 


Min. 
t. 


z. 


s. 


P- 


y- 


of 
beam. 


24" 


80-00 


7-00 


•50 


3-250 


•60 


•542 


1-142 


20" 


64-00 


6-25 


•50 


2-875 


-55 


•479 


1-029 


15" 


42-00 


5-50 


-41 


2-545 


•41 


•424 


0-834 


12" 


31-50 


5-00 


-35 


2-325 


-35 


•388 


0-738 


10" 


25-00 


4-66 


-31 


2-175 


-31 


-363 


0-673 


9" 


21-00 


4-33 


-29 


2-020 


•29 


-337 


0-627 


8" 


18-00 


4-00 


-27 


1-865 


-27 


-311 


0-581 


7" 


15-00 


3-66 


-25 


1-705 


•25 


-284 


0-534 


6' 


12-25 


3-33 


-23 


1-550 


-23 


-258 


0-488 


5" 


9-75 


3-00 


-21 


1-395 


-21 


•233 


0-443 


4" 


7-50 


2-66 


•19 


1-235 


-19 


•206 


0-396 


3" 


5-50 


2-33 


-17 


1-080 


-17 


•180 


0-350 



WEIGHT PER FOOT. 



Intermediate. 



Vary by 5 lbs. 

65 lbs. then by 5 lbs. 

45 " " 5 " 



Vary by 5 lbs. 

25 lbs. then by 5 lbs, 

Vary by 2^ lbs. 

" " 2i " 



" 2i " 

" 2i " 

" 1 lb. 

" 1 " 



Increase 
of b and t 
for each 
lb. inc. of 
weight. 



•0123 
•015 
•020 
•025 

-029 
-033 
-037 
-042 

•049 
-059 
-074 
•098 



Max. 



100-00 
75-00 
55-00 
35-00 

40-00 
35-00 
25-50 
20 00 

17-25 

14-75 

10-50 

7-50 



STANDARD CHANNELS. 



Depth 
of 


Min. wt. 


Min. 


Min. 










chan- 
nel. 


foot. 


b. 


t. 




s. 


P- 


y- 


15" 


33-00 


3-40 


•40 


3^00 


•40 


•500 


•900 


12" 


20^50 


2-94 


•28 


2^66 


•28 


•443 


•723 


10" 


15^00 


2-60 


•24 


2^36 


•24 


•393 


•633 


9" 


13-25 


2-43 


-23 


2^20 


•23 


•367 


•597 


8" 


11^25 


2-26 


•22 


2-04 


•22 


•340 


•560 


7" 


9^75 


2-09 


•21 


1-88 


•21 


•313 


•523 


6" 


8^00 


1-92 


•20 


1-72 


•20 


•287 


•487 


5" 


6-50 


1-75 


•19 


1-56 


•19 


•260 


•450 


4" 


5-25 


1-58 


•18 


1-40 


•18 


-233 


•413 


3" 


4-00 


1-41 


•17 


1-24 


•17 


-207 


•377 



WEIGHT PER FOOT. 



Intermediate. 



35 lbs. then by 5 lbs. 
25 " " ' 5 " 

Vary by 5 lbs. 
15 lbs. then by 5 lbs. 
Vary by 24- lbs. 



2i " 
2i " 
2i " 
1 lb. 
1 " 



Increase 
of b and t 
for each 
lb. inc. of 
weight. 



020 
025 
•029 
•033 
•037 

•042 
•049 
•059 
•074 
•098 



Max. 



55^00 
40^00 
35^00 
25^00 

21^25 

19^75 

15^50 

11^50 

7-25 

6-00 



During the preparation of this work the Association of American Steel Manufacturers 
has been formed, from whose circular the above table has been extracted. 



GRADES OF STEEL. 

Rimt Steel. — Ultimate strength, 48,000 to 58,000 pounds per square inch. 
Elongation, 26 per cent. 



780 



APPENDIX. 



Soft Steel. — intimate strength, 52,000 to 62,000 pounds per square inch. 
Elongation, 25 per cent. 

Medium Steel. — Ultimate strength, 60,000 to 70,000 pounds per square inch. 
Elongation, 22 per cent. 

Elastic limit, not less than one half the ultimate strength. 

Bending test, 180 degrees flat on itself, or equal to thickness of piece tested, without 
fracture on outside of bent portion. 





WEIGHTS OF 


LEAD PIPE PEE FOOT IN LENGTH. 








Maek. 


Caliber. 


AAA 


AA 


A 


B 


C 


D 


E 




i 
1 


Lbs. oz. 
1 12 


Lbs. oz. 
1 5 


Lbs. oz. 

1 2 


Lbs oz. 
1 


Lbs. oz. 
14 


Lbs. oz. 

7 


Lbs. oz. 
2 


Lbs. oz. 
2 

10 




3 .. 


2 


1 10 


1 3 


1 


10 


.. .. 


9i 




2 8 


. . 


o . 


. . 




12 


.. 


.. .. 


f 


3 8 


2 12 


2 8 


2 


1 7 


1 4 


12 


.... 


f 


4 14 


3 3 


3 


2 3 


1 12 


1 3 


1 


.... 


1 


6 .. 


4 8 


4 


3 4 


2 8 


2 4 


2 


1 8 


li 


6 12 


6 12 


4 11 


3 11 


_ 3 


2 8 


2 


.... 


H 


8 


7 


6 4 


5 


4 4 


3 8 
3 


2 


.. .. 


If 


.. .. 


8 8 


6 7 


5 


4 


3 10 


. . . . 


. . . . 


2 


10 11 


8 14 


7 


6 


5 


4 


, . , , 


.... 






c . 


. . 


. . 


Wa 


3 

8TE. 




, , . . 




Thickness. 






1 


-h 


i 


A 




H 


16 11 


13 10 


10 10 


7 3 


6 


4 


. . . . 


3 


19 9 


16 


12 9 


9 4 


5 


3 8 


. . . . 


. • . . 


H 


22 8 


18 7 


14 8 


10 12 


.... 


. . . . 


. . . . 


.. .. 


4 


25 6 


20 14 


16 7 


12 2 


8 


6 




. . . . 


H 


. . 


.. 


18 6 


13 9 


.... 


. . . . 


10 8 


7 6 


5 


31 3 


.. 


20 5 


15 


.... 


. . . . 


10 8 


. . . . 


6 


.. .. 


.. .. 




.. .. 


.. .. 


.. .. 


12 


.. .. 



TABLE OF THE WEIGHT OF A CUBIC FOOT OF WATEE AT DIFFERENT TEM- 

PEEATUEES. 



Fahren- 
heit. 


Centi- 
grade. 


Weight in 
pounds. 


Fahren- 
heit. 


Centi- 
grade. 


Weight in 
pounds. 


Fahren- 
heit, 


Centi- 
grade. 


Weight in 
pounds. 


Degrees. 
32 


Degrees. 



62-42 


Degrees. 
95 


Degrees. 
35 


62-06 


Degrees, 
167 


Degrees. 
75 


60-87 


39 


4 


62-42 


104 


40 


61-95 


176 


80 


60-68 


41 


5 


62-42 


113 


45 


61-83 


185 


85 


60-48 


50 


10 


62-41 


122 


50 


61-69 


194 


90 


60-27 


59 


15 


62-37 


131 


55 


61-55 


203 


95 


60-04 


68 


20 


62-32 


140 


60 


61-39 


212 


100 


59-83 


77 


25 


62-25 


149 


65 


61-23 








86 


30 


62-16 


158 


70 


61-06 









APPENDIX. 



781 




Fig. 1863. 



THE FLOW OF WATER. 

With the increased consumption of water by the mills at Lowell, Mass. , there was 
found a necessity for the accurate gauging of the quantities severally used, and, as at 
times the total was beyond the flow of the stream, that it should be properly distributed 
and that none should be wasted. At this time the late James B. Francis was the engi- 
neer of the Locks and Canals Company, to whom the charge of the canals and water dis- 
tribution was committed. He decided that the weir was 

the form in which the water from the several wheels 
should be measured as most economical in application and 
accurate in results. 

Figs. 1863 and 1864 are the sectional elevation and 
plan of the common form of weir, in which the lower 
edges, bottom, and sides are chamfered off, with edges 
about i" wide, making a perfect rectangle. In his ex- 
periments Mr. Francis made the bottom plate of cast iron 
with the upper edge planed and set accurately horizontal 
and the sides planed for the vertical edges and for the 
joints with the bottom plate. The iron rectangle could 
be accurately measured, but it was necessary to deter- 
mine the wetted rectangle from the height of the water 
above the bottom edge. This was done by the hook 
gauge, in which the hook was submerged in the water 
and gradually raised by a micrometer screw till it showed 
the sign of a rising at the surface of the water (Fig. 1865). 
The of the scale of the gauge was accurately referred 
to the edge of the weir. It was necessary that the surface 
of the water at the hook be kept perfectly still. It was 
therefore submerged in a tight box which had communi- 
cation with the water in the flume by a very small hole or 
by a small pipe on the bottom of the flume, across it par- 
allel to the weir and at a slight distance from it. In this 
pipe at equal intervals in the width of the weu- small holes 
were drilled. The effect of this pipe was to give an aver- 
age water level in the gauge box. 

The general formula established by the experiments, 
on which the following table is calculated, is Q = 3-33 
{I _ -^h) A|, in which Qis the discharge in cubic feet per 
second, I the length of the weir, and h the height of water 
above the crest of the weir, both in feet. 

For complete end contractions the side of the weir 
should be at least equal to the depth of the water on it 
from the side of the canal. The bottom contraction, also 
complete, is shown by a body of air below the crest of 
the weir. Where there is no end contraction, provision 
should be made for introducing and maintaining free 
communications of the air beneath the water sheet. For 
large velocities of approach to the weir, divide the area of 
water section above it by its discharge from the table for \ 
add h' to previous depth for corrected discharge. 

In the table, the discharge is given for one foot in length ; but as in weirs there are 
usually two end contractions, virtually reducing the length, and met in the formula above 
by — -2^, a column of correction has been added, which is to be subtracted from the 
product of discharge, as shown in example. 




Fig. 1864. 




Fig. 1865. 



in the equation h' 



2? 



and 



'82 



APPENDIX. 



DISCHARGE, IN CUBIC FEET PEE SECOND, OF A WEIR ONE FOOT LONG, WITH- 
OUT CONTRACTION AT THE ENDS ; FOR DEPTHS FROM 0-200 TO 0-999 FEET. 



Correction 
























for con- 


Depth. 





1 


2 


3 


4 


5 


6 


7 


8 


9 


tractions. 
























•012 


0-20 


0-298 


0-300 


0-302 


0-305 


0-307 


0-309 


0-311 


0-314 


0-316 


0-318 


•013 


•21 


0-320 


0-323 


0-325 


0-327 


0-330 


0-332 


0-334 


0-337 


0-339 


0-341 


-015 


•22 


0^344 


0-346 


0-348 


0-351 


0-353 


0-355 


0-358 


0-360 


0-362 


0-365 


•OlY 


•23 


0-367 


0-370 


0-372 


0-374 


0-377 


0-379 


0-382 


0-384 


0-387 


0-389 


•019 


•24 


0-391 


0-394 


0-396 


0-399 


0-401 


0-404 


0-406 


0-409 


0-411 


0-414 


•021 


•25 


0-416 


0-419 


0-421 


0-424 


0-426 


0-429 


0-431 


0-434 


0-436 


0-439 


-023 


•26 


0-441 


0-444 


0-447 


0-449 


0-452 


0-454 


0-457 


0-459 


0-462 


0-465 


•025 


•27 


0-467 


0-470 


0-472 


0-475 


0-478 


0-480 


0-483 


0-485 


0-488 


0-491 


-028 


•28 


0-493 


0-496 


0-499 


0-501 


0-504 


0-507 


0-509 


0-512 


0-515 


0-517 


•030 


•29 


0-520 


0-523 


0-525 


0-528 


0-531 


0-534 


0-536 


0-539 


0-542 


0-544 


•033 


0-30 


0-547 


0-550 


0-553 


0-555 


0-558 


0-561 


0-564 


0-566 


0-569 


0-572 


•036 


•31 


0-575 


0-577 


0-580 


0-583 


0-586 


0-589 


0-591 


0-594 


0-597 


0-600 


•039 


•32 


0-603 


0-606 


0-608 


0-611 


0-614 


0-617 


0-620 


0-623 


0-625 


0-628 


•042 


•33 


0-631 


0-634 


0-637 


0-640 


0-643 


0-646 


0-649 


0-651 


0-654 


0-657 


•045 


•34 


0-660 


0-663 


0-666 


0-669 


0-672 


0-675 


0-678 


0-681 


0-684 


0-687 


•048 


•35 


0-689 


0-692 


0-695 


0-698 


0-701 


0-704 


0-707 


0-710 


0-713 


0-716 


•052 


•36 


0-719 


0-722 


0-725 


0-728 


0-731 


0-734 


0-737 


0-740 


0-743 


0-746 


•056 


•37 


0-749 


0-752 


0-755 


0-759 


0-762 


0-765 


0-768 


0-771 


0-774 


0-777 


•059 


•38 


0-780 


0-783 


0-786 


0-789 


0-792 


0-795 


0-799 


0-802 


0-805 


0-808 


•063 


•39 


0-811 


0-814 


0-817 


0-820 


0-823 


0-827 


0-830 


0-833 


0-836 


0-839 


•067 


0-40 


0-842 


0-846 


0-849 


0-852 


0-855 


0-858 


0-861 


0-865 


0-868 


0-871 


•072 


•41 


0-874 


0-877 


0-881 


0-884 


0-887 


0-890 


0-893 


0-897 


0-900 


0-903 


-076 


•42 


0-906 


0-910 


0-913 


0-916 


0-919 


0-923 


0-926 


0-929 


0-932 


0-936 


-081 


•43 


0-939 


0-942 


0-945 


0-949 


0-952 


0-955 


0-959 


0-962 


0-965 


0-969 


-085 


•44 


0-972 


0-975 


0-978 


0-982 


0-985 


0-988 


0-992 


0-995 


0-998 


1-002 


•090 


•45 


1-005 


1-009 


1-012 


1-015 


1-019 


1-022 


1-025 


1-029 


1-032 


1-035 


•095 


•46 


1-039 


1-042 


1-046 


1-049 


1-052 


1-056 


1-059 


1-063 


1-066 


1-070 


•100 


•47 


1-073 


1-076 


1-080 


1-083 


1-087 


1-090 


1-094 


1-097 


1-100 


1-104 


•106 


•48 


1-107 


1-111 


1-114 


1-118 


1-121 


1-125 


1-128 


1-132 


1-135 


1-139 


•111 


•49 


1-142 


1-146 


1-149 


1-153 


1-156 


1-160 


1-163 


1-167 


1-170 


1-174 


•118 


0-50 


1-177 


1-181 


1-184 


1-188 


1-191 


1-195 


1-199 


1-202 


1-206 


1-209 


•124 


•51 


1-213 


1-216 


1-220 


1-223 


1-227 


1-231 


1-234 


1-238 


1-241 


1-245 


•130 


•52 


1-249 


1-252 


1-256 


1-259 


1-263 


1-267 


1-270 


1-274 


1-278 


1-281 


•136 


•53 


1-285 


1-288 


1-292 


1-296 


1-299 


1-303 


1-307 


1-310 


1-314 


1-318 


•143 


•54 


1-321 


1-325 


1-329 


1-332 


1-336 


1-340 


1-343 


1-347 


1-351 


1-355 


•150 


•55 


1-358 


1-362 


1-366 


1-369 


1-373 


1-377 


1-381 


1-384 


1-388 


1-392 


•157 


•56 


1-395 


1-399 


1-403 


1-407 


1-410 


1-414 


1-418 


1-422 


1-425 


1-429 


•164 


•57 


1-433 


1-437 


1-441 


1-444 


1-448 


1-452 


1-456 


1-459 


1-463 


1-467 


•171 


-58 


1-471 


1-475 


1-478 


1-482 


1-486 


1-490 


1-494 


1-498 


1-501 


1-505 


•178 


•59 


1-509 


1-513 


1-517 


1-521 


1-524 


1-528 


1-532 


1-536 


1-540 


1-544 


•186 


0-60 


1-548 


1-551 


1-555 


1-559 


1-563 


1-567 


1-571 


1-575 


1-579 


1-583 


•194 


•61 


1-586 


1-590 


1-594 


1-598 


1-602 


1-606 


.1-610 


1-614 


1-618 


1-622 


•202 


•62 


1-626 


1-630 


1-633 


1-637 


1-641 


1-645 


1-649 


1-653 


1-657 


1-661 


•210 


•63 


1-665 


1-669 


1-673 


1-677 


1-681 


1-685 


1-689 


1-693 


1-697 


1-701 


•218 


•64 


1-705 


1-709 


1-713 


1-717 


1-721 


1-725 


1-729 


1-733 


1-737 


1-741 


•227 


•65 


1-745 


1-749 


1-753 


1-757 


1-761 


1-765 


1-769 


1-773 


1-777 


1-781 


•236 


•66 


1-785 


1-790 


1-794 


1-798 


1-802 


1-806 


1-810 


1-814 


1-818 


1-822 


•245 


•67 


1-826 


1-830 


1-834 


1-838 


1-843 


1-847 


1-851 


1-855 


1-859 


1-863 


•254 


•68 


1-867 


1-871 


1-875 


1-880 


1-884 


1-888 


1-892 


1-896 


1-900 


1-904 


•263 


•69 


1-909 


1-913 


1-917 


1-921 


1-925 


1-929 


1-934 


1-938 


1-942 


1-946 


•273 


0-70 


1-950 


1-954 


1-959 


1-963 


1-967 


1-971 


1-975 


1-980 


1-984 


1-988 


•283 


•71 


1-992 


1-996 


2-001 


2-005 


2-009 


2-013 


2-017 


2-022 


2-026 


2-030 


•293 


•72 


2-034 


2-039 


2-043 


2-047 


2-051 


2-056 


2-060 


2-064 


'2-068 


2-073 


•303 


•73 


2-077 


2-081 


2-085 


2-090 


2-094 


2-098 


2-103 


2-107 


2-111 


2-115 


•314 


•74 


2-120 


2124 


2-128 


2-133 


2-137 


2-141 


2-146 


2-150 


2-154 


2-159 


•324 


•75 


2-163 


2-167 


2-172 


2-176 


2-180 


2-185 


2-189 


2-193 


2-198 


2-202 



APPENDIX. 



783 



DISCHAKGE, IN CUBIC FEET PER SECOND, OF A WEIR ONE FOOT LONG, WITH- 
OUT CONTRACTION AT THE ENDS ; FOR DEPTHS FROM 0-200 TO 0-999 FEET. 

( Continued. ) 



Correction 
























for con- 


Depth. 





1 


2 


3 


4 


5 


6 


7 


8 


9 


tractions. 
























•335 


•76 


2^206 


2-211 


2-215 


2^219 


2^224 


2-228 


2-232 


2-237 


2-241 


2-246 


•346 


•77 


2-250 


2-254 


2-259 


2^263 


3-267 


2-272 


2-276 


2-281 


2-285 


2-290 


•358 


•78 


2-294 


2-298 


2-303 


2-307 


2-312 


2-316 


2^320 


2-325 


2-329 


2-334 


•369 


•79 


2-238 


2-343 


2-347 


2-351 


2-356 


2-360 


2^365 


2-369 


2-374 


2-378 


•381 


0-80 


2-383 


2-387 


2-392 


2-396 


2-401 


2^405 


2-410 


2-414 


2-419 


2-423 


•393 


-81 


2-428 


2432 


2^437 


2-441 


2-446 


2-450 


2-455 


2-459 


2-464 


2-468 


•406 


•82 


2-473 


2^477 


2-482 


2-486 


2-491 


2-495 


2-500 


2-504 


2-509 


2-513 


•413 


-83 


2-518 


2-523 


4-527 


2-532 


2-536 


2-541 


2-545 


2-550 


2-554 


2-559 


•431 


•84 


2-564 


2^568 


2-573 


2-577 


2-582 


2-587 


2-591 


2-596 


2-600 


2-605 


•444 


•85 


2-610 


2-614 


2-619 


2-623 


2-628 


2-633 


2-637 


2-642 


2-646 


2-651 


•457 


•86 


2-656 


2-660 


2-665 


2-670 


2-674 


2-679 


2-684 


2-688 


2-693 


2-698 


•470 


•87 


7^702 


2-707 


2-712 


2-716 


2-721 


2^726 


2-730 


2-735 


2-740 


2-744 


•484 


•88 


2^749 


2-154: 


2-758 


2-763 


2-768 


2-772 


2-777 


2-782 


2^786 


2-791 


•498 


•89 


2^796 


2-801 


2-805 


2-810 


2-815 


2-819 


2-824 


2-829 


2^834 


2-838 


•512 


0-90 


2-843 


2-848 


2-853 


2-857 


2-862 


2-867 


2-872 


2-876 


2^881 


2-886 


•526 


•91 


2-891 


2-895 


2-900 


2-905 


2-910 


2-915 


2-919 


2-924 


2^929 


2-934 


•541 


•92 


2-938 


2-943 


2-948 


2-953 


2-958 


2-963 


2-967 


2-972 


2^977 


2-982 


•555 


•93 


2-986 


2-991 


2-996 


3-001 


3-006 


3-011 


3-015 


3-020 


3^025 


3-030 


•570 


•94 


3-035 


3-040 


3-044 


3-049 


3-054 


3-059 


3-064 


3-069 


3-074 


3-078 


•586 


•95 


3-083 


3-088 


3-093 


3-098 


3-103 


3-108 


3-113 


3-117 


3-122 


3^127 


•601 


•96 


3-132 


3-137 


3142 


3-147 


3-152 


3-157 


3-162 


3-166 


3-171 


3^176 


•677 


•97 


3-181 


3-186 


3^191 


3-196 


3-201 


3-206 


3-211 


3-216 


3-221 


3^226 


•632 


•98 


3-231 


3^235 


3-240 


3^245 


3-250 


3-255 


3-260 


3-265 


3-270 


3^275 


•648 


•99 


3-280 


3-285 


3-290 


3^295 


3-300 


3-305 


3-310 


3-315 


3^320 


3^325 



Example. — Let the weir, with end contractions, be 5*3 feet long, and depth of water, 
OTh = 0-612. 

By table the discharge for one foot in length is 1^594 

8 •4483 
Correction •196 

Discharge in cubic feet per second 8 '2522 

The measures of the discharge of the different wheels was accurately determined ; it 
was equally important to determine the quantities used by the different corporations. 
Mr. Francis's arrangements for this purpose were the construction of rectangular plank 
flumes in the different canals or feeders, of which the widths w^ere divided into feet 
marked on the upstream faces of the timbers, extending above and across the ends of the 
flume, which enabled the average thread of the float in its passage through the flume to 
be ascertained. The depth of the water in the flume was measured by a gauge placed 
centrally on one side of the flume. The floats measuring the velocity of the currents 
were adjusted to the depths of water, having some two inches clearance from the bottom. 
The tubes were of two to three inches diameter, loaded at the bottom, and marked with 
their water line. They were brought to the flume and those of length appropriate to 
its depth were selected. From the notes thus taken the average path of the float was 
determined, on which was plotted its velocity, as represented by the different circles 
(Fig. 182). Through the average of these circles on the lines of flow is drawn the full 
line of averages from which the average of the total flow was determined. 



784: 



APPENDIX. 



In a similar way gaugings may be made of natural streams where the sections are ap- 
proximately smaller. Soundings are to be made across the stream and sections drawn. 
The average velocities may be taken through these sections, which multiplied by the 
products of the sections and nine tenths of their sum will give approximately the flow 
of the streams. For this kind of measure I have used two rubber balls connected by an 
adjustable soft cotton cord, the lower ball being filled with water. A light strong thread 
is attached to the upper ball with the ends in the hands of the observers on each side of 
the stream, by which the ball may be guided in the thread of its appropriate section. 

It was customary to find the average flow of a stream from the surface velocities in 
different threads of it according to the sections by means of apples loaded with shingle 
nails to nearly the specific gravity of the water, casting them into the stream, and taking 
the time of transit between two cords stretched across it, and taking as an average about 
eighty per cent that of the whole observations by the area of the entire section. Surface 
velocities only to be considered as loose approximations, as they are very much influenced 
by the direction and strength of the wind and the uniformities of flow in the different 
sections and diversions or eddies. 

The miner's inch is designated as the flow through one square inch, but under vari- 
ous heads in different states. P. J. Flynn in "Irrigation Canals" gives one cubic foot 
per second as the equivalent flow through fifty miner's inches under a mean head of four 
inches. 




3 a ^ 

FfG. 1866. 



FLOW OF WATER IN PIPES AND CONDUITS. 



The general formula for the flow of water in all channels is v = c |/^s, in which xi is 
the velocity, c a coefficient determined for the particular form of channel, R the 
hydraulic mean depth — that is, the area of water cross-section— divided by its wetted 
perimeter of channel; s is the slope of difference of level or pressure in feet between two 
points divided by the length in feet. 

Fig. 1866 is a section of a water pipe in which the capacities are shown of its differ- 
ent sections from the bottom to a full section without any head. The friction of the 
sides of the full pipe reduces the velocity, and the maximum is at about eighty per cent 
of full, and the maximum of the curve of discharge or velocity by area of section a little 
above ninety per cent. It must be observed that the velocity at half section is the same 
as when the pipe is full. 

Messrs. Ganguillet and Kutter have established formulae, of which there is a modifi- 
cation according to the character of the surface of the wetted perimetre. 

The Kutter formula, as it is called, is very complicated, but it has been simplified 
graphically by Mr. Rudolph Bering and published in the " Transactions of the A. S. C. 
E.," January, 1879, from which the figures have been redrawn. 



APPENDIX. 



785 



IRON ; CEMENT ; TERRA COTTA PIPES, WELL-JOINTED AND IN BEST ORDER ; CAREFULLY 

PLASTERED SURFACE. 










Grd 

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des in 


feef per 
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51 



786 



APPENDIX. 



OLD IRON ; CEMENT AND TERRA COTTA PIPES NOT WELL-JOINTED NOR IN PERFECT 
ORDER : WELL LAID BRICKWORK. 






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APPENDIX. 



Y8T 



FOUL AND SLIGHTLY TUBERCULATED IRON ; CEMENT AND TERRA COTTA PIPES WITH 
IMPERFECT JOINTS, AND IN BAD ORDER ; WELL-DRESSED STONEWORK AND SECOND 
CLASS BRICKWORK. 



Grades in feet per hundred /?= .0/6 

.1 .2 A .6 .8 /. 2. 3. 4. 6. 6. 



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'88 



APPENDIX. 



IRON ; CEMENT I TERRA COTTA PIPES, WELL-JOINTED AND IN BEST ORDER. 



Grddes in feet per hundred] 

.02.04.06\/ .2 .3 A .6 .6 .7 .8 .3 /.O A5 



n. -Oil 

ZO Z6 3.0 




16XZ3 



Z'X3' 



?'6/3'3 



3^46 



36X63 



4X6 



APPENDIX. 



789 



OT,D FROX ; CEMENT AND TERRA COTTA PIPES NOT WELL-JOINTED NOR IN PERFECT 
ORDER ; WELL LAID BRICKWORK. 



Grades m feef per hundred /?= 0/3 

02 04.06 ./ 2 .3 .4 .6 6 .7 .8 .3 /.O /.J 2.0 16 3.0 




/6A23 



■x.r 



z 6 yss 



3'X^'^' 



36A63 



4'X6 



6X9 66X83 6X76 



46X69 



790 



APPENDIX. 



FOUL AND SLIGHTLY TUBERCULATED IRON ; CEMENT AND TERRA COTTA PIPES WITH 
IMPERFECT JOINTS, AND IN BAD ORDER ; WELL-DRESSED STONEWORK AND SECOND 
CLASS BRICKWORK. 



Grades /r? feet per hundred n^.0/6 

.0?.mm ./ . ■? -3 -^ .6 .6 .7.8.9/.0 /.5 ?.0 ?.6 3.Q 



Z'6"X^^^ 




s'e'xSjT 



6X9' S6"X8'3" 6'X7'6" 



46X6'a 



APPENDIX. 



791 



For tables of the Kutter formula see "Irrigation Canals," by P. J. Flynn, C. E. 

It will be observed that n depends on the condition of the wetted surface, and that 
with iron surfaces it must vary largely with the time exposure of these surfaces and the 
characteristics of the water passing through. 

Where pipes of iron can not be cleaned, it is impossible for the engineer to form re- 
liable judgment of their condition after years of use. They can be tested 
by measuring flows through a hydrant which discharges from a single 
length of pipe and determining the s in that length. 

For a main with no available gate the following is suggested •. 

Let ad he the, main ; establish s between a h and cdhy reliable gauges. 
At g put in a branch controlled by a gate. After s s are established as 
above, open the gate and measure its discharge accurately by a weir. With 
this factor see what s is between a and h and check the quantities by the 
changes between c and d and compare with flows at different values of n. 

Should the values of n, as thus established by experiment, be outside 
of the limits of ?i = 'Oil, '013, "015, as given by the diagrams, curves 
can be established from these values and extended to include those of 
the experiments, which may answer as approximations. 



FLOW OF AIR. 

The flow of air is subject to the same laws as the flow of water. The 
preceding diagrams may therefore be used in finding the discharge of air in cubic feet 
per second, under the same heads of water in feet, by multiplying by 27*6, the square 
root of 761, the difference in density of a cubic foot of the two fluids. 

The theoretical discharge of a pipe is as the square root of the fifth power of the 
diameter, from which the following table, derived from the circular of the B. F. Sturte- 
vant Company, is based: ' 



5^; 



TABLE FOR EQUALIZING THE DIAMETER OF PIPES. 



1 1 



2 I 57712] 



I 2.-| 31 



4 I 32 I 5.7| 2. I 4 



5 I 



I 0.8| 3. 



I 88 I IC I 



l.G| 



7 I 



I 23j 8.3| 4.1| 2.3| 1.5| 7 ] 



I 180 I 32 I 12 J 5.7| 3.2| 2.l | 1.4| 8 | 



42 I 



7.6| 4.3| 2.8! 1.9| M9| 



10 I 317 



u I 



12 I oOl I 



Parties putting up blast pipes are very liable to think, because the combined area of 
four 6-inch pipes is the sanie as one 12-inch pipe, that the four pipes will convey the 
same quantity of air with the same ease and freedom that the 12-inch will, where- 
as it actually does take 57— almost six 6-inch pipes. Again, 16 3-inch pipes 
~) have the combined area of one 12-inch pipe, but in actual practice it takes 

just 32 3-inch pipes to do the work of one 12-inch. 

This is due to the excess of friction for every cubic foot of air in 
the small pipes over that in the large. 
20 I 9.9| 5./1 3.6| 2.4| i .7| i.3| 10 1 j,^^ ,jj,.^g figurgg ^t the top of each column give the di- 

ameters in inches of the branch pipes. 

The figures at the intersection of the horizontal 

line with the vertical give the number of 

pipes, of the diameter given at the top 

of the column, that will be equal in 

capacity for conveying air to 

one given opposite in the 

first column. 



I 71, I 26 I 12 I 7.0| 4.5, 3.1| 2.2| 1.7| 1.3| 11 | 



32 I 16 I 9.0| 5.7) 3.8| 2.8| 2.0| l.C| 1.2| 12| 



13 I 613 I 107 I 39 I 19 I 11 I 6.9| 4. 7| 3.4| 2 .j| 1.9[ 1.5| 1.2| 13] 



14 I 737 I 129 I 47 I 23 I 13 I 8.3| 5.7| 4.1| 3.0| 2.3| 1.8| 1.5| 1.2| 14 ) 



15 I 876 I 152 I 56 I 27 I 16 I 9.9| C.7| 4.8| 3.6| 2.8| 2.2| 1.8| 1.4| 1.2| 15 



I 1026 I 180 I 65 I 32 I 18 I 11 I 7.9| 5.7| 4.2| 3.2| 2.6| 2.l| 1.7| 1. i\ 1.2| 16 | 



17 I 1197 I 208 I 76 I 37 I 21 I 13 I 9.2| 6.6[ 4.9| 3.8| 2.9| 2.4| 2.0| 1.6| 1.4| 1.2| 17 | 



18 I 1375 I 239 I 88 I 43 I 24 I 16 I 10 I 7.7| 5.7i 4.3| 3.4| 2.8| 2.3| 1.9( l.G| 



ilTsl 



19 I 1580 I 275 I 100 I 49 I 28 I 18 I 12 I 8.8| 6.5| 5. | 3.9| 3.2j 2.C| 2.2| 1.8| l.i| 1.3] 1.2| 19 | 



2 I 1797 I 313 I 114 I 56 I 32 I 20 I 14 I 9.9| 7.4| 5.7| 4.5; 3.6| 2.9| 2.5| 2.1| 1.7| 1.5| 1.3[ l.l|20| 



22 I 2284 



145 ( 71 I 41 I 26 I 18 I 13 I 9.3j 7.2| 5.7| 4.5j 3.7| 3.l| 2.G| 2.2| r.9| 1 . 7| 1.4| 1.3|22| 



24 I 2834 I 493 | 180 | 88 | '50 | 32 | 22 | 16. | 12 | 8.0[ 7.6| 5.7| 4.6| 3.8| 3.2i 2.9| 2.4| 2.1| 1.8| 1.6| 1.2|24| 



I 3474 I 605 I 219 |108 | 62 | 39 | 27 | 19 | 14 | 1 1 | 8.6| 6^''i| 3.7| 4.7| 4.0| 3.4| 2.9| 2.5| 2.2| 1.9| 1.5| 1.2| 26 | 



I 4165 I 725 I 2C5 |129 | 74 | 48 | 32 | 23 | 17 | 13 [ 10 | 8.3| 6:8| 5.7| 4.8[ 4.1| 3.5| 3.0| 2.6| 2.3| 1.8| 1.5| 1.2|; 



I 4963 I 864 | 315 |154 | 88 | 56 | 38 | 28 | 20 | 16 | 12 | 9.9| 8.0| 6.7| 5.71 ^-^i ''•'I 3.G| 3.0J 2.C| 2.2[ 1.7| l.-t|1.2|30| 
I 7818 |13C1 I 497 [243 |139 | 88 j 60 | 43 | 32 | 25 | 19 | 16 | 13 | Jl | 8.9| 7.g; 6.5| 5.7| 5.0| 4.3i 3.4| 2.7[ 2.2[l.9|l .61361 



42 |11488 12000 I 730 |358 [205 ll29 \ 88 | 63 | 47 | 36 [ 29 | 23 | 19 | 16 | 13 | 11 | 9.G| 8.5| 7.3| G.4{ 5.0| 4 



1| 3.3;2.82.3|1.5|42| 

-; 4.7;3.83.2|2.l|l.4|48| 



48 |15989 |2792 I1O8I [492 1232 II8O |123 | 88 j 66 | 50 | 39 | 32 | 26 | 22 | 18 | 16 | 13 | 12 | 10 | 8.9| 7.01 5. 



54 |21560 ]3753 11368 '671 1384 ;244 )166 1119 | 88 | 68 | 53 | 43 j 35 | 29 | 24 | 21 | 18 | 16 | 15 | 12 | 9.4| 7.6j 6.2,5.2.4.3 2. e|l .9|l .3|54 
60 |27913 14879 |l781 |872 [499 ]314 |215 |l54 |115 | 88 j 69 1 56 | 46 | 38 | 32 | 27 | 23 1 20 j 18 | 16 | 12 | 9.9| 8. li6.7|5.7;3.6)2.4|l .sll .; 



792 



APPENDIX. 



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I'J 1 1 III II 1 MiirnnwwU^ i'^ 


i^:zz^z::^[£2S=::;p:::::±— :.: 



APPENDIX. 



'93 



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I 



794 



APPENDIX. 



The foregoing diagrams of the flow of gas have been made from the formula con- 
tained in "Practical Treatise on Heat," by Thomas Box, and is as follows : 

Q = (H X (3•7D)^-^L)*, 

in which Q = discharge cubic feet per minute; H = pressure (grade) in inches of water; 
D = diameter of pipe in inches; L = length in yards. The specific gravity (G) of the 
g-'ds in this formula is '43. , 

/TT -pv 

Formula in previous editions of this work was Q = 1350 D^|/ , and agrees very 

closely with the results from the diagrams given below. 

The diagrams for the flows of water (pages 785-790) in pipes are equally applicable 
to the movement of gaseous fluids, the velocities being directly as the square roots of 
their specific gravities. Thus, the water discharge of a conduit 2 feet in diameter under 
a grade of .0833' per 100 feet in the diagram n = '015 is 5*5 cubic feet per second. By 
Tables of the Weight of Water (page 780) compared with that of air below it will be 
seen that at 62° F. the weight of a cubic foot of water is to that of air as 1 to 820. 
5-5 X 4/820 = 5-5 X 28-636 = 157 cubic feet per second. 

As the diagrams for the flow of water are in feet per hundred and those of air or gas 
in inches, to convert the grades of the former into those of the latter, multiply the dis- 
charge by the square root of -0833' {!") or -2889'. Taking above example, diagram 
under 1 : 100 gives a discharge of 19 cubic feet per second, which x '2889 x 28*636 = 157 
cubic feet per second ; but as the flow of air is usually given in cubic feet per minute, 
multiply by 60 and we obtain 9,420 cubic feet of air per minute. 

In the movement of compressed air by the action of the pump the air is heated, and in 
its passage through the pipe this heat is gradually dissipated with a change of its specific 
gravity, for which allowance is to be made in velocity of movement. With illuminating 
gas the specific gravity of '42 adopted in the diagram is a common one. 

The products of combustion escaping into a large chimney may be taken as of the 
same specific gravity as illuminating gas at -42, but the velocity in the general rules is 
much less than that given by the diagrams. There is no objection to large chimneys ex- 
cept in their cost and back draughts, which last may be met by uniformity of section 
without eddies or by a Venturi converging and diverging tube, at the bottom. 

Insufiicient draught in short chimneys, induced by positions or necessities of con- 
struction, is met by fans discharging directly into a fire-room or ash-pit, or by steam-jet 
blowers, as illustrated on page 368. 



VOLUME AND WEIGHT OF DRY AIR 

At Different Temperatures under a Constant Atmospheric Pressure of 29' 
Barometer, the Volume at S2° F. heing the Unit. 



Inches of the 







Weisrht per 






Weight per 






Weight per 


Temp. F. 


Volume. 


cub. ft., 
Pounds. 


Temp. F. 


Volume. 


cub. ft., 
Pounds. 


Temp. F. 


Volume. 


cub. ft., 
Pounds. 


0° 


•935 


•0864 


132° 


1^204 


• ^0671 


325° 


1-597 


•0506 


12 


•960 


•0842 


142 


1-224 


•0659 


350 


1-648 


•0490 


22 


•980 


•0824 


152 


1-245 


•0649 


375 


1-689 


•0477 


32 


1^000 


•0807 


162 


1-265 


•0638 


400 


1-750 


-0461 


42 


1^020 


•0791 


172 


1-285 


•0628 


450 


1-852 


-0436 


52 


r041 


•0776 


182 


r306 


•0618 


500 


1-954 


-0413 


62 


ro6i 


•0761 


192 


1-326 


•0609 


550 


2-056 


•0384 


72 


1-082 


•0747 


202 


1-347 


•0600 


600 


2-150 


•0376 


82 


1^102 


•0733 


212 


1-367 


•0591 


650 


2-260 


-0357 


92 


M22 


•0720 


230 


1-404 


•0575 


700 


2-362 


•0338 


102 


1^143 


•0707 


250 


1-444 


•0559 


800 


2-566 


•0315 


112 


1^163 


•0694 


275 


1-495 


•0540 


900 


2-770 


•0292 


122 


1^184 


•0682 


300 


1-546 


•0522 


1000 


2-974 


•0268 



APPENDIX. 



T95 




790 



APPENDIX. 



A Babcock and Wilcox water tube boiler (Fig. 1867) is composed of lap-welded 
wrought-iron tubes placed in an inclined position and connected with each other and 
with a horizontal steam and water drum, by vertical passages at each end, while a mud 
drum is connected to the rear and lowest point in the boiler. 

The end connections are in one piece for each vertical row of tubes, and are of such 
form that the tubes are staggered. The sections thus formed are connected with the 
drum, and with the mud drum also, by short tubes expanded into bored holes. The 
openings for cleaning, opposite the end of each tube, are closed by hand-hole plates. 

To utilize waste heat heaters are set in a chamber in connection with the flues leading 
to the chimney. Fig. 1868 is an elevation of one of these forms of apparatus, the Green 
economizer, consisting of ranges of vertical pipes, connected at the top and bottom 
with horizontal pipes, into which the feed water is introduced at the bottom and leaves 
at the top. The whole is inclosed in a brick chamber wdth the products of combustion 
passing among the pipes. The outsides of the pipes are cleaned by automatic scrapers. 
Where the heat is necessary to insure draft in the smoke flue there can be no economy in 
the apparatus, but an obstruction to the draft. 

In operation, the fire is made under the front and higher ends of the tubes, and the 
products of combustion pass up between the tubes into a combustion chamber under the 
steam and water drum ; from thence they pass down between the tubes, then once more 
up through the spaces between the tubes and off to the chimney. The water inside the 
tubes, as it is heated, tends to rise toward the higher end, and as it is converted into 
steam, the mingled column of steam and water rises through the vertical passages into 
the drum above the tubes, where the steam separates from the water, and the latter flows 
back to the rear and down again through the tubes in'a continuous circulation. 

The steam is taken out at the top of the steam drum, near the back end of the boiler, 
after it has thoroughly separated from the water. 




Fig 1868. 



APPENDIX. 



'97 




The Heine boiler (Fig. 1869) is composed of wrought-iron tubes extending between 
the inside of two "water legs," or end connections, between the tubes and a steam and 
water drum placed above them. These end chambers are of approximately rectangular 
shape, drawn in at the top to fill the curvature of the shells. Each is composed of a 
head plate and a tube sheet, flanged all around and joined at bottom and sides by a butt 
strap of the same material, strongly riveted to both. They are further stayed by hollow 
stay bolts of hydrnulic tubing of large diameter, so placed that two stays support each 
tube and hand hole. The water legs are joined to the shell by flanged and riveted joints, 
and the shells are cylinders with heads dished. The steam space in front is about two 
thirds the diameter of the shell, while at the rear the water occupies two thirds of the 
shell, the whole contents being equally divided between steam and water. On the top 
of the shell, near the front end, is riveted a nozzle for a steam and safety valve. A flue, 
or breeching, connects the furnace to the chimney. 



798 



APPENDIX. 



TABLE OF SATURATED STEAM. 

english units. 
Cecil H. Peabody, B. S. 



l-s 


u 
^ 


-d 




§ 


<D 


Density. 


u 


;-<- 


r^ 




§ 


6 


Density. 


3 




'3 




.2 


a 
3 


•So| 


§1 


gl 


'3 




"cS 


1 


•S'S-SJ 


^6 


11 


|3 


1- 


o 


o 
> 


J 


%s 


li 


1^ 


1 


"u 
o 


1 


J2 




S fcjo 


o 

1 




f 


s 






u u 




W 


¥ 


I 


■^a^ 
'^^O^ 


p-i 


H 


ffi 


H 


W 


m 


^ 


H 


M 


H 


w 


cc 


^ 


p 


t 


Q 


A 


r 


' 


y 


V 


t 


Q. 


A 


r 


s 


Y 


1 


101-99 


70-0 


1113-1 


1048-0 


384-6 


0-00299 


51 


282-10 


251-5 


1168-0 


916-5 


8-259 


0-1211 


2 


126-27 


94-4 


1120-5 


1026-1 


178-6 


0-00576 


52 


283-32 


252-7 


1168-4 


915-7 


8-110 0-1288 


3 


141-62 


109-8 


1125-1 


1015-3 


118-4 


0-00844 


58 


284-53 


258-9 


1168-7 


914-8 


7-968,0-1255 


4 


158-09 


121-4 


1128-6 


1007-2 


90-81 


0-01107 


54 


285-72 


255-1 


1169-1 


914 


7-8290-1277 


5 


162-34 


130-7 


1181-5 


1000-8 


73-22 


0-01366 


55 


286-89 


256-3 


1169-4 


913-1 


7-696|0-1299 


6 


170-14 


138-6 


1138-8 


995-2 


61-67 


0-01622 


56 


288-05 


257-5 


1169-8 


912-3 


7-568 


0-1321 


7 


176-90 


145-4 


1185-9 


990-5 


58-87 


0-01874 


57 


289-19 


258-6 


1170-1 


911-5 


7-443 


0-1844 


8 


182-92 


151-5 


1137-7 


986-2 


47-07 


0-02125 


58 


290-31 


259-7 


1170-5 


910-8 


7-828 


0-1866 


9 


188-83 


156-9 


1139-4 


982-5 


42-13 


0-02874 


59 


291-42 


260-8 


1170-8 


910-0 


7-208 


0-1887 


10 


193-25 


161-9 


1140-9 


979-0 


88-16 


0-02621 


60 


292-51 


261-9 


1171-2 


909-3 


7-096 


0-1409 


11 


197-78 


166-5 


1142-8 


975-8 


84-88 


0-02866 


61 


293-59 


263-0 


1171-5 


908-5 


6-987 


0-1481 


12 


201-98 


170-7 


1148-6 


972-9 


82-14 


0-08111 


62 


294-65 


264 1 


1171-8 


907-7 


6-882 


0-1453 


13 205-89 

14 209-57 


174-6 


1144-7 


970-1 


29-82 


0-03355 


63 


295-70 


265-2 


1172 1 


906-9 


6-779 


0-1475 


178-3 


1145-8 


967-5 


27-79 


0-08600 


64 


296-74 


266-2 


1172-4 


906-2 


6-680 0-1497 


15 213-03 


181-8 


1146-9 


965-1 


26-15 


0-03826 


65 


297-77 


267-2 


1172-7 


905-5 


6-583 


0-1519 


16216-32 


185-1 


1147-9 


962-8 


24-59 


0-04067 


66 


298-78 


268-8 


1178-0 


904-7 


6-490 


0-1541 


17 219-44 


188-3 


1148-9 


960-6 


23-22 


0-04307 


67 


299-77 


269-8 


1173-3 


904-0 


6-401 


0-1562 


18,222-40 


191-3 


1149-8 


958-5 


22-00 


0-04547 


68 


300-76 


270-3 


1173-6 


903-8 


6-814 


0-1584 


19|225-24 


194-1 


1150-7 


956-6 


20-90 


0-04786 


69 


301-74 


271-2 


1173-9 


902-7 


6-228 


0-1606. 


•30 227-95 


196-9 


1151-5 


954-6 


19-91 


0-05028 


70 


302-71 


272-2 


1174-3 


902-1 


6-144 


0-1628 


21230-55 


199-5 


1152-3 


952-8 


19-01 


0-05259 


71 


803-66 


273-2 


1174-6 


901-4 


6-068 


0-1649 


22 233-06 


202-0 


1158-0 


951-0 


18-20 


0-05495 


72 


304-61 


274-1 


1174-9 


900-8 


5-984 


0-1671 


23 235-47 


204-5 


1153-7 


949-2 


17-45 


0-05731 


73 


805-54 


275-1 


1175-2 


900-1 


5-908 


0-1693 


24 237-79 


206-8 


1154-4 


947-6 


16-76 


0-05966 


74 


306-46 


276-0 


1175-4 


899-1 


5-884 


0-1714 


25 240 04 


209-1 


1155-1 


946-0 


16-13 


0-06199 


75 


307-88 


276-9 


1175-7 


898-8 


5-762 


0-1736 


26 242-21 


211-2 


1155-8 


944-6 


15-55 


0-06432 


76 


308-28 


277-8 


1176-0 


898-2 


5-691 


0-1757 


27 244-32 


213-4 


1156-5 


943-1 


15-00 


0-06666 


77 


809-18 


278-7 


1176-2 


897-5 


5-621 


0-1779 


28 246-36 


215-4 


1157-1 


941-7 


14-49 


0-06899 


78 


810 06 


279-6 


1176-5 


896-9 


5-554 


0-1801 


29,248-34 


217-4 


1157-7 


940-8 


14-03 


0-07180 


79 


310-94 


280-5 


1176-8 


896-8 


5-488 


0-1822 


80 250-27 


219-4 


1158-3 


988-9 


18-59 


0-07860 


80 


811-80 


281-4 


1177-0 


895-6 


5-425 


0-1848 


31252-15 


221-3 


1158-8 


987-5 


13-18 


0-07590 


81 


312-66 


282-3 


1177-3 


895-0 


5-362 


0-1865 


32 253-98 


223-1 


1159-4 


986-8 


12-78 


0-07821 


82 


318-51 


283-2 


1177-6 


894-4 


5-301 


0-1886 


33 255-76 


224-9 


1159-9 


935-0 


12-41 


0-08051 


83 


814-36 


284-1 


1177-8 


893-7 


5-240 


0-1908 


341257-50 


226-7 


1160-4 


933-7 


12-07 


0-08280 


84 


315-19 


285-0 


1178-1 


893-1 


5-182 


0-1980 


35 259-19 


228-4 


1161-0 


932-6 


11-75 


p- 08508 
0-08736 


85 


316-02 


285-8 


1178-3 


892-5 


5-125 


0-1951 


36 260-85 


230-0 


1161-5 


931-5 


11-45 


86 


316-84 


286-7 


1178-6 


891-9 


5-069 


0-1973 


37,262-47 


231-7 


1162-0 


930-3 


11-16 


0-08964 


87 


317-65 


287-5 


1178-8 


891-8 


5-014 


0-1994 


38 264-06 


233-3 


1162-5 


929-2 


10-88 


0-09191 


88 


818-45 


288-4 


1179-1 


890-7 


4-961 


0-2016 


39265-61 


234-8 


1163-0 


928-2 


10-62 


0-09417 


89 


319-25 


289-2 


1179-3 


890-1 


4-909 0-2037 


40 267-13 


236-4 


1168-4 


927-0 


10-37 


0-09644 


90 


320-04 


290-0 


1179-6 


889-6 


4-858 


0-2058 


41 


268-62 


237-9 


1168-9 


926-0 


10-18 


0-09869 


91 


320-88 


290-8 


1179-8 


889-0 


4-808 


0-2080 


42 270-08 


239-3 


1164-3 


925-0 


9-906 


0-10090 


92 


321-60 


291-6 


1180-0 


888-4 


4-760 0-2101 


43 271-51 


240-8 


1164-8 


924-0 


9-690 


0-10320 


98 


322-37 


292-4 


1180-3 


887-9 


4-7120-2122 


44272-91 


242-2 


1165-2 


923-0 


9-484 


0-10540 


94 


328-14 


293-2 


1180-5 


887-8 


4-665i0-2144 


45 274-29 


243-6 


1165-6 


922-0 


9-287 


0-10770 


95 


823-89 


294-0 


1180-7 


886-7 


4-6190-2165 


46,275-65 


245-0 


1166-0 


921-0 


9-097 


0-10990 


96 


824-64 


294-8 


1181-0 


886-2 


4-5740-2186 


47,276 -99 


246-3 


1166-4 


920-1 


8-914 


0-11220 


97 


325-88 


295-6 


1181-2 


885-6 


4-530 0-2208 


48 278-30 


247-6 


1166-8 


919-2 


8-740 


0-11440 


98 


3-26-12 


296-4 


1181-4 


885-0 


4-486 


0-2229 


49 279-58 


248-9 


1167-2 


918-3 


8-573 


0-11660 


99 


326-86 


'297-1 


1181-6 


884-5 


4-444 


0-2250 


50 280-85 


250-2 


1167-6 917-4 


8-414 


0-11880 


100 


327-58 


297-9 


1181-9 


884-0 


4-403 0-2271 



APPENDIX. 



799 



TABLE OP SATURATED STEA^L—Cojitinued. 



ii 


^ 


■d 




d 


6 


Density. 


-s-s 


^ 


_'d 




a 


a; 


Density. 


c 


gl 


3 




•J 

c3 


3 


•So.§ 


ii 


s£ 


3 




% 





.5*5.2 


^J 


li 


1^ 


1 


1 


1 


Xi 

.43 


^-s 


3 02 

Vs 

be 
£0 


1^ 


1 





> 


s6 


2 


1^ 


O 

1 


W 


r 


O 

o 

ft 


pll 


u u 


1 







(3 
'0 


Mrs 


(^ 


H 


X 


H 


w 


M 


^ 


E-i 


K 


H 


hH 


m 


1^ 


P 


t 


Q 


A 


7- 


S 


V 


P 


t 


Q 


A 


r 


s 


y 


101 


328-30 


298-6 


1182-1 


883-5 


4-362 


0-2293 


151 


358-78 


330-5 


1191-4 


860-9 


2-992 


0-3342 


102 


329-02 


299-4 


1182-3 


882-9 


4-322 


0-2314 


152 


359-30 


331-1 


1191-5 


860-4 


2 


973 


0-3363 


103 


329-73 


300-1 


1182-5 


882-4 


4-282 


0-2335 


153 


359-82 


331-6 


1191-7 


860-1 


2 


955 


0-3384 


104 


330-43 


300-9 


1182-7 


881-8 


4-244 


0-2356 


154 


360-34 


332-2 


1191-8 


859-6 


2 


937 


0-3405 


105 


331-13 


301-6 


1182-9 


881-3 


4-206 


0-2378 


155 


360-86 


332-7 


1192-0 


859-3 


2 


919 


0-3426 


106 


331-83 


302-3 


1183-1 


880-8 


4-169 


0-2399 


156 


361-37 


333-3 


1192-2 


858-9 


2 


901 


0-3447 


107 


332-52 


302-0 


1183-4 


880-4 


4-132 


0-2420 


157 


361-88 


333-8 


1192-3 


858-5 


2 


884 


0-3467 


108 


333-20 


303-8 


1183-6 


879-8 


4-096 


0-2441 


158 


362-39 


334-3 


1192-5 


858-2 


2- 


867 


0-3488 


109 


333-88 


304-5 


1183-8 


879-3 


4-061 


0-2462 


159 


362-90 


334-9 


1192-7 


857-8 


2- 


850 


0-3509 


110 


334-56 


305-2 


1184-0 


878-8 


4-026 


0-2484 


160 


363-40 


335-4 


1192-8 


857-4 


2 


833 


0-3530 


111 


335-23 


305-9 


1184-2 


878-3 


3-992 


0-2505 


161 


363-90 


335-9 


1193-0 


857-1 


2- 


816 


0-3551 


112 


335-89 


306-6 


1184-4 


877-8 


3-959 


0-2526 


162 


364-40 


336-4 


1193-1 


856-7 


2 


799 


0-3572 


113 


336-55 


307-3 


1184-6 


877-3 


3-926 


2547 


163 


364-90 


337-0 


1193-3 


856-3 2 


783 


0-3593 


114 


337-20 


308-0 


1184-8 


876-8 


3-894 


0-2568 


164 


365-39 


337-5 


1193-4 


855-9 


2 


767 


0-3614 


115 


337-86 


308-7 


1185-0 


876-3 


3-862 


0-2589 


165 


365-88 


338-0 


1193-6 


855-6 


2 


751 


0-3635 


116 


338-50 


309-4 


1185-2 


875-8 


3-831 


0-2610 


166 


366-37 


338-5 


1193-7 


855-2 


2 


736 


0-3655 


117 


339-14 


310-0 


1185-4 


875-4 


3-801 


0-2631 


167 


366-85 


339-0 


1193-9 


854-9 


2 


721 


0-3675 


118 


339-78 


310-7 


1185-6 


874-9 


3-770 


0-2653 


168 


367-33 


339-5 


1194-0 


854-5 


2 


706 


0-3695 


119 


340-42 


311-4 


1185-8 


874-4 


3-740 


0-2674 


169 


367-81 


340-0 


1194-2 


854-2 


2 


691 


0-3716 


120 


341-05 


312-0 


1186-0 


874-0 


3-711 


0-2695 


170 


368-29 


340-5 


1194-3 


853-8 


2 


676 


0-3737 


121 


341-67 


312-7 


1186-2 


873-5 


3-683 


0-2715 


171 


368-77 


341-0 


1194-4 


853-4 


2 


661 


0-3758 


122 


342-29 


313-3 


1186-3 


873-0 


3-655 


0-2736 


172 


369-24 


341-5 


1194-6 


853-1 


2 


647 


0-3778 


123 


342-91 


314-0 


1186-5 


872-5 


3-627 


0-2757 


173 


369-71 


342-0 


1194-7 


852-7 


2 


632 


0-3799 


124 


343-52 


314-6 


1186-7 


872-1 


3-599 


0-2779 


174 


370-18 


342-5 


1194-8 


852-3 


2 


618 


0-3820 


125 


344-13 


315-2 


1186-9 


871-7 


3-572 


0-2800 


175 


370-65 


343-0 


1195-0 


852-0 


2 


603 


0-3841 


126 


344-73 


315-9 


1187-1 


871-2 


3-546 


0-2820 


176 


371-12 


343-5 


1195-1 


851-6 


2 


589 


0-3862 


127 


345-33 


316-5 


1187-3 


870-8 


3-520 


:o-284i 


177 


371-59 


344-0 


1195-3 


851-3 


2 


575 


0-3883 


128 


345-93 


317-1 


1187-4 


870-3 


3-494 


,0-2862 


178 


372-05 


344-4 


1195-4 


851-0 


2 


501 


0-3904 


129 


346-53 


318-7 


1187-6 


869-9 


3-469 


0-2883 


179 


372-51 


344-9 


1195-6 


850-7 


2 


548 


0-3925 


130 


347- 12 


318-4 


1187-8 


869-4 


3-444 


0-2904 


180 


372-97 


345-4 


1195-7 


850-3 


2 


535 


0-3945- 


131 


347-71 


319-0 


1188-0 


869-0 


3-419 


0-2925 


181 


373-43 


345-9 


1195-9 


850-0 


2 


52^ 


0-3966 


132 


348-29 


319-6 


1188-2 


868-6 


3-395 


0-2946 


182 


373-88 


346-4 


1196-0 


849-6 


2 


508 


0-3987 


133 


348-87 


320-2 


1188-4 


868 2 


3-371 


0-2967 


183 


374-33 


346-8 


1196-1 


849-3 


2 


495 


0-4008 


134 


349-45 


320-8 


1188-5 


867-713-347 


0-2988 


184 


374-78 


347-3 


1196-2 


848-9 


2 


482 


0-4029 


135 


350-03 


321-4 


1188-7 


867-3 


3-323 


0-3009 


185 


375 23 


347-8 


1196-4 


848-6 


2 


470 


0-4049 


136 


350-60 


322-0 


1188-9 


866-9 


3-300 


0-3030 


186 


375-68 


348-2 


1196-5 


848-3 


2 


457 


0-4070 


137 


351-17 


322-6 


1189-0 


866-4 


3-277 


0-3051 


187 


376-12 


348-7 


1196-6 


847-9 


2 


445 


0-4090 


138 


351-73 


323-2 


1189-2 


866-0 


3-255 


0-3072 


188 


376-56 


349-2 


1196-8 


847-6 


2 


432 


0-4111 


139 


352-29 


323-8 


1189-4 


865-6 3-234 


0-3092 


189 


377-00 


349-6 


1196-9 


847-3 


2 


-420 


0-4132 


140 


352-85 


334-4 


1189-5 


865-1 


8-212 


0-3113 


190 


377-44 


350-1 


1197-1 


847-0 


2 


-408 


0-4153 


141 


353-40 


325-0 


1189-7 


864-7 


3-191 


0-3134 


191 


377-88 


350-5 


1197-2 


846-7 


2 


396 


0-4174 


142 


353-95 


325-6 


1189-9 


864-3 


3-170 


0-3155 


192 


378-32 


351-0 


1197-3 


846-312 


385 


0-4194 


143 


354-50 


326-1 


1190-1 


864-0 


3-149 


0-3176 


193 


378-75 


351-4 


1197-4 


846-012 


378 


0-4215 


144 


355-05 


326-7 


1190-2 


863-5 


3-128 


0-3197 


194 


379-18 


351-9 


1197-6 


845-7 2 


-301 


0-4236 


145 


355-59 


327-2 


1190-4 


863-2 


3 107 


0-3218 


195 


379-61 


352-4 


1197-7 


845-3 2 


-349 


0-4257 


146 


356-13 


327-8 


1190-6 


862-8 


3-087 


0-3239 


196 


380-04 


352-8 


1197-8 


845-0 2 


-337 


0-4278 


147 


356-67 


328-3 


1190-7 


862-4 


3-068 


0-3259 


197 


380-47 


353-3 


1198-0 


844-7 2 


-325 


0-4298 


148 


357-20 


328-9 


1190-9 


862 013 -049 


0-3280 


198 


380-891353-7 


1198-1 


844-42 
844-12 


-314 


0-4318 


149 


357-73 


329-4 


1191-0 


861-63-030 


0-3300 


199 


381-311354-1 


1198-2 


-304 


0-4338 


150 


358-26 


330-0 


1191-2 


861-23-011 


0-3321 


200 


381-73i354-6 


1198-4 


843-812-294 


0-4359 



800 



APPENDIX. 



EXPANSIVE WORKING OF STEAM. 







MEAN ABSOLUTE PRESSURE, 




1 MEA 


N ABSOLUTE PRESSURE, 






IN DECIMAL PARTS, OF 




I> 


DECIMAL PARTS, OP 


Cut-ofiE in 


Number 


ABSOLUTE PRESSURE OP 


Cut-off in 


Number -^^ 


SOLUTE PRESSURE OP 


percentage 


of expan- 


ADMISSION. 


percentage 


of expan- 


ADMISSION. 


of stroke. 


sions. 






of stroke. 


sions. 










Dry satu- 


Moderately 




Dr 


y satu- 


Moderately 






rated steam. 


moist steam. 




rate 


d Steam. 


moist steam. 


•800 


li 


•9760 


•9784 


•1 


10 


8145 


•8303 


•667 


li 


•9403 


•9366 


•095 


10^ 


3035 




3189 


•571 


If 


•8857 


•8910 


•091 


11 


2938 




3089 


•500 


2 


•8394 


•8465 


•087 


Hi 


2889 




2991 


•444 


21 


•7960 


•8050 


•083 


12 


2751 




2904 


•400 


2i 


•7560 


•7664 


•080 


m 


2669 




2818 


•364 


2i 


•7200 


•7316 


•077 


13 


2592 




2742 


•383 


3 


•6870 


•6997 


•074 


18i 


2520 




2666 


•308 


H 


•6570 


•6705 


•071 


14 


2452 




2599 


•286 


3i 


•6300 


•6437 


•069 


14J 


2388 




2532 


•267 


3f 


•6051 


•6192 


•067 


15 


2327 




2472 


•250 


4 


•5820 


•5965 


•065 


15i 


2270 




2411 


•235 


41 


•5608 


•5757 


•063 


16 


2216 




2358 


•222 


^ 


•5410 


•5564 


•061 


16i 


2164 




2308 


•211 


4f 


•5230 


•5386 


•059 


17 


2115 




2255 


•200 


5 


•5060 


•5218 


•057 


17i 


2069 




2205 


•191 


51 


•4904 


•5063 


•056 


18 


2024 




2161 


•182 


4 


•4760 


•4918 


•054 


18i 


1982 




2116 


•174 


si 


•4620 


•4781 


•053 


19 


1942 




2181 


•167 


6 


•4490 


•4653 


•051 


19i 


1903 




2084 


•160 


6i 


•4370 


•4538 


•050 


20 


1866 




1998 


•154 


6i 


•4250 


•4418 


•048 


21 


1796 




1926 


•148 


6f 


•4150 


•4311 


•045 " 


22 


1736 




1860 


•143 


7 


•4046 


•4208 


•048 


28 


1672 




1790 


•138 


n 


•3950 


•4112 


•042 


24 


1610 




1741 


•133 


4 


•3857 


•4020 


•040 


25 


1566 




1688 


•129 


n 


•3770 


•3938 


•038 


26 


1518 




1688 ' 


•125 


8 


•3688 


•8849 


•087 


27 


1474 




1591 


•121 


Bi 


•3608 


•3769 


•036 


28 


1431 




1547 


•117 


8i 


•8533 


•3694 


•084 


29 


1392 




1506 


•114 


8i 


•3461 


•3622 


•038 


80 


1355 




1467 


•111 


9 


•3392 


•3552 










•108 


9^ 


•3826 


•3494 










•105 


9i 


•8274 


•8422 










•103 


9| 


•8203 


•8859 











TABLE OF FACTORS OF EVAPORATION. 



Pressure 


Boiling 






INITIAL TEMPERATURE OP 


PEED WATER, T2. 








Pounds 


Point 
























per 
Sq. Inch. 


Fahr. 


32^ 


50° 


68° 


86° 


104° 


122° 


140° 


158° 


176° 


194° 


212° 


14^70 


212° 


1^19 


1^17 


1^15 


M8 


1-11 


1^10 


1^08- 


1^06 


1^04 


1-02 


1-00 


20-78 


280 


1^20 


1^18 


1-16 


1^14 


1-12 




10 


1^08 


1^06 




04 


1-02 


1-01 


28-82 


248 


1^20 


M8 


1^16 


1^14 


1-18 




11 


1-09 


1^07 




05 


1-03 


1-01 


89^26 


266 


1^21 


M9 


1^17 


1^15 


1-13 




11 


1-09 


1^07 




06 


1-04 


1^02 


52^56 


284 


1^21 


1^20 


1-18 


1-16 


1^14 




12 


1-10 


1-08 




06 


1^04 


1^02 


69^27 


802 


1^22 


1-20 


M8 


1^16 


1-U 




12 


1-11 


1^09 




07 


1-05 


1^03 


89^95 


320 


1-22 


1-21 


1^19 


1-17 


1^15 




13 


1^11 


1^09 




07 


1^05 


1^03 


115^22 


838 


1^23 


1-21 


M9 


M7 


1^15 




14 


1^12 


1-10 




08 


1^06 


1^04 


145-75 


856 


1-28 


1^22 


1^20 


1^18 


1-16 




14 


1^12 


1-10 




08 


1^06 


1^04 


182-27 


374 


1^24 


1^22 


1-20 


1-18 


1-17 




15 


1^13 


1^11 




09 


1^07 


1^05 


225-56 


392 


1-24 


1^23 


1-21 


1-19 


1-17 




15 


1^13 


Ml 




09 


1^07 


1-06 


276^54 


410 


1^25 


1-23 


1^22 


1-20 


M8 




16 


1-U 


M2 




10 


1^08 


1-06 


386^26 


428 


1^25 


1^24 


1^22 


1-20 


M8 


1-16 


I'U 


M2 


Ml 


1-09 


1-07 



APPENDIX. 



801 



The Twenty-eighth Street Central Station of the United Electric Light and Power 
Company. By H. W. York, ''Trans. A. S. C. E.," March 18, 1896. 

In this station 20,000 H. P. of engines, together with the boilers, condensing appa- 
ratus, dynamos, and switchboard, and storage for 6,000 tons of coal, are all on a plot of 
ground 160 feet 11 inches by 197 feet 6 inches. All machinery, including the boilers, is 
on the ground floor, and yet there is plenty of light, air, and ample space for working 
around all the apparatus. Fig. 1870 is a plan of the foundation walls and piers of the 



-.6,^^ 



^ 




^cS;O T > | < „^ H;Sr ^^ViX^-ci -^^-A^-^Kn^^l- > k „^H;g i --j< „9 i7fr0l7H- 




802 



APPENDIX. 



building. The entire front wall is hollow and carried up above the roof to prevent the 
noise of the machinery annoying the patients in Bellevue Hospital, which is du-ectly 
across the street. Fig. 1871 is a cross-section of the entire structure. 

Loop System. — The main steam and exhaust piping is shown in plan on Fig. 1872. A 
16-inch header is run the length of the boiler-room, and a similar header is run the length 
of the engine room between the two rows of foundations and parallel to the boiler-room 
header. Each of these headers are divided into five sections by means of four gate- 




APPENDIX. 



803 



valves, and each section of the boiler-room header is connected to the corresponding sec- 
tion of the engine-room header by a 14-inch branch rising from the top of one and dis- 
charging into the top of the other, a valve being placed on each end where a connection 
is made to the header. Each boiler has an independent connection to the boiler-room 
header, supplied with two stop-valves, one in the customary position just beyond the 
safety-valves, and the other at the i)oint where the pipe enters the header. This second 
valve has its stem extended through the wall into the repair shop, so that in case of 
trouble any boiler may be cut out of a room having no communication with the boiler 
house. 

Each engine on the east side of the engine room is connected to one of the 14-inch 



>;m//Mmm/Am >JW?MJM/^M^j/M/jjj///JMJ^^^^^^^ 




804 



APPENDIX 



branches previously mentioned, while outlets are left on the engine-room header for con- 
nections to the west row of the engines as soon as they are placed in position. In case 
any section of the engine-room header is cut out, one engine connected to this section 
can be fed directly from the 14-inch branch, leaving only one which can not be run, and 
in case any section of the boiler-room header is cut out no engine need be shut down, as 

the one connected to the 14-inch branch can be 
fed back from the engine-room header. 

The boilers are of the upright water-tube 
type of the Clonbrock pattern, and are in 600 
H.-P. units, occupying little ground room per 
unit of capacity (Fig. 1873). 

The conveyer for handling coal and ashes 
consists of an endless chain of gravity buckets, 
which are loaded by means of a filler and can be 
dumped at any desired point. The driver is in 
the north end of the ventilator over the coal 
bunker. The coal filler is in a vault under the 
sidewalk, and the coal is dumped into this ap- 
paratus through a grating situated about the 
street level. After being deposited in the buck- 
ets the coal is carried up into the ventilator over 
the coal bunker and dumped into any portion 
of the bunker desired. From the hoppers in 
the bottom of the bunker the coal is spouted 
to the different boilers. The arrangement is 
such that the coal trims itself and will con- 
tinue running down the spouts as required and 
without assistance so long as any remains in the 
bunker. 

Under each boiler is an ash hopper deliver- 
ing the ashes to a second movable filler, which 
deposits them in the buckets of the conveyer 
when it is not uspd for coal. The conveyer 
dumps the ashes at a point from which they are 
spouted over to a tank in the southeast corner 
of the coal bunker. 

The engines are Westinghouse double acting 
"Columbian steepled compounds." Fig. 1874 
shows one of these engines in section. The low 
pressure is placed over the high pressure, and 
both pistons are connected to the same rod. 
The crank is inclosed in the same manner as 
the Westinghouse engines. The low-pressure 
valve is operated by a fixed eccentric placed in- 
side the crank case, while the high-pressure 
valve receives its motion from a shifting eccen- 
tric outside the crank case, operated automati- 
cally by the governor, which is placed on the 
shaft outside of the eccentric. The low-pressure valve is of the slide-valve type, while 
that for the high-pressure cylinder is a hollow piston valve, being constructed in this 
manner to allow the exhaust from the lower end of the high-pressure cylinder to 
pass up through it. Diameter high-pressure cylinder, 21^ inches ; diameter low- 
pressure cylinder, 37 inches ; stroke, 32 inches. The speed is 200 revolutions per 




Elevation. 




APPENDIX. 



805 



minute and the rated horse power 1,200 when operating condensing, with 150 pounds 
initial steam pressure. 

Each main engine is directly connected to a 600- kilowatt Westinghouse alternator by 
a rigid coupling, both engine and generator being set on a firm cast-iron bedplate. The 
generator has but one bearing, the armature being swung between the engine and this 
single support. 

For exciting the fields of the alternators, 75-kilowatt direct-current Westinghouse 
dynamos of the railway generator type are used. 




Fig. 1874. 









^^im!' ' ii''i'i^^'^^^'"i^'/-<^i 






I I 



FOUNDATION FOR VERTICAL ENGINES. 



i??^ 



806 



APPENDIX. 



/a ^o 



3o feef <<? 




s ay /? A? 2. 
loss JM /a/fs. 




Fig. 1875. 



In the "Universal "Wiring Com- 
putor," by Carl Hering, charts are giv- 
en which give directly, and without 
calculation or the use of formulae, the 
gauge number or cross section in cir- 
cular mils of lead for any number of 
lamps of any make at any distance or 
for any loss. One of these tables is 
given above as an illustration on 
"graphics." 

Follow the general direction of 
the broken line and the arrows from 
one set of diagonals to the next. 

Example : What size wire is re- 
quired for 10 lamps of -775 amperes 
each, at 50 feet, for a loss of one volt ? 

Solution: Starting with the cur- 
rent for one lamp, '775 amperes (see 
scale below centre), follow it to the 
left until it intersects the diagonal 
representing one volt loss, thence up 
to the diagonal representing 10 lamps, 
thence to the right to the diagonal 
representing 50 feet, and from here 
down to the scale of the circular mils 
or gauge numbers, on which the read- 
ing is found to be about 8,200 circu- 
lar mils, or a No. 11 B. S. wire. 

Fig. 1875 is an incandescent elec- 
tric lamp socket of the Bryant Elec- 
tric Company. 

Fig. 1876 is a switch of the Hart 
and Hegeman Company. 



APPENDIX. 



807 



All of the above drawings are made in a style in which the exterior shell is trans- 
parent, showing the interior mechanism, and known as "gliost cuts." 















Fig. 187( 







Area. 


OhmsprlnOOtt. 
at 70° F. 


No. 
B. &S. 


Diameter, 
Mils. 






Circular 


Current 


Guage. 




Mils (d2) 


allowed bv 






1 mil = 'OUI in. 


Underwriter's 
Code. 


0000 


460-000 


211600-00 


175 


000 


409-640 


167805-00 


145 


00 


364-800 


133079 04 


120 





324-860 


105.534-03 


100 


1 


289-300 


83694-20 


95 


2 


257-630 


66.373-00 


70 


3 


229-420 


52633-40 


60 


4 


204-310 


41742-57 


50 


5 


181-940 


33102-00 


45 


6 


162-020 


26250-50 


35 


7 


144-280 


20816-70 


30 


8 


128-490 


16.509-00 


25 


9 


114-4.30 


13094-00 




10 


101-890 


10381-00 


20 


11 


90-742 


8234-10 




1-2 


80-808 


6529-90 


15 


13 


71-961 


5178-40 




14 


64 084 


4106-80 


10 




LUNDELL MOTOR. 



808 



APPENDIX 



TABLE OF DENSITY OF GASES AND VAPOUHS, AIR AT THE SAME TEM- 
PERATURE AND PRESSURE BEING 1-0: ALSO THE WEIGHT OF A 
CUBIC FOOT AT 62° FAHR., UNDER AN ATMOSPHERIC PRESSURE 
OF 29-92 INCHES OF MERCURY. 



Air (atmospheric) 

Hydrogen gas 

Oxygen gas 

Nitrogen gas 

Carbonic-acid gas 

Carbonic-oxide gas 

Vapour of water 

•' -" alcohol 

" " sulphuric ether.. 

" " oil of turpentine 



Density of 
air. 



•00000 
■06926 
■10563 
•97137 
52901 
■9674 
6235 
589 
586 
•760 



Specific 
gravity. 



•001221 

•000085 

•001350 

•001185 

•001870 

•00118 

•000761 

•00194 

•00316 

•00581 



Weight of 
cubic foot 
in pound. 



•07610 
•00527 
■08414 
■07383 
11636 
07364 
04745 
12092 
19680 
36224 



Cubic feet. 



14 

70 



13' 

189' 

11^88 

13^54 

8-59 

13^60 

21^07 

8-27 

5-08 

2-76 



Acid, muriatic 1 • 200 

Acid, nitric 1-217 

Acid, sulphuric 1 • 849 

Alcohol, pure • 794 

Ammonia, 27*9 per cent -891 
Carbon disulphide 1-260 



SPECIFIC GRAVITY OF LIQUIDS AT 60 

Ether, sulphuric -720 

Oil, linseed ^940 

Oil, olive ^920 

Oil, petroleum '780- -880 

Oil, turpentine -870 



FAHR. 

Oil, whale -920 

Tar 1^000 

Vinegar 1-080 

Water I'OOO 

Water, sea 1- 026-1 • 030 



SPECIFIC GRAVITIES AND WEIGHTS OF EARTHS, ETC. 



SUBSTAXCE. 



Alabaster 

Asbestos 

Asphalt, California 

" Trinidad . 

Barvtes 

Basalt 

Borax 

Brick, masonry 

Bricks 

" fire 

Cement, Portland.. 

" Rosendale. 

Clay 

Coal 

Coal tar 

Coke 

Concrete 

Earth 

Emery 

Feldspar 

Glass 

Gneiss and granite. 

Graphite 

Gravel 

Grindstone 

Gutta-percha 



Common 
specific 
gravity. 



2-73 

3^57 

1^13 

1-40 
•0-4^86 

2-74 

1-71 
-6-1-8 
•6-2-16 

2-3 

1-28 
-96 

1-93 

1-40 
30 



24-1 
1-0 
2-08 

4-6" 
2-60 



2^20 

2-14 

•98 



Average I 

weight I 

per cubic ; 

foot. I 



171 I 
192 ! 
70 
87 
250-^04 i 
171 1 
107 I 
100-115 ; 
100-125 i 
140-150 i 
80 I 
60 I 
121 I 
80-95 
77-81 

62 I 
120-140 
80-110 
250 ! 
162 
150-200 ! 
160-170 ■ 
138 
110 I 
135 ' 
61 



Substance. 



Gypsum 

Lime, quick 

Limestone 

Magnesia carbonate . . . 

Marble 

Masonry, concrete 

" rubble 

" granite 

'• limestone.... 

" sandstone . . . 

Mica 

Porphyry 

Pumice stone 

Quartz 

Red lead 

Resin 

Rubber, pure 

Salt, common and rock 

Sand 

Sandstone 

Slate 

Soapstone . . 

Sulphur 

Terra cotta 

Trap. 



Common 
specific 
gravity. 



■24 

■80 



4 

72 
08 
08 
72 
72 
2^24 
2-80 
2^80 
-96 
2-64 
8-96 
1-09 
•95 
2-16 
1-60 
232 
2-80 
2-72 
2-03 
1-95 
2-88 



Average 

weight 

per cubic 

foot. 



140 
50 
180 
150 
170 
130 
130 
170 
170 
140 
175 
175 
60 
165 
560 
68 
60 
135 
100 
145 
175 
170 
127 
122 
180 



APPENDIX. 



809 



SPECIFIC GRAVITY AND WEIGHT OF WOOD. 



Wood. 



Apple 

Ash 

Bamboo . . . . 

Beech 

Birch 

Box 

Butternut.. . 

Cedar 

Cherry 

Chestnut.. . . 

Cork 

Cypress 

Ebony 

Elm 

Fir 

Gum 

Hackmatack 
Hemlock.. . . 
Hickory . . . . 
Hornbeam . . 







Average 


Specific 


weight 


gravity. 


per cubic 
foot. 


•73- •SO 


47 


•60- 


84 


45 


•31- 


40 


22 


•62- 


85 


46 


•56- 


74 


41 


•91-1 


33 


70 




38 


24 


•49- 


75 


39 


•61- 


72 


41 


•46- 


66 


35 




24 


15 


•41- 


66 


33 


1 • 13-1 


33 


76 


•55- 


78 


38 


•48- 


70 


37 


•84-1 


00 


57 




59 


37 


•36- 


41 


24 


•69- 


94 


48 


1 
1 


76 


47 



Wood. 



Lignum-vita? . . 

Lime 

Linden 

Locust , 

Mahogany 

Maple 

Oak, live 

" white 

" red 

Palmetto 

Pine, long leaf. 

" white. 

" yellow . . . 

Poplar , 

Spruce , 

Sycamore , 

Tamarack 

Teak 

Walnut 

black. . 



Specific 
gravity. 



•65- 



1-33 
•80 
•60 
•73 

1^06 
•79 

1^10 

•86 

- ^75 



•35- 
•46- 
•38- 
•40- 
•59- 

•66- 
•50- 



■70 
55 
76 
58 
50 
62 
•40 
■98 
67 
50 



Average 

weight 

per cubic 

foot. 



62 
50 
37 
46 
51 
42 
64 
48 
46 

44 
25 
38 
30 
28 
37 
25 
51 
36 
31 



PROPERTIES OF METALS. 



Metal. 



Aluminum . . . 

Antimony.. . . 

Bismuth 

Cadmium . . . . 

Calcium 

Chromium . . . 

Cobalt 

Copper 

Gold, pure . . . 
" 22 carati 
" 20 " 

Iron, cast . . . . 
" wrought 

Lead 

Magnesium.. . 

Manganese . . . 

Mercu^ry, 60' . 

Nickel 

Platinum 

Potassium.. . . 

Seliniuni 

Silver 

Sodium 

Steel 

Strontium.. . . 

Tellmra 

Thallium 

Tin 

Tungsten . , , . 

Uranium 

Zinc 



Specific 
gravity. 



8-9 



2-63 
6-76 

9-82 

8-65 

1-58 

5-00 

8-60 

7 to 

19-30 

17-49 

15-71 

7^20 

7-68 

11-36 

1-70 

8-00 

13-58 

3 to 8 

21-50 

0-86 

4-30 

10-50 

0-97 



7-84 



2-54 

6-11 
11-85 

7^35 
17-00 
18-33 

7-14 



Weight per 
cubic foot. 



166 
421 
612 
539 



450 

1,215 



450 

480 
709 
106 
499 
847 
537 
1,341 



655 



490 



458 



445 



Melting point, 
degrees Fahr. 



1,400 

842 
510 



1,930 
1,915 



2,000 to 2,200 
2,700 to 2,900 
625 
1,200 

662 
3,000 

'144 

220 

1,750 



2,500 



Tensile strength, 

pounds per square 

inch. 



26,000 
6,466* 

20,000 to 30,000 

46,000 to 48,666 



fHigh grade, 70,- 
I 000 to 80,000. 
J Medium grade, 
^ 60,000 to 70,000. 
Soft grade, 52,000 
to 60,000. 



442 3,500 

780 I 5,000 to 6,000 



Expansion 

in 100 ft. 
from temp. 
32° to 212° F. 



1083 
1392 



•1722 
•1552 



•1109 
•1220 

•2848 



•0857 
•1909 

•1079 

•2173 
•2942 



810 



APPENDIX. 



SOLDERS. 



Lead, melts at 441 
Tin, melts at 340°. 

Spelter, soft 

" hard 

Steel 

Brass or copper . . . 

Fine brass 

Iron 

Copper .. . 

German silver . . . . 



Copper. 



50 
65 
13 
50 
47 
66 
53 



Tin. 



33 

67 



47 



Lead. 



67 
33 



Zinc. 



50 

35 

5 

50 
47 
83 

54 



Antimony, 



Silver. 



82 
'6 



Nickel. 



Solders of lead and tin are termed soft solders, in plumbers' work the joints are wiped 
and the solder is in a mass. In soldering cornices, where there is a strain, the metal 
should be riveted as well. Solders containing copper are used for brazing. 

Sheet lead for sulphuric-acid chambers is joined by burning the sheets by a blowpipe. 
The welding of various metals is now effected by electricity. In joining one metal to 
another, one must be fluid; and mercury, being usually fluid, combines with most metals 
except iron and platinum. An amalgam of tin or cold solder can be applied by friction 
to polished iron and form a surface which admits of being soldered. 

Fusible Alloys. — A fusible alloy composed of 50 bismuth, 25 tin, and 25 lead melts at 
212°; the melting point may be still further reduced by a larger percentage of bismuth, 
and it is used either as a solder or a fusible plug. In automatic fire extinguishers the 
cap of the sprinkler is soldered with this alloy, and melts at about 170°. For fusible 
plugs in boilers, the United States supervising inspectors specify Banca tin, which melts 
at about 445° F. The plug must be at least ^" smallest diameter. 

ALLOYS AND COMPOSITIONS. 





Cop- 
per. 


Zinc. 


Tin. 


Nickel. 


Lead. 


Alu- 
mi- 
num. 


Steel. 




Anti- 
mony. 


Tensile 

strength 

persq. 

inch. 


Aluminum, bronze 

" brass 


90-0 
33i 

'i's' 

3-7 
2-0 

si-i' 

"6"25 
67-3 


38i 

"i-6' 

3'l"-'9' 

93-75 
13-0 


Add 
10-0 
89-3 

88-9 
81-0 

'3-2 


33i per 


cent £ 


10-0 

lumi 
90-0 


num br 


onze. 


.... 


75.000- 
90,000 

78.327 


" composition . 
Babbitt's metal, light duty 
" " for bear- 
ings . . 




'8-9 

7-4 
16-0 




13-8' 





... 


98'6' 


'2-6* 




Britannia metal 




Chrome steel 

German silver 





Gun metal 

Muntz metal 


42.560 

49,280 


Manganese alloy f 

Nickel steel 


.... 


*3'25 


75 '-6 

87-5 


1-2 
l'2-'0 


96-75 

Iron. 
2-0 


18-0^ 


-5|| 

Anti- 
mony. 
25-0 
12-5 

56-8 


57,000 


Sheathing metal 


56-0 
66-0 
50-0 

61-0 


44-0 
2i'6' 
35-0 


22-6 
29-0 

2-0 




Sneoulum " 




u u 




Sterrometal 


85,120 


Tvne metal . .... 




a u 













White " 


7-4 
69-8 


7-4 
25-8 


28-4 
4-4 






" hard 





.... 












* Chromium, 2-0. f Twenty-five per cent manganese to copper doubles its tensile strength 
without diminishing its ductility. X Manganese, 18-0. 1| Silicon, -5. 



APPENDIX. 



811 



TABLES OF THE CIRCUMFERENCES OF CIRCLES TO THE NEAREST FRACTION OF 
PRACTICAL MEASUREMENT ; ALSO, THE AREAS OF CIRCLES, IN INCHES AND 
DECIMAL PARTS, LIKEWISE OF FEET AND DECIMAL PARTS. 



Circumfer- 


Diameter 


Area 


Area 


Circumfer- 


Diameter 


Area 


Area 


ence in feet 


in 


in square 


in square 


ence in feet 


in 


in square 


in square 


and inches. 


inches. 


inches. 


feet. 


and inches. 


inches. 


inches. 


feet. 










1 6^, 


6 


28-27 


•196 


•20 


iV 


•003 




1 7i 


6i 


29-46 


•204 


•39 


1 


•012 




1 n 


6i 


30-68 


•212 


•59 


A 


•028 




1 8 


6f 


31-92 


-220 


•78 


i 


•049 




1 8f 


6i 


33-18 


-228 


•98 


A 


•077 




1 8f 


6t 


34^47 


•237 


1-18 


f 


•110 




1 9i 


6f 


35-78 


•246 


1-37 


■iV 


•150 




1 9^ 


6| 


37-12 


•256 


1^5Y 


i 


•196 




1 10 


7 


38-48 


•267 


177 


1^ 


•248 




1 lOf 


7^ 


39-87 


•277 


1-96 


8 


•307 




1 loi 


7i 


41-28 


•287 


2'1& 


1^ 


•371 




1 lU 


7f 


42-72 


•297 


2-36 


f 


•442 




1 Hi 


7i 


44-18 


•307 


2-55 


H 


•518 




. 1 11^ 


7f 


45-66 


•318 


2-75 


i 


•601 




2 of 


7f 


47-17 


•328 


2-94 


If 


•690 




2 o| 


7i 


48-71 


•338 


Si 


1 


•785 


-0054 


2 n 


8 


50-26 


•349 


3i 


li 


•994 


•0069 


2 H 


8i 


51^85 


•360 


s- 


li 


1-23 


•0085 


2 1^ 


8i 


53-46 


•371 


4t 


If 


1-48 


•0103 


2 2i 


8f 


5509 


•388 


^ 


li 


1-77 


•0123 


2 2f 


8i 


56-74 


•394 


51- 


11 


2-07 


•0144 


2 3 


81 


58-43 


•406 


4 


If 


2-40 


•0167 


2 3i 


8i 


60-13 


-428 


5l 


1^ 


2-76 


•0192 


2 Si 


Si 


61-86 


•430 


6i 


2 


314 


•0218 


2 4i 


9 


63-62 


•442 


61 


2i 


3-55 


•0246 


2 4f 


9i 


65-40 


-455 


7 


2i 


3-98 


•0276 


2 5 


9i 


67^20 


•467 


7f 


2f 


4-43 


•0307 


2 5f 


9f 


69-03 


-480 


7i 


2i 


.4-91 


•0341 


2 5f 


9j 


70-88 


-493 


84 


2| 


5-41 


•0376 


2 6i 


9f 


72-76 


•506 


81 


2f 


5-94 


•0412 


2 6f 


9| 


74-66 


-519 


9 


21- 


6-49 


•0450 


2 7 


9| 


76-59 


•532 


n 


3 


7-07 


•0490 


2 71 


10 


78-54 


•545 


91 


3^ 


7-67 


•0532 j 


2 7f 


lOi 


80-51 


-559 


lOi 


3i 


8 29 


-0576 


2 8i 


lOi 


82-52 


•573 


101 


3f 


8-95 


•0621 


2 8i 


lOf 


84-54 


•587 


11 


3i 


9-62 


•0668 


2 9 


lOi 


86-59 


•601 


111 


3f 


10-32 


•0716 


2 9f 


lOf 


88-66 


•615 


n'i 


3f 


11-04 


-0766 


2 9f 


lOf 


911-76 


•630 


i2i 


3i 


11-79 


•0818 


2 lOi 


lOi 


92-88 


-645 


1 oi 


4 


12-57 


•087 


2 10-L 


11 


95-03 


•660 


1 1 


4^ 


13-36 


•093 


2 10| 


Hi 


97-21 


-675 


1 1^ 


4i 


14-19 


•099 


2 II7 


Hi 


99-40 


•690 


1 If 


4f 


15 03 


•105 


2 llf 


llf 


101-62 


•705 


1 2| 


4i 


15-90 


•111 


3 Oi 


Hi 


103-87 


-720 


1 2^ 


4f 


16-80 


•118 


3 Oi 


iif 


106-14 


•736 


1 2i 


4f 


17-72 


•124 


3 0| 


iif 


108-43 


-752 


1 3i 


4l 


18-66 


•130 


3 li 


111 


110-75 


•768 


1 3f 


5 


19-63 


•136 


3 1| 


12 


113-10 


•785 


1 4i 


5k 


20-63 


•143 


3 2 


12i 


115-47 


•802 


1 4i 


5i 


21-65 


•150 


3 2i 


12i 


117-86 


-819 


1 4J 


51 


22-69 


•157 


3 2^ 


12f 


120-28 


-836 


1 5i 


5i 


23-76 


•165 


3 3i 


12i 


122-72 


•853 


1 5f 


5f 


24-85 


•173 


3 3| 


12f 


125-19 


•870 


1 6 


5f 


25-97 


181 


3 4 


12f 


127-68 


•887 


1 6f 


5| 


27-11 


•189 


3 41 


121- 


130-19 


-904 



812 



APPENDIX. 



TABLES OF THE CIECUMFEEENCES OF CIECLES, ETC— (Continued.) 



Circumfer- 


Diameter 


Area 


Area 


Circumfer- 


Diameter 


Area 


Area 


ence in feet 


in 


in square 


in square 


ence in feet 


in feet and 


in square 


in square 


and inches. 


inches. 


inches. 


feet. 


and inches. 


inches. 


inches. 


feet. 


3 4| 


13 


132-73 


•922 


5 2| 


20 


314-16 


2-182 


3 5^ 


13i 


135-30 


•939 


5 3i 


20^ 


318-10 


2-209 


3 5f 


13i 


137-89 


•956 


5 3f 


20i 


322-06 


2-237 


3 6 


13f 


140-50 


•974 


5 4 


20| 


326-05 


2-265 


3 6f 


13i 


143-14 


•992 


5 4f 


20^ 


330-06 


2-293 


3 6f 


13f 


145-80 


roil 


5 4f 


20| 


334-10 


2-321 


3 n 


13f 


148-49 


1-030 


5 5^ 


20|- 


338-16 


2-349 


3 n 


131 


151-20 


1^050 


5 5i 


20^ 


342-25 


2-377 


3 8 


14 


153-94 


r069 


5 6 


21 


346-36 


2-405 


3 8f 


14i 


156-70 


1-088 


5 6f 


2H 


350-50 


2-434 


3 8f 


14i 


159-49 


1-107 


5 6| 


211 


354-66 


2-463 


3 9i 


14f 


162-30 


1-126 . 


5 7^ 


21f 


358-84 


2-492 


3 9i 


14i 


165-13 


1^146 


5 7i 


2U 


36305 


2-521 


3 n 


14f 


167-99 


1-166 


5 71 


21| 


367-28 


2-55a 


3 lOi 


141 


170-87 


1-186 


5 8i 


211 


371-54 


2-580 


3 lOf 


Ut 


173-78 


1-206 


5 8| 


2U 


375-83 


2-6ia 


3 Hi 


15 


176-71 


1-227 


5 9J 


22 


380-13 


2-640 


3 Hi 


15i 


179-67 


1-247 


5 91 


22^ 


384-46 


2-670 


3 HI 


15i 


182-65 


1-267 


5 9i 


221 


388-82 


2-700 


4 Oi 


15| 


185-66 


1-288 


5 lOi 


221 


39320 


2-730 


4 Of 


15i 


188-69 


1-309 


5 lOf 


22i 


397-61 


2-761 


4 1 


15f 


191-75 


1-330 


5 11 ^ 


22f 


402-04 


2-792. 


4 li 


15f 


194-83 


1-352 


5 111 


22f 


406-49 


2-823 


4 n 


15i 


197-93 


1-374 


5 11| 


22| 


410-97 


2-854 


4 2i 


16 


201-06 


1-396 


6 01 


.23 


415-48 


2-885 ' 


4 2f 


16i 


204-22 


1-418 


6 Of 


23i 


42000 


2-917 


4 3 


16i 


207-39 


1-440 


6 1 


23ir 


424-56 


2-949 


4 3f 


16f 


210-60 


1-462 


6 If 


23| 


429-13 


2-981 


4 3| 


16i 


213-82 


1-484 


6 If 


23^ 


433-74 


3-013 


4 4i 


16f 


217-08 


1-507 


6 21 


23f 


438-36 


3-045 


4 4| 


16f 


220-35 


1-530 


6 2f 


23| 


443-01 


3-077 


4 5 


161 


223-65 


1-553 


6 3 


23| 


447-69 


3-109' 


4 5| 


11 


226-98 


1-576 


6 3f 


2 


452 39 


3-142 


4 5f 


m 


280-33 


1-599 


6 4} 


2 Oh 


461-86 


3-207 


4 6i 


17i 


233-70 


1-622 


6 4i 


2 01 


471-44 


3-273 


4 6i 


17i . 


237-10 


1-645 


6 5| 


2 0| 


481-11 


3-341 


4 61 


m 


240-53 


1-669 


6 6i 


2 1 


490-87 


3-408 


4 71 


171 


243-98 


1-693 


6 7i 


2 11 


500-74 


3-477 


4 71 


171 


247-45 


1-718 


6 8i 


2 n 


510-71 


3-547 


4 8i 


171- 


250-95 


1-743 


6 8i 


2 If 


520-77 


3-617 


4 8i 


18 


254-47 


1-767 


6 9f 


2 2 


530-93 


3-687 




18^ 


258-02 


1^792 


6 10^ 


2 21 


541-19 


3-758 


4 9i 


18i 


261-59 


1-817 


6 lU 


2" 21 


651-55 


3-830 


4 9f 


18f 


265-18 


1-842 


7 


2 2f 


562-00 


3-904 


4 lOi 


18i 


268-80 


1-868 


7 - 01 


2 3 


572-56 


3-976 


4 lOi 


18f 


272-45 


1-893 


7 If 


2 3i 


583-21 


4-050 


4 lot 


181 


276-12 


1-918 


7 2| 


2 34 


593-96 


4-124 


4 Hi 


18^ 


279-81 


1-943 


1 H 


2 3f 


604-81 


4-200 


4 Hf 


19 


283-53 


1-969 


7 3| 


2 4 


615-75 


4-276 


5 


m 


287-27 


1-995 


7 4f 


2 41 


626-80 


4-352 


5 Of 


19i 


291-04 


2-021 


7 5^ 


2 4i 


637-94 


4-430 


5 0| 


19| 


294-83 


2-047 


7 6} 


2 4f 


649-18 


4-508 


5 li 


19h 

19| 


298-65 


2-074 


7 7 


2 5 


660-52 


4-586 


5 If 


302-49 


2-101 


7 1i 


2 51 


671-96 


4-666 


5 2 


191 


306-36 


2-128 


7 8f 


2 5i - 


683-49 


4-747 


6 2| 


19^ 


310-25 


2-155 


7 91 


2 51 


695-13 


. 4-827 



APPENDIX. 



813 



TABLES OF THE CIRCUMFERENCES OF CIRCLES, ^HC. -{Continued.) 



Circumfer- 


Diameter 


Area 


Area 


Circumfer- 


Diameter 


Area 


Area 


ence in feet 


in feet and 


in square 


in square 


ence in teet 


in feet and 


in square 


in square 


and inches. 


inches. 


inches. 


feet. 


and inches. 


inches. 


inches. 


feet. 


7 10^ 


2 


6 


706-86 


4-908 


11 6i 


3 


8 


1520-5 


10-56 


7 11 


2 


64^ 


718-69 


4-990 


11 7 


3 


8i 


1537-9 


10-68 


7 llf 


2 


65 


730-62 


5-073 


11 7f 


3 


8i 


1555-3 


10-80 


8 0| 


2 


61 


742-64 


5-157 


11 .8^ 


3 


8| 


1572-8 


10-92 


•8 1| 


2 


7 


754-77 


5-241 


11 9| 


3 


9 


1590-4 


11-04 


8 2^ 


2 


n 


766-99 


5-326 


11 lOi 


3 


9i 


1608-1 


11-17 


8 2J 


2 


n 


779-31 


5-411 


11 101 


3 


9^ 


1626-0 


11-29 


'8 3| 


2 


71 


791-73 


5-498 


11 llf 


3 


9f 


1643-9 


11-41 


8 4^ 


2 


8 


804-25 


5-585 


12 OJ 


3 


10 


1661-9 


11-54 


8 5| 
8 6^ 


2 


8i 


816-86 


5-673 


12 1^ 


3 


m 


1680-0 


11-67 


2 


H 


829-58 


5-761 


12 2 


3 


lOi 


1698-2 


11-79 


8 6^ 


2 


8| 


842-39 


5-849 


12 2| 


8 


lOi 


1716-5 


11-92 


8 71 


2 


9 


855-30 


5-939 


12 3f 


3 


11 


1734-9 


12-05 


8 8^ 


2 


9i 


868-31 


6-029 


12 4| 


3 


lU 


1753-4 


12-18 


8 9i 


2 


9^ 


881-41 


6-120 


12 5i 


3 


lU 


1772-0 


12-30 


« 10 


2 


n 


894-62 


6-212 


12 6 


3 


llf 


1790-8 


12-43 


8 10| 


2 


10 


907-92 


6-305 


12 6f 


4 





1809-6 


12-57 


8 11^ 


2 


lOi 


921-32 


6-398 


12 7i 


4 


0^ 


1828-5 


12-70 


9 Of 


2 


m 


934-82 


6-491 


12 8| 


4 


of 


1847-4 


12-83 


^ li 


2 


101 


948-42 


6-586 


12 n 


4 


Of 


1866-5 


12-96 


9 1| 


2 


11 


962-11 


6-681 


12 n 


4 


1 


1885-7 


13-09 


9 2| 


2 


114- 


975-91 


6-777 


12 lOf 


4 


n 


1905-0 


13-23 


^ U 


2 


lU 


989-80 


6-874 


12 111 


4 


H 


1924-4 


13-36 


9 4 


2 


llf 


1003-8 


6-970 


13 Oi 


4 


11 


1943-9 


13-50 


9 5 


3 





1017-9 


7-069 


13 1 


4 


2 


1963-5 


13-63 


9 5^ 


3 


ot 


1032-1 


7-167 


13 1| 


4 


2i 


1983-2 


13-77 


9 6j 


3 


0^ 


1046-3 


7-266 


13 2| 


4 


H 


2003-0 


13-91 


9 7^ 


3 


of 


1060-7 


7-366 


13 3f 


4 


2f 


2022-8 


14-05 


9 St 


3 


1 


1075-2 


7-466 


13 41 


4 


3 


2042-8 


14-19 


9 9 


3 


Ir 


1089-8 


7-567 


13 5 


4 


'^i 


2062-9 


14-32 


9 91 


3 


1; 


1104-5 


7-669 


13 5f 


4 


3i 


2083-1 


14-46 


9 lOf 


3 


1| 


1119-2 


7-772 


13 6i 


4 


3f 


21 OS -3 


14-61 


9 llf 


3 


2 


1134-1 


7-876 


13 7| 


4 


4 


2123-7 


14-75 


10 Oi 


3 


2i 


1149-1 


7-979 


13 8i 


4 


4i 


2144-2 


14-89 


10 01 


3 


2i 


1164-2 


8-085 


13 81 


4 


4i 


2164-7 


15-03 - 


10 If 


3 


2| 


1179-3 


8-189 


13 9| 


4 


4| 


2185-4 


15-18 


10 2i 


3 


3 


1194-6 


8-295 


13 lOi 


4 


5 


2206-2 


15-32 


10 H 


3 


H 


1209-9 


8-403 


13 Hi 


4 


5i 


2227-0 


15-46 


10 4 


3 


Sk 


1225-4 


8-509 


14 


4 


5i 


2248-0 


15-61 


10 4J 


3 


3f 


1241-0 


8-617 


14 01 


4 


5| 


2269-1 


15-76 


10 5| 


3 


4 


1256-6 


8-727 


14 If 


4 


6 


2290-2 


15-90 


10 6| 


3 


4i 


1272-4 


8-836 


14 2| 


4 


H 


2311-5 


16-05 


10 7i 


3 


44 


1288-2 


8-946 


14 Si 


4 


H 


2332-8 


16-20 


10 8 


3 


4f 


1304-2 


9056 


14 4 


4 


6f 


2354-3 


16-35 


10 8f 


3 


5 


1320-2 


9-169 


14 4f 


4 


7 


2375-8 


16-50 


10 9i 


3 


5t 


1336-4 


9-211 


14 5J- 


4 


Vi 


2397-5 


16-65 


10 10| 


3 


5J 


1352-6 


9-394 


14 6f 


4 


7* 


2419-2 


16-80 


10 lU 


3 


of 


1369-0 


9-506 


14 7J 


4 


7| 


2441-1 


16-95 


10 111 


3 


6 


1385-4 


9-62 


14 71 


4 


8 


• 2463-0 


17-10 


11 Of 


3 


6i 


1402-0 


9-73 ' 


14 8i 


4 


8i 


2485-0 


17-26 


11 1^ 


3 


6^ 


1418-6 


9-84 


14 9i 


4 


sl 


2507-2 


17-41 


11 2i 


3 


6f 


1435-4 


9-96 


14 lOi 


4 


8| 


2529-4 


17-56 


11 3 


3 


7 


1452-2 


10-08 


14 11 


4 


9 


2551-8 


17-72 


11 3| 


3 


7i 


1469-1 


10-20 


14 111 


4 


n 


2574-2 


17-88 


11 4| 


3 


7^ 


1486-2 


10-32 


15 0| 


4 


n 


2-596-7 


18-03 


11 5^ 


3 


7f 


1503-3 


10-44 


15 If 


4 


9f 


2619-3 


18-19 



814 



APPENDIX. 



TABLES OF 


THE CIE( 


:UMrEEEN( 


]ES OF CIECLES, ETC 


.— ( Continued. ) 


Circumfer- 


Diameter 


Area 


Area 


Circumfer- 


Diameter 


Area 


Area 


ence in feet 


in feet and 


in square 


in square 


ence in feet 


in teet and 


in square 
inches. 


in square 


and Inches. 


inches. 


inches. 


feet. 


and inches. 


inches. 


feet. 


15 2| 


4 10 


2642-1 


18-35 


18 lOi 


6 


4071-5 


28-27 


15 3 


4 101 


2664-9 


18-51 


18 10^ 


6 01 


4099-8 


28-47 


15 3| 


4 10^ 


2687-8 


18-66 


18 llf 


6 Oi 


4128-2 


28-67 


15 4i 


4 lOf 


2710-8 


18-82 


19 0^ 


6 Of 


4156-8 


28-87 


15 5h 


4 11 


2734-0 


18-98 


19 1; 


6 1 


4185-4 


29-07 


15 6^ 


4 lU 


2757-2 


19-15 


19 2^ 


6 li 


4214-1 


29-27 


15 6i 


4 Hi 


2780-5 


19*31 


19 2i 


6 U 


4242-9 


29-47 


15 Vf 


4 llf 


2803-9 


19-47 


19 3f 


6 If 


4271-8 


29-67 


15 8i 


5 


2827-4 


19-63 


19 4i 


6 2 


4300-8 


29-87 


15 9^ 


5 Oi 


2861-0 


19-80 


19 6^ 


6 2i 


4329-9 


30-07 


15 10 


5 Oi 


2874-8 


19-96 


19 6 


6 2^ 


4359-2 


30-27 


15 lOf 


5 Of 


2898-6 


20-13 


19 6f 


6 2^ 


4388-5 


30-47 


15 111 


5 1 


2922-5 


20-29 


19 U 


6 3 


4417-9 


30-68 


16 Of 


5 11 


2946-6 


2046 


19 8| 


6 3i 


4447-4 


30-88 


16 U 


5 IJ 


2970-6 


20-63 


19 9| 


6 3i 


4477-0 


31-09 


16 2 


5 If 


2994-8 


20-80 


19 9| 


6 3f 


4506-7 


31-30 


16 2f 


5 2 


3019-1 


20-96 


19 lOf 


6 4 


4536-5 


31-50 


16 3i 


5 2i 


3043-5 


21-13 


19 Hi 


6 4i 


4566-4 


31-71 


16 41 


5 2i 


3068-0 


21-30 


20 Oi 


6 4i 


46963 


31-92 


16 5^ 


5 21 


3092-6 


21-48 


20 li 


6 4f 


4626-4 


32-13 


16 6i 


5 3 


3117-2 


21-65 


20 li 


6 5 


4666-6 


32-34 


16 6f 


5 Si 


3142-0 


21-82 


20 2f 


6 5i 


4686-9 


32-55 


16 7J 


5 3J 


3166-9 


21-99 


20 3^ 


6 5J 


4717-3 


32-76 


16 Si 


5 3f 


3191-9 


22-17 


20 41 


6 5f 


4747-8 


32-97 


16 9 


5 4 


32170 


22-34 


20 5 


6 6 


4778-3 


33-18- 


16 9f 


5 4^ 


3242-2 


22-51 


20 6| 


6 61 


4809-0 


33-40 


16 lOf 


5 4^ 


3267-5 


22-69 


20 6^ 


6 6J 


4839-8 


33-61 


16 llf 


5 4f 


3292-8 


22-87 


20 7| 


6 6| 


4870-7 


33-82 


IV Oi 


5 5 


3318-3 


23-04 


20 8^ 


6 7 


4901-6 


34-04 


IV 1 


5 51 


3343-9 


23-22 


20 8i 


6 7i 


4932-7 


34-25 


IV If 


5 H 


3369-6 


23-40 


20 9| 


6 7* 


4963-9 


34-47 


IV 2^ 


5 5f 


3396-3 


23-58 


20 lOi 


6 7| 


4995-1 


34-69 


IV 3f 


5 6 


3421-2 


23-76 


20 111 


6 8 


5026-5 


34-91 


IV 4J 


5 6^ 


3447-2 


23-94 


21 OJ 


6 81 


5068-0 


35-12 


IV 44 


5 6i 


3473-2 


24-12 


21 0| 


6 8* 


5089-5 


35-34 


IV 51 


5 6f , 


3499-4 


24-30 


21 If 


6 8f 


6121-2 


35-56 


IV 6i 


5 7 


3525-1 


24-48 


21 2f 


6 9 


5158-0 


35-78 


17 Vi 


5 7i 


3552-0 


24-67 


21 3i 


6 9i 


5184-8 


36-01 


17 8 


5 7l 


3578-5 


24-85 


21 4 


6 9^ 


5216-8 


36-23 


IV 8f 


5 7f 


3605-0 


25-03 


21 41 


6 9^ 


5248-8 


36-45 


17 9f 


5 8 


3631-7 


25-22 


21 5f 


6 10 


5281-0 


36-67 


17 lOf 


5 8J 


3658-4 


26-40 


21 6f 


6 10^ 


5313-2 


36-89 


17 lU 


5 8} 


3685-3 


25-59 


21 V| 


6- lOi 


5345-6 


37-12 


IV 11* 


5 8| 


3712-2 


25-78 


21 7- 


6 10| 


5378-0 


37-35 


18 Of 


5 9 


3739-3 


25-96 


21. 85 


6 11 


5410-6 


37-57 


18 U 


5 9i 


3766-4 


26-15 


21 99 


6 111 


5443-2 


37-80 


18 2i 


5 9i 


3793-7 


26-34 


21 lOzf 


6 11^ 


5476-0 


38-03 


18 3i 


5 9f 


3821-0 


26-53 


21 Hi 


6 llf 


5508-8 


38-26 


18 3* 


5 10 


3848-5 


26-72 


21 11| 


7 


5541-7 


38-48 


18 4f 


5 lOir 


3876-0 


26-92 


22 Oi 


V 01 


6674-8 


38-71 


18 5i 


5 lOJ 


3903-6 


27-11 


22 If 


V o.v 


5607-9 


38-94 


18 ei 


6 lOf 


3931-4 


27-30 


22 2^ 


V 9| 


5641-1 


39-17 


18 7 


6 11 


3959-2 


27-49 


22 3 


V 1 


5674-5 


39-41 


18 7| 


5 lli 


3987-1 


27-69 


22 Si 


V U 


5707-9 


39-64 


18 8| 


5 Hi 


4015-2 


27-88 


22 4^ 


7 u 


5741-4 


39-87 


18 9| 


5 llf 


4043-3 


28-08 


22 5i 


7 If 


5775-0 


40-10 



APPENDIX. 815 

TABLES OF THE CIRCUMFERENCES OF CIRCLES, ETC —{Co?itinued.) 



Circumfer- 


Diameter 


Area 


Area 


Circu 


mfer- 


Diameter 


Area 


Area 


ence in feet 


in feet and 


in square 


in square 


ence 


in feet 


in feet and 


in square 


in square 


and inches. 


inches. 


inches. 


feet. 


and inches. 


inches. 


inches. 


leet. 


22 6J 


7 


2 


5808-8 


40-34 


26 


2i 


8 


4 


7853-9 


54-54 


22 6J 


7 


H 


5842-6 


40-57 


26 


5i 


8 


5 


8011-9 


55-64 


22 71 


7 


^ 


5S76-5 


40-80 


26 


85 


8 


6 


8171-3 


56-75 


22 8J 


7 


2I 


5910-5 


41-04 


26 


lU 


8 


7 


8332-3 


57-86 


22 H 


7 


3 


5944-6 


41-28 


27 


2f 


8 


8 


8494-9 


58-99 


22 10^ 


7 


31: 


597S-9 


41-52 


27 


5i 


8 


9 


8659-0 


60-13 


22 lOs^ 


7 


H 


6013-2 


41-76 


27 


9 


8 


10 


8824-7 


61-28 


22 lit 


7 


H 


6047-6 


42-00 


28 


0^ 


8 


11 


8892-0 


62-44 


23 Of 


7 


4 


6082-1 


42-24 


28 


H 


9 




9160-9 


63-62 


23 U 


7 


4i 


6116-7 


42-48 


28 


H 


9 


1 


9331-3 


64-80 


23 2 


7 


44 


6151-4 


42-72 


28 


n 


9 


2 


9503-3 


66-00 


23 2f 


7 


4i 


6186-2 


42-96 


29 


o| 


9 


3 


9676-9 


67-20 


23 3i 


7 


5 


6221-1 


43-20 


29 


3f 


9 


4 


9852-1 


68-42 


23 4f 


7 


5i 


62561 


43-44 


29 


7 


9 


5 


10028-8 


69-64 


23 5^ 


7 


5^ 


6291-2 


43-68 


29 


lOi 


9 


6 


10207-1 


70-88 


23 6 


7 


5J 


6326-4 


43-93 


30 


U 


9 


7 


10386-9 


72-13 


23 6| 


7 


6 


6361-7 


44-18 


30 


4| 


9 


8 


10568-3 


73-39 


23 7^ 


7 


H 


6397-1 


44-43 


30 


n 


9 


9 


10751-3 


74-66 


23 Si 


7 


6.V 


6432-6 


44-67 


30 


lOf 


9 


10 


10935-9 


75-94 


23 9^ 


7 


6| 


6468-2 


44-92 


31 


If 


9 


11 


11122-0 


■ 77-24 


23 9^ 


7 


7 


6503-8 


45-17 














23 10^ 


7 


n 


6539-6 


45-41 


31 


5 


10 




11309-8 


78-54 


23 llf 


7 


'7? 


6575-5 


45-66 


31 


8^ 


10 


1 


11499-0 


79-85 


24 0^ 


7 


n 


66115 


45-91 


31 


Hi 


10 


2 


11689-9 


81-18 












32 


2| 


10 


3 


11882-3 


82-52 


24 1 


7 


8 


6647-6 


46-16 


32 




10 


4 


12076-3 


83-86 


24 11 


7 


81 


6683-8 


46-42 


32 


10 


5 


12271-9 


85-22 


24 2^ 


7 


8j 


6720-0 


46-67 


32 


llf 


10 


6 


12469-0 


86-59 


24 3i 


7 


8i 


6756-4 


46-92 


33 


H 


10 


7 


12667-7 


87-97 


24 4^ 


7 


9 


6792-9 


47-17 


33 


6i 


10 


8 


12868-0 


89-36 


24 4^ 


7 


9i 


6829-4 


47-43 


33 


n 


10 


9 


13069-8 


90-76 


24 5J 


7 


9^ 


6866-1 


47-68 


34 


Of 


10 


10 


13273-3 


92-17 


24 &} 


7 


9i 


6902-9 


47-94 


34 


3^ 


10 


11 


13478-2 


93-60 


24 7i 


7 


10 


6939-7 


48-19 


34 


6^ 


11 




13684-8 


95-03 


24 8 


7 


lOL 


6976-7 


48-45 


34 


9f 


11 


1 


13892-9 


96-48 


24 8| 


7 


10^ 


7013-8 


48-71 


35 


oi 


11 


2 


14142-6 


97-93 


24 9| 


7 


10| 


7050-9 


48-96 


35 


4i 


11 


3 


14313-9 


99-40 - 


24 10| 


7 


11 


7088-2 


49-22 


35 


'^i 


11 


4 


14526-8 


100-88 


24 lU 


7 


Hi 


7125-5 


49-48 


35 


io| 


11 


5 


14741-2 


102-37 


25 


7 


ii| 


7163-0 


49-^4 


36 


H 


11 


6 


14957-2 


103-87 


25 Oi 


7 


llf 


7200-5 


50-00 


36 


4| 


11 


7 


15174-7 


105-38 












86 


n 


11 


8 


15393-8 


106-90 


25 U 


8 





7238-2 


50-26 


36 


m 


11 


9 


15614-5 


108-43 


25 2f 


8 


OL 


7275-9 


50-53 


37 


2 


11 


10 


15836-8 


109-98 


25 3^ 
25 3^ 


8 


0^ 


7313-8 


50-79 


37 


5i 


11 


11 


16060-6 


111-53 


8 


Of 


7351-7 


51-05 














25 4| 


8 


1 


7389-8 


51-32 


37 


8| 


12 




16286-0 


113-10 


25 5J 


8 


1^ 


7427-9 


51-58 


■ 37 


IH 


12 


1 


16513-0 


114-67 


25 61 


8 


u 


7466-2 


51-85 


38 


2| 


12 


2 


16741-6 


116-26 


25 7 


8 


If 


7504-5 


52-11 


38 


5f 


12 


3 


16971-7 


117-86 












38 


H 


12 


4 


17203-4 


119-47 


25 7^ 


8 


2 


7542-9 


52-38 


39 





12 


5 


17436-7 


121-09 


25 8| 


8 


2\ 


7o81-5 


52-65 


j 39 


34^ 


12 


6 


17671-5 


122-72 


25 9| 


8 


%■ 


7620-1 


52-92 • 


1 39 


6| 


12 


7 


17907-9 


1-24-36 


25 10^ 


8 


2| 


7658-8 


53-19 


39 


9.V 


12 


8 


18145-9 


126-01 


25 11 


8 


3 


7697-7 


53-46 


; 40 


^4 


12 


9 


18385-4 


127-68 


25 llf 


8 


H 


7736-6 


53-73 


40 


3f 


12 


10 


18626-6 


129-35 


26 0^ 


8 


3? 


7775-6 


54-00 


40 


H 


12 


11 


18869-2 


131-04 


26 li 


8 


3f 


7814-7 


54-27 















816 



APPENDIX. 



TABLE OF 


DIAMETERS, CIRCUMFERENCES, AND AREAS OF CIRCLES. 


Diam- 


Circum- 


Circular 


Diam- 


Circum- 


Circular 


Diam- 


Circum- 


Circular . 


eter. 


ference. 


area. 


eter. 


ference. 


area. 


eter. 


ference. 


area. 


1 


3-1416 


0-7854 


51 


160-22 


2042-82 


101 


317-30 


8011-85 


2 


6-28 


3-14 


52 


163-36 


2123-72 


102 


320-41 


8171-28 


3 


9-42 


7-07 


53 


166-50 


2206-18 


103 


323-58 


8332-29 


4 


12-57 


12-57 


54 


169-65 


2290-22 


104 


326-73 


8494-87 


5 


15-71 


19-63 


55 


172-79 


2375-83 


105 


329-87 


8659-01 


6 


18-85 


28-27 


56 


175-93 


2463-01 


106 


333-01 


8824-73 


7 


21-99 


38-48 


57 


179-07 


2551-76 


107 


336-15 


8992-02 


8 


25-13 


50-27 


58 


182-21 


2642-08 


108 


339-29 


9160-88 


9 


28-27 


63-62 


59 


185-35 


2733-97 


109 


342-43 


9331-32 


10 


31-42 


78-54 


60 


188-50 


2827-43 


110 


345-57 


9503-32 


11 


34-56 


95-03 


61 


191-64 


2922-47 


111 


348-72 


9676-89 


12 


37-70 


113-10 


62 


194-78 


3019-07 


112 


351-86 


9852-03 


13 


40-84 


132-73 


63 


197-92 


3117-25 


113 


355-00 


10028-75 


14 


43-98 


153-94 


64 


201-06 


3216-99 


114 


358-14 


10207-03 


15 


47-12 


176-71 


65 


204-20 


3318-31 


115 


361-28 


10386-89 


16 


50-26 


201-06 


66 


207-34 


3421-19 


116 


364-42 


10568-32 


17 


53-41 


226-98 


67 


210-49 


3525-65 


117 


367-57 


10751-32 


18 


56-55 


254-47 


68 


213-63 


3631-68 


118 


370-71 


10935-88 


19 


59-69 


283-53 


69 


216-77 


3739-28 


119 


373-85 


11122-02 


20 


62-83 


314-16 


70 


219-91 


3848-45 


120 


376-99 


11309-73 


21 


65-97 


346-36 


71 


223-05 


3959-19 


121 


380-13 


11499-01 


22 


69-11 


380-13 


72 


226-19 


4071-50 


122 


383-27 


11689-87 


23 


72-26 


415-48 


73 


229-34 


4185-39 


123 


386-42 


11882-29 


24 


75-40 


452-39 


74 


232-48 


4300-84 


124 


389-56 


12076-28 


25 


78-54 


490-87 


75 


235-62 


4417-86 


125 


392-70 


12271-85 


,26 


81-68 


530-93 


76 


238-76 


4536-46 


126 


395-84 


12468-98 


27 


84-82 


572-56 


77 


241-90 


4656-63 


127 


398-98 


12667-69 


.28 


87-96 


615-75 


78 


245-04 


4778-36 


128 


402-12 


12867-96 


29 


91-11 


660-52 


79 


248-19 


4901-67 


129 


405-26 


13069-81 


30 


94-25 


706-86 


80 


251-33 


•5026-55 


130 


408-41 


13273-23 


51 


97-39 


754-77 


81 


254-47 


5153-00 


131 


411-55 


13478-22 


52 


100-53 


804-25 


82 


257-61 


5281-02 


132 


414-69 


13684-78 


S3 


103-67 


855-30 


83 


260-75 


5410-61 


133 


417-83 


13892-91 


34 


106-81 


907-92 


84 


263-89 


5541-77 


134 


420-97 


14102-61 


S5 


109-96 


962-11 


85 


267-03 


5674-50 


135 


424-11 


14313-88 


36 


113-10 


1017-88 


86 


270-18 


5808-80 


136 


427-26 


14526-72 


S7 


116-24 


1075-21 


87 


273-32 


5944-68 


137 


430-40 


14741 - 14 


38 


119-38 


1134-11 


88 


276-46 


6082-12 


138 


433-54 


14957-12 


39 


122-52 


1194-59 


89 


279-60 


6221-14 


139 


436-68 


15174-68 


40 


125-66 


1256-64 


90 


282-74 


6361-73 


140 


439-82 


15393-80 


41 


128-80 


1320-25 


91 


285-88 


6503-88 


141 


442-96 


15614-50 


42 


131-95 


1385-44 


92 


289-03 


6647-61 


142 


446-11 


15836-77 


43 


135-09 


1452-20 


93 


292-17 


6792-91 


143 


449-25 


16060-61 


44 


138-23 


1520-53 


94 


295-31 


6939-78 


144 


452-39 


16286-02 


45 


141-37 


1590-43 


95 


298-45 


7088-22 


145 


455-53 


16513-00 


46 


144-51 


1661-90 


96 


301-59 


7238-23 


146 


458-67 


16741-55 


47 


147-65 


1734-94 


97 


304-73 


7389-81 


147 


461-81 


16971-67 


48 


150-80 


1809-56 


98 


307-88 


7542-96 


148 


464-96 


17203-36 


49 


153-94 


1885-74 


99 


311-02 


7697-69. 


149 


468-10 


17436-62 


50 


157-08 


19,63-50 


100 


314-16 


7853-98 


150 


471-24 


17671-46 



APPENDIX. 317 

TABLE OF DIAMETERS, CIRCUMFERENCES, AND AREAS OF CIRCLES. 



Diam- 


Circum- 


Circular 


Diam- 


Circum- 


Circular 


Diam- 


Circum- 


Circular 


eter. 


ference. 


area. 


eter. 


ference. 


area. 


eter. 


ference. 


area. 


151 


474-38 


17907-86 


201 


631-46 


31730-87 


251 


788-54 


49480-87 


153 


477-52 


18145-84 


202 


634-60 


32047-39 


252 


791-68 


49875-92 


153 


480-66 


18385-39 


203 


637-74 


32365-47 


253 


794-82 


50272-55 


154 


483-80 


18626-50 


204 


640-88 


32685-13 


'254 


797-96 


50670-75 


155 


486-95 


18869-19 


205 


644-03 


33006-36 


255 


801-11 


51070-52 


156 


490-09 


19113-45 


206 


647-17 


33329-16 


256 


804-25 


51471-86 


157 


493-23 


19359-28 


207 


650-31 


33653-53 


257 


807-39 


51874-76 


158 


496-37 


19606-68 


1 208 


653-45 


33979-47 


258 


810-53 


52279-24 


159 


499-51 


19855-65 


i 209 


656-59 


34306-98 


259 


813-67 


52685-29 


160 


502-65 


20106-19 


' 210 

i 


659-73 


34636-06 


260 


816-81 


53092-96 


161 


505-80 


20358-34 


1 211 


662-88 


34966-71 


261 


819-96 


53502-11 


162 


508-94 


20611-99 


212 


666-02 


35298-94 


262 


823-10 


53912-87 


163 


512-08 


20867-24 


213 


069-16 


35632-73 


263 


826-24 


54325-21 


164 


515-22 


21124-07 


214 


672-30 


35968-09 


264 


829-38 


54739-11 


165 


518-36 


21382-46 


! 215 

1 


675-44 


36305-03 


265 


832-52 


55154-59 


166 


521-50 


21642-43 


216 


678-58 


36643-61 


266 


835-66 


55571-63 


167 


524-65 


21903-97 


217 


681-73 


36983-61 


267 


838-80 


55990-25 


168 


527-79 


22167-08 


218 


684-87 


37325-26 


268 


841-95 


56410-44 


169 


530-93 


22431-76 


219 


688-01 


37668-48 


269 


845-09 


56832-20 


170 


534-07 


22698-01 


220 


691-15 


38013-27 


270 


848-23 


57255-53 


171 


537-21 


22965-83 


221 


694-29 


38359-63 


271 


851-37 


57680-43 


172 


540-35 


23235-22 


222 


697-43 


38707-56 


272 


854-51 


58106-90 


173 


543-50 


23506-18 


223 


700-57 


39057-07 


273 


857-65 


58534-94 


174 


546-64 


23778-71 


224 


703-72 


39408-14 


274 


860-80 


58964-55 


175 


549-78 


24052-82 


i 225 


706-86 


39760-78 


275 


863-94 


59395-74 


176 


552-92 


24328-49 


226 


710-00 


40115-00 


276 


867-08 


59828-49 


177 


556-06 


24605-79 


227 


713-14 


40470-78 


277 


870-22 


60262-82 


178 


559-20 


24884-56 


228 


716-28 


40828-14 


278 


873-36 


60698-72 


179 


562-34 


25164-94 


229 


719-42 


41187-07 


279 


876-50 


61136-18 


180 


565-49 


25446-90 


230 


722-57 


41547-56 


280 


879-65 


61575-22 


181 


568-63 


25730-43 


231 


725-71 


41909-63 


281 


882-79 


62015-82 


182 


571-77 


26015-53 


232 


728-85 


42273-27 


282 


885-93 


62458-00 


183 


574-91 


26302-20 


233 


731-99 


42638-48 


283 


889-07 


62901-75 


184 


578-05 


26590-44 


234 


735 13 


43005-26 


284 


892-21 


63347-07 


185 


581-19 


26880-25 


235 


738-27 


43373-61 


285 


895-35 


63793-97 


186 


584-34 


27171-63 


236 


741-42 


43743-54 


286 


898-49 


64242-43 


187 


587-48 


27464-59 


237 


744-56 


44115-03 


287 


901-64 


64692-46 


188 


590-62 


27759-11 


238 


747-70 


44488-09 


288 


904-78 


65144-07 


189 


593-76 


28055-21 


239 


750-84 


44862-73 


289 


907-92 


65597-24 


190 


596-90 


28352-87 


240 


753-98 


45238-93 


290 


911-06 


66051-99 


191 


600-04 


28652-11 


j 241 


757-12 


45616-71 


291 


914-20 


66508-30 


192 


603-19 


28952-92 


242 


760-26 


45996-06 


292 


917-34 


66966-19 


193 


606-33 


29255-30 


243 


763-41 


46376-98 


293 


920-49 


67425-65 


194 


609-47 


29559-26 


244 


766-55 


46759-47 


294 


923-63 


67886-68 


195 


612-61 


29864-77 


245 


769-69 


47143-52 


295 


926-77 


68349-28 


196 


615-75 


30171-86 


246 


772-88 


47529-16 


296 


929-91 


68813-45 


197 


618-89 


30480-52 


247 


775-97 


47916-36 


297 


933-05 


69279-19 


198 


622-03 


30790-75 ' 


248 


779-11 


48305-13 ! 


298 


936-19 


69746-50 


199 


625-18 


31102-55 


249 


782-26 


48695-47 1 


299 


939-34 


70215-38 


200 


628-32 


31415-93 , 


250 


785-40 


49087-39 j 


300 


942-48 


70685-83 



53 



818 APPENDIX. 

TABLE OF DIAMETERS, CIRCUMFERENCES, AND AREAS OF CIRCLES. 



Diam- 


Circum- 


Circular 


Diam- 


Circum- 


Circular 


Diam- 


Circum- 


Circular 


eter. 


ference. 


area. 


eter. 


ference. 


area. 


eter. 


ference. 


area. 


301 


945-62 


71157-86 


351 


1102-70 


96761-84 


401 


1259-78 


126292-81 


302 


948-76 


71631-45 


352 


1105-84 


97314-76 


402 


1262-92 


126923-48 


303 


951-90 


72106-62 


353 


1108-98 


97867-68 


403 


1266-06 


127553-73 


304 


955-04 


72583-36 


354 


1112-12 


98422-96 


404 


1269-20 


128189-55 


305 


958-19 


73061-66 


355 


1115-26 


98979-80 


405 


1272-34 


128824-93 


306 


961-33 


73541-54 


356 


1118-41 


99538-22 


406 


1275-49 


129461-89 


307 


964-47 


74022-99 


357 


1121-55 


100098-21 


407 


1278-63 


130100-42 


308 


967-61 


74506-01 


358 


1124-69 


100659-27 


408 


1281-77 


130740-52 


309 


970-75 


74990-60 


359 


1127-83 


101222-90 


409 


1284-91 


131382-19 


310 


973-89 


75476-76 


360 


1130-97 


101787-60 


410 


1288-05 


132025-43 


311 


977-03 


75964-50 


361 


1134-11 


102353-87 


411 


1291-19 


132670-24 


313 


980-18 


76453-80 


362 


1137-26 


102921-72 


412 


1294-34 


133316-63 


313 


983-32 


76944-67 


363 


1140-40 


103491-13 


413 


1297-48 


133964-58 


314 


986-46 


77437-12 


364 


1143-54 


104062-12 


414 


1300-62 


134614-10 


315 


989-60 


77931-13 


365 


1146-68 


104634-67 


415 


1303-76 


135265-20 


316 


992-74 


78426-72 


366 


1149-82 


105208-80 


416 


1306-90 


135917-86 


317 


995-88 


78923-88 


367 


1152-96 


105784-49 


417 


1310-04 


136572-10 


318 


999-03 


79422-60 


368 


1156-11 


106361-76 


418 


1313-19 


137227-91 


319 


1002-17 


79922-90 


369 


1159-25 


106940-60 


419 


1316-33 


137885-29 


320 


1005-31 


80424-77 


370 


1162-39 


107521-01 


420 


1319-47 


138544-24 


321 


1008-45 


80928-21 


371 


1165-53 


1081^2-99 


421 


1322-61 


139204-70 


322 


1011-59 


81433-22 


372 


1168-67 


108686-54 1 


422 


le325-75 


139866-85 


323 


1014-73 


81939-80 


373 


1171-81 


109271-66 


423 


1328-89 


140530-51 


324 


1017-88 


82447-96 


374 


1174-96 


109858-35 


424 


1332-03 


141195-74 


325 


1021-02 


82957-68 


375 


1178-10 


110446-62 


425 


1335-18 


141862-54 


326 


1024-16 


83468-98 


376 


1181-24 


111036-45 


426 


1338-32 


142530-92 


327 


1027-30 


83981-84 


377 


1184-38 


111627-86 


427 


1341-46 


143200-86 


328 


1030-44 


84496-28 


378 


1187-52 


112220-83 


428 


1344-60 


143872-38 


329 


1033-58 


85012-28 


379 


1190-66 


112815-38 


429 


1347-74 


144545-46 


330 


1036-73 


85529-86 


380 


1193-80 


113411-49 


430 


1350-88 


145220-12 


331 


1039-87 


86049-01 


381 


1196-95 


114009-18 


431 


1354-03 


145896-35 


332 


1043-01 


86569-73 


382 


1200-09 


114608-44 


432 


1357-17 


146574-15 


333 


1046-15 


87092-02 


383 


1203-23 


115209-27 


433 


1360-31 


147253-52 


334 


1049-29 


87615-88 


384 


1206-37 


115811-67 


434 


1363-45 


147934-46 


335 


1052-43 


88141-31 


385 


1209-51 


116415-64 


435 


1366-59 


148616-97 


336 


1055-57 


88668-31 


386 


1212-65 


117021-18 


436 


1369-73 


149301-05 


337 


1058-72 


89196-88 


387 


1215-80 


117628-30 ! 


437 


1372-88 


149986-70 


338 


1061-86 


89727-03 


388 


1218-94 


118236-98 1 


438 


1376-02 


150673-93 


339 


1065-00 


90258-74 


389 


1222-08 


118847-24 1 


439 


1379-16 


151362-72 


340 


1068-14 


90792-03 


390 


1225-22 


119459-06 


440 


1382-30 


152053-08 


341 


1071-28 


91326-88 


391 


1228-36 


120072-46 


441 


1385-44 


152745-02 


342 


1074-42 


91863-31 


392 


1231-50 


120687-42 


442 


1388-58 


153438-53 


343 


1077-57 


92401-31 


393 


1234-65 


121303-96 


443 


1391-73 


154133-60 


344 


1080-71 


92940-88 


394 


1237-79 


121922-07 


444 


1394-87 


154830-25 


345 


1083-85 


93482-02 


395 


1240-93 


122541-75 i 

I 


445 


1398-01 


155528-47 


346 


1086-99 


94024-73 


396 


1244-07 


123163-00 ! 


446 


1401-15 


156228-26 


347 


1090-13 


94569-01 


397 


1247-21 


123785-82 | 


447 


1404-29 


156929-62 


348 


1093-27 


95114-86 


398 


1250-35 


124410-21 


448 


1407-43 


157632-55 


349 


1096-42 


95662-28 


399 


1253-49 


125036-17 


449 


1410 57 


158337-06 


350 


1099-56 


96211-28 


400 


1256-64 

1 


125063-71 


450 


1413-72 


159043-13 



APPENDIX. 819 

TABLE OF DIAMETERS, CIRCUMFERENCES, AND AREAS OF CIRCLES. 



Diam- 


Circum- 


Circular 


Diam- 


Circum- 


Circular 


Diam- 


Circum- 


Circular 


eter. 


ference. 


area. 


- eter. 


ference. 


area. 


eter. 


ference. 


area. 


45r 


1416-86 


159750-77 


! 501 


1573-94 


197135-72 


551 


1731-02 


238447-67 


452 


1420-00 


160459-99 


! 502 


1577-08 


197923-48 


552 


1734-16 


239313-96 


453 


1423-14 


161170-77 


1 503 


1580-22 


198712-80 


553 


1737-30 


240181-83 


454 


1426-28 


161883 13 


504 


1583-36 


199503-70 


554 


1740-44 


241051-26 


455 


1429-42 


162597-06 


505 


1586-50 


200296-17 


555 


1743-58 


241922-27 


456 


1432-57 


163312-55 


506 


1589-65 


201090-20 


556 


1746-73 


242794-85 


457 


1435-71 


164029-62 


507 


1592-79 


201885-81 


557 


1749-87 


243668-99 


458 


1438-85 


164748-26 


508 


1595-93 


202682-99 


558 


1753-00 


244544-61 


459 


1441-99 


165468-47 


i 509 


1599-07 


203481-74 


559 


1756-15 


245422-00 


460 


1445-13 


166190-25 


1 510 


1602-21 


204282-06 


560 


1759-29 


246300-86 


461 


1448-27 


166913-60 


511 


1605-35 


205083-95 


561 


1762-43 


247181-30 


463 


1451-42 


167638-53 


512 


1608-49 


205887-42 


562 


1765-57 


248062-30 


463 


1454-56 


168365-02 


513 


1611-64 


206692-45 


563 


1768-72 


248946-87 


464 


1457-70 


169093-08 


514 


1614-78 


207499-05 


564 


1771-86 


249832-01 


465 


1460-84 


169822-72 


515 


1617-92 


208307-23 


565 


1775-00 


250718-73 


466 


1463-98 


170553-92 


516 


1621-06 


209116-97 


566 


1778-14 


251607-01 


467 


1467-12 


171286-70 


517 


1624-20 


209928-29 


567 


1781-28 


252496-87 


•468 


1470-26 


172021-05 


518 


1627-34 


210741-18 


568 


1784-42 


253388-30 


469 


1473-41 


172756-97 


519 


1630-49 


211555-63 


569 


1787-57 


254281-30 


470 


1476-55 


173494-45 


520 


1633-63 


212371-66 


570 


1790-71 


255175-86 


471 


1479-69 


174233-51 


521 


1636-77 


213189-26 


571 


1793-85 


256072-00 


472 


1482-83 


174974-14 


522 


1639-91 


214008-43 


572 


1796-99 


256969-71 


473 


1485-97 


175716-35 


523 


1643-05 


214829-17 


573 


1800-13 


257868-99 


474 


1489-11 


176460-12 


524 


1646-19 


215651-49 


574 


1803-27 


258769-85 


475 


1492-26 


177205-46 


525 


1649-34 


216475-37 


575 


1806-42 


259672-27 


476 


1495-40 


177952-37 


526 


1652-48 


217300-82 


576 


1809-56 


260576-26 


477 


1498-54 


178700-86 


527 


1655-62 


218127-85 


577 


1812-70 


261481-83 


478 


1501-68 


179450-91 


528 


1658-76 


218956-44 


578 


1815-84 


262388-96 


479 


1504-82 


180202-54 


1 529 


1661-90 


219786-61 


579 


1818-98 


263297-67 


480 


1507-96 


180955-74 


530 


1665-04 


220618-32 


580 


1822-12 


264207-94 


481 


1511-11 


181710-50 


531 


1668-19 


221451-65 


581 


1825-26 


265119-79 


482 


1514-25 


182466-84 


532 


1671-33 


222286-53 


582 


1828-41 


266033-21 


483 


1517-39 


183224-75 


533 


1674-47 


223122-98 


583 


1831-55 


266948-20 


484 


1520-53 


183984-23 


534 


1677-61 


223961-00 


584 


1834-69 


267864-76 


485 


1523-67 


184745-28 


535 


1680-75 


224800-59 


585 


1837-83 


268782-80 


486 


1526-81 


185507-90 


536 


1683-89 


225641-75 


586 


1840-97 


269702-59 


487 


1529-96 


186272-10 


537 


1687-04 


226484-48 


587 


1844-11 


270623-86 


488 


1533-10 


187037-86 


538 


1690-18 


227328-77 


588 


1847-26 


271546-70 


489 


1536-24 


187805-19 


539 


1693-32 


228174-66 


589 


1850-40 


272471-12 


490 


1539-38 


188574-10 


540 


1696-46 


229022-10 


590 


1853-54 


273397-10 


491 


1542-52 


189344-57 j 


541 


1699-60 


229871-12 


591 


1856-68 


274324-66 


492 


1545-66 


190116-62 1 


542 


1702-74 


230721-71 ! 


592 


1859-82 


275253-78 


493 


1548-80 


190890-24 


543 


1705-88 


231573-86 


593 


1862-96 


276184-48 


494 


1551-95 


191665-43 


544 


1709-03 


232427-59 


594 


1866-11 


277116-75 


495 


1555-09 


192442-19 


545 


1712-17 


233282-89 

1 


595 


1869-25 


278050-59 


496 


1558-23 


193220-51 


546 


1715-31 


1 
234139-76 


596 


1872-39 


278985-99 


497 


1561-37 


194000-42 


547 


1718-45 


234998-20 ! 


597 


1875-53 


279922-97 


498 


1564-51 


194781-89 i 


548 


1721-59 


235858-21 


598 


1878-67 


280861-53 


499 


1567-05 


195564-93 i 


549 


1724-73 


236719-79 


599 


1881-81 


281801-65 


500 


1570-80 


196349-54 


550 


1727-88 


237582-94 


600 


1884-96 


282743-34 



820 



APPENDIX. 



TABLE OF SQUARES, CUBES, SQUAEE AND CUBE EOOTS OF NUMBERS. 



Squares. 


Cubes. 


No. 


Square 
roots. 


Cube 
roots. 

■ 


! 
Squares. 


Cubes. 


No. 


1 Square 
roots. 


Cube 
roots. 


1 


1 


1 


1-000 


1-000 


4096 


262144 


64 


8-000 


4-000 


4 


1 8 


2 


1-414 


1-259 


4225 


274625 


65 


8'062 


4-020 


9 


1 27 


3 


1-732 


1-442 


1 4356 


287496 


66 


8-124 


4-041 


16 


! 64 


4 


2-000 


1-587 


1 4489 


300763 


67 


8-185 


4-061 


25 


1 125 


5 


2-236 


1-709 


4624 


314432 


68 


8-246 


4-081 


36 


216 


6 


2-449 


1-817 


4761 


328509 


69 


8-306 


4-101 


49 


343 


7 


2-645 


1-912 


4900 


343000 


70 


8-366 


4-121 


64 


512 


■ 8 


2-828 


2-000 


5041 


357911 


71 


8-426 


4-140 


81 


729 


9 


3-000 


2-080 


5184 


373248 


72 


8-485 


4-160 


100 


1000 


10 


3-162 


2-154 


5329 


389017 


73 


8-544 


4-179 


121 


1331 


11 


3-316 


2-223 


5476 


405224 


74 


8-602 


4-198 


144 


1728 


12 


3-464 


2-289 


5625 


421875 


75 


8-660 


4-217 


169 


2197 


13 


3-605 


2-351 


5776 


438976 


76 


8-717 


4-235 


196 


2744 


14 


3-741 


2-410 


5929 


456533 


77 


8-774 


4-254 


225 


3375 


15 


3-872 


2-466 


6084 


474552 


78 


8-831 


4-272 


256 


4096 


16 


4-000 


2-519 


6241 


493039 


79 


8-888 


4-290 


289 


4913 


17 


4-123 


2-571 


6400 


512000 


80 


8-944 


4-308 


324 


5832 


18 


4-242 


2-620 


6561 


531441 


81 


9-000 


4-326 


361 


6859 


19 


4-358 


2-668 


6724 


551368 


82 


9-055 


4-344 


400 


8000 


20 


4-472 


2-714 


6889 


571787 


83 


9-110 


4-362 


441 


9261 


21 


4-582 


2-758 


7056 


592704 


84 


9-165 


4-379 


484 


10648 


22 


4-690 


2-802 


7225 


614125 


85 


9-219 


4-396 


529 


12167 


23 


4-795 


2-843 


7396 


636056 


86 


9-273 


4-414 


576 


13824 


24 


4-898 


2-884 


7569 


658503 


87 


9-327 


4-431 


625 


15625 


25 


5-000 


2-924 


7744 


681472 


88 


9-380 


4-447 


676 


17576 


26 


5-099 


2-962 


7921 


704969 


89 


9-433 


4-464 


729 


19683 


27 


5-196 


3-000 


8100 


729000 


90 


9-486 


4-481 


784 


21952 


28 


5-291 


3-036 


8281 


753571 


91 


9-539 


4 497 


841 


24389 


29 


5-385 


3-072 


8464 


778688 


92 


9-591 


4-514 


900 


27000 


30 


5-477 


3-107 


8649 


804357 


93 


9-643 


4-530 


961 


29791 


31 


5-567 


3-141 


8836 


830584 


94 


9-695 


4-546 


1024 


32768 


32 


5-656 


3=174 


9025 


857374 


95 


9-746 


4-562 


1089 


35937 


33 


5-744 


3-207 


9216 


884736 


96 


9-797 


4-578 


1156 


393U4 


34 


5-830 


3-239 


9409 


912673 


97 


9-848 


4-594 


1225 


42875 


35 


5-916 


3-271 


9604 


941192 


98 


9-899 


4-610 


1296 


46656 


36 


6-000 


3-301 


9801 


970299 


99 


9-949 


4-626 


1369 


50653 


37 


6-082 


3-332 


10000 


1000000 


100 


10-000 


4-641 


1444 


54872 


38 


6-164 


3-361 


10201 


1030301 


101 


10-049 


4-657 


1521 


59319 


39 


6-244 


3-391 


10404 


1061208 


102 


10-099 


4-672 


1600 


64000 


40 


6-324 


3-419 


10609 


1092727 


103 


10-148 


4-687 


1681 


68921 


41 


6-403 


3-448 


10816 


1124864 


104 


10-198 


4-702 


1764 


74088 


42 


6-480 


3-476 


11025 


1157625 


105 


10-246 


4-717 


1849 


79507 


43 


6-557 


3-503 


11236 


1191016 


106 


10-295 


4-732 


1936 


85184 


44 


6-633 


3-530 


11449 


1225043 


107 


10-344 


4-747 


2025 


91125 


45 


6-708 


3-556 


11664 


1259712 


108 


10-392 


4-762 


2116 


97336 


46 


6-782 


3-583 


11881 


1295029 


109 


10-440 


4-776 


2209 


103823 


47 


6-855 


3-608 


12100 


1331000 


110 


10-488 


4-791 


2304 


110592 


48 


6-928 


3-634 


12321 


1367631 


111 


10-535 


4-805 


2401 


117649 


49 


7-000 


3-659 


12544 


1404928 


112 


10-583 


4-820 


2500 


125000 


50 


7071 


3-684 


12769 


1442897 


113 


10-630 


4-834 


2601 


132651 


51 


7-141 


3-708 


12996 


1481544 


114 


10-677 


4-848 


2704 


140608 


52 


7-211 


3-732- 


13225 


1520875 


115 


10-723 


4-862 


2809 


148877 


53 


7-280 


3-756 


13456 


1560896 


116 


10-770 


4-876 


2916 


157464 


54 


7-348 


3-779 


13689 


1601613 


117 


10-816 


4-890 


3025 


166375 


55 


7-416 


8-802 


13924 


1643032 


118 


10-862 


4-904 


3136 


175616 


56 


7-4S3 


3-825 


14161 


1685159 


119 


10-908 


4-918 


3249 


185193 


57 


7-549 


3-848 


14400 


1728000 


120 


10-954 


4-932 


3364 


195112 


58 


7-615 


3-870 


14641 


1771561 


121 


11-000 


4-946 


3481 


205379 


59 


7-681 


3-892 


14834 


1815848 


122 


11-045 


4-959 


3600 


216000 


60 


7-745 


3-914 


15129 


1860867 


123 


11-090 


4-973 


3721 


226981 


61 


7-810 


3-930 1 


15376 


1906624 


124 


11-135 


4-986 


3844 


238328 


62 


7-874 


3-957 ! 


15625 


1953125 


125 


11-180 


5-000 


3969 


250047 


63 


7-937 


3-979 i 


15876 


2000376 


126 


11-224 


5-013 



APPENDIX. 



821 



TABLE OF SQUAEES, CUBES, SQUARE AND CUBE EOOTS OF ^VMB^^^— (Continued). 



Squares. 


Cubes. 


No. 


Square 
roots. 


Cube 
roots. 


Squares. 


Cubes. 


No. 


Square 
roots. 


Cube 
roots. 


16129 


2048383 


127 


11-269 


5-026 


36100 


6859000 


190 


13-784 


5-748 


16384 


2097152 


128 


11-313 


5-039 


36481 


6967871 


191 


13-820 


5-758 


16641 


2146689 


129 


11-357 


5-052 


36864 


7077888 


192 


13-856 


5-768 


16900 


2197000 


130 


11-401 


5-065 


37249 


7189517 


193 


13-892 


5-778 


17161 


2248091 


131 


11-445 


5-078 


37636 


7301384 


194 


13-928 


5-788 


17424 


2299968 


132 


11-489 


5-091 


38025 


7414875 


195 


13-964 


6-798 


17689 


2352637 


133 


11-532 


5-104 


38416 


7529536 


196 


14-000 


6-808 


17956 


2406104 


134 


11-575 


5-117 


38809 


7645373 


197 


14-035 


5-818 


18225 


2460375 


135 


11-618 


5-129 


39204 


7762392 


198 


14-071 


5-828 


18496 


2515456 


136 


11-661 


5-142 


39601 


7880599 


199 


14-106 


5-838 


18769 


2571353 


137 


11-704 


5-155 


40000 


8000000 


200 


14-142 


5-848 


19044 


2628072 


138 


11-747 


5-167 


40401 


8120601 


201 


14177 


5-857 


19321 


2685619 


139 


11-789 


5-180 


1 40804 


8242408 


202 


14-212 


5-867 


19600 


2744000 


140 


11-832 


5-192 


41209 


8365427 


203 


14-247 


5-877 


19881 


2803221 


141 


11-874 


5-204 


41616 


8489664 


204 


14-282 


5-886 


20164 


2863288 


142 


11-916 


5-217 


42025 


8615125 


205 


14-317 


5-896 


20449 


2924207 


143 


11-958 


5-229 


42436 


8741816 


206 


14-352 


5-905 


20736 


2985984 


144 


12-000 


5-241 


42849 


8869743 


207 


14-387 


5-915 


21025 


3048625 


145 


12-041 


5-253 


43264 


8998912 


208 


14-422 


5-924 


21316 


3112136 


146 


12-083 


5-265 


43681 


9129329 


209 


14-456 


5-934 


21609 


3176523 


147 


12-124 


5-277 


44100 


9261000 


210 


14-491 


5-943 


21904 


3241792 


148 


12-165 


5-289 


44521 


9393931 


211 


14-525 


5-953 


22201 


3307949 


149 


12-206 


5-301 


44944 


9528128 


212 


14-560 


5-962 


22500 


3375000 


150 


12-247 


5-313 


45369 


9663597 


213 


14-594 


5-972 


22801 


3442951 


151 


12-288 


5-325 


45796 


9800344 


214 


14-628 


5-981 


23104 


3511008 


152 


12-328 


5-336 


46225 


9938375 


215 


14-662 


5-990 


23409 


3581577 


153 


12-369 


5-348 


46656 


10077696 


216 


14-696 


6-000 


23716 


3652264 


154 


12-409 


5-360 


47089 


10218312 


217 


14-730 


6-009 


24025 


3723875 


155 


12-449 


5-371 


47524 


10360232 


218 


14-764 


6-018 


24336 


3796416 


156 


12-489 


5-383 


47961 


10503459 


219 


14-798 


6-027 


24649 


3869893 


157 


12-5-29 


5-394 


48400 


10648000 


220 


14-832 


6-036 


24964 


3944312 


158 


12-569 


5-406 


48841 


10793861 


221 


14-866 


6-045 


25281 


4019679 


159 


12-609 


5-417 


49284 


10941048 


222 


14-899 


6-055 


25600 


4096000 


160 


12-649 


5-428 


49729 


11089567 


223 


14-933 


6-064 


25921 


4173281 


161 


12-688 


5-.440 


50176 


11239424 


224 


14-966 


6-073 


26244 


4251528 


162 


12-727 


5-451 


50625 


11390625 


225 


15-000 


6-082 


26569 


4330747 


163 


12-767 


5-462 


51076 


11543176 


226 


15-033 


6-099 


26896 


4410944 


164 


12-806 


5-473 1 


51529 


11697083 


227 


15-066 


6-100 


27225 


4492125 


165 


12-845 


5-484 


51984 


1185'2352 


228 


15-099 


6-109 


27556 


4574296 


166 


12-884 


5-495 


52441 


12008989 


229 


15-132 


6-118 


27889 


4657463 


167 


12-922 


5-506 


52900 


12167000 


230 


15-165 


6-126 


28224 


4741632 


168 


12-961 


5-517 


53361 


12326391 


231 


15-198- 


6-135 


28561 


4826809 


169 


13-000 


5-528 


53824 


12487168 


232 


15-231 


6-144 


28900 


4913000 


170 


13-938 


5-539 


54289 


12649337 


233 


15-264 


6-153 


29241 


5000211 


171 


13-076 


5-550 


54756 


12812904 


234 


15-297 


6-162 


29584 


5088448 


172 


13114 


5-561 


55225 


12977875 


235 


15-329 


6-171 


29929 


5177717 


173 


13-152 


5-572 


55696 


13144256 


236 


15-362 


6-179 


30276 


5268024 


174 


13-190 


5-582 


56169 


13312053 


237 


15-394 


6-188 


30625 


5359375 


175 


13-228 


5-593 


56644 


13481272 


238 


15-427 


6-197 


30976 


5451776 


176 


13-266 


5-604 


57121 


13651919 


239 


15-459 


6-205 


31329 


5545233 


177 


13-304 


5-614 


57600 


13824000 


240 


15-491 


6-214 


31684 


5639752 


178 


13-341 


5-625 


58081 


13997521 


241 


15-524 


6-223 


32041 


5735339 


179 


13-379 


5-635 


58564 


1417-2488 


242 


15-556 


6-231 


32400 


58S2000 


180 


13-416 


5-646 


59049 


14348907 


243 


15-588 


6-240 


32761 


5929741 


181 


13-453 


5-656 


59536 


14526784 


244 


15-620 


6-248 


33124 


6028568 


182 


13-490 


5-667 


60025 


14706125 


245 


15-652 


6-257 


33489 


6128487 


183 


13-527 


5-677 


60516 


14886936 


246 


15-684 


6-265 


33856 


6229504 


184 


13-664 


5-687 


61009 


15069223 


247 


15-716 


6-274 


34225 


6331625 


185 


13-601 


5-698 


61504 


15252992 


248 


15-748 


6-282 


34596 


6434856 


186 


13-638 


5-708 


62001 


15438249 


249 


15-779 


6-291 


34969 


6539203 


187 


13-674 


5-718 


62500 


15625000 


250 


15-811 


6-299 


35344 


6644672 


188 


13-711 


5-728 


63001 


15813251 


251 


15-842 


6-307 


35721 


6751269 


189 


13-747 


5-738 


63504 


16003008 


252 


15-874 


6-316 



822 



APPENDIX. 



TABLE OF SQUARES, CUBES, SQUAEE AND CUBE ROOTS OF l^UMBEH^— (Continued) 



Squares. 


Cubes. 


No. 


Square 
roots. 


Cube 
roots. 


Squares. 


Cubes. 


No. 


1 

Square 
roots. 


Cube 
roots. 


64009 


16194277 


253 


15-905 


6-324 


99856 


31554496 


316 


17-776 


6-811 


64516 


16387064 


254 


15-937 


6-333 


100489 


31855013 


317 


17-804 


6-818 


65025 


16581375 


255 


15-968 


6-341 


101124 


32157432 


318 


17-832 


6-825 


65536 


16777216 


256 


16-000 


6-349 


101761 


32461759 


319 


17-860 


6-832 


66049 


16974593 


257 


16-031 


6-357 


102400 


32768000 


320 


17-888 


6-839 


66564 


17173512 


258 


16-062 


6-366 


103041 


33076161 


821 


17-916 


6-847 


67081 


17373979 


259 


16 093 


6-374 


103684 


33386248 


322 


17-944 


6-854 


6T600 


17576000 


260 


16-124 


6-382 


1 104329 


33698267 


323 


17-972 


6-861 


68121 


17779581 


261 


16-155 


6-390 


104976 


34012224 


324 


18-000 


6-868 


68644 


17984728 


262 


16-186 


6-398 


105625 


34328125 


325 


18-027 


6-875 


69169 


18191447 


263 


16-217 


6-406 


106276 


34645976 


326 


18-055 


6-882 


69696 


18399744 


264 


16-248 


6-415 


106929 


34965783 


327 


18-083 


6-889 


70225 


18609625 


265 


16-278 


6-423 


107584 


35287552 


328 


18-110 


6-896 


70756 


18821096 


266 


16-309 


6-431 


108241 


35611289 


329 


18-138 


6-903 


71289 


19034163 


267 


16-340 


6-439 


108900 


35937000 


330 


18-165 


6-910 


71824 


19248832 


268 


16-370 


6-447 


109561 


36264691 


331 


18-193 


6-917 


72361 


19465109 


269 


16-401 


6-455 


110224 


36594368 


332 


18-220 


6-924 


72900 


19683000 


270 


16-431 


6-463 


110889 


36926037 


333 


18-248 


6-931 


73441 


19902511 


271 


16-462 


6-471 


111556 


37259704 


334 


18-275 


6-938 


73984 


20123643 


272 


16-492 


6-479 


112225 


37595375 


335 


18-303 


6-945 


74529 


20346417 


273 


16-522 


6-487 


112896 


37933056 


336 


18-330 


6-952 


75076 


20570824 


274 


16-552 


6-495 


113569 


38272753 


337 


18-357 


6-958 


75625 


20796875 


275 


16-583 


6-502 


114244 


38614472 


388 


18-384 


6-965 


76176 


21024576 


276 


16-613 


6-510 


114921 


38958219 


339 


18-411 


6-972 


76729 


21253933 


277 


16-643 


6-518 


115600 


^9304000 


340 


18-439 


6-979 


77284 


21484952 


278 


16-678 


6-526 


116281 


89651821 


341 


18-466 


6-986 


77841 


21717639 


279 


16-703 


6-534 


116964 


40001688 


342 


18-493 


6-993 


78400 


21952000 


280 


16-733 


6-542 


117649 


40353607 


343 


18-520 


7-000 


78961 


22188041 


281 


16-763 


6-549 


118336 


40707584 


344 


18-547 


7-006 ' 


79524 


22425768 


282 


16-792 


6-557 


119025 


41063625 


345 


18-574 


7-013 


800S9 


22665187 


283 


16-822 


6-565 


119716 


41421736 


346 


18-601 


7020 


80656 


22906304 


284 


16-852 


6-573 


120409 


41781923 


347 


18-627 


7-027 


81225 


23149125 


285 


16-881 


6-580 


121104 


42144192 


348 


18-654 


7-033 


81796 


23393656 


286 


16-911 


6-588 


121801 


42508549 


349 


18-681 


7-040 


82369 


23639903 


287 


16-941 


6-596 


122500 


42875000 


350 


18-708 


7-047 


82944 


23887872 


288 


16-970 


6-603 


123201 


43243551 


351 


18-734 


7-054 


83521 


24137569 


289 


17-000 


6-611 


123904 


43614208 


352 


18-761 


7-060 


84100 


24389000 


290 


17-029 


6-619 


124609 


43986977 


353 


18-788 


7-067 


84681 


24642171 


291 


17-058 


6-626 


125316 


44361864 


354 


18-814 


7-074 


85264 


24897088 


292 


17-088 


6-634 


126025 


44738875 


355 


18-841 


7-080 


85849 


25153757 


,293 


17-117 


6-641 


126736 


45118016 


356 


18-867 


7-087 


86436 


25412184 


294 


17-146 


6-649 


127449 


45499293 


357 


18-894 


7-093 


87025 


25672375 


295 


17-175 


6-656 


128164 


45882712 


358 


18-920 


7-100 


87616 


25934836 


296 


17-204 


6-664 


128881 


46268279 


359 


18-947 


7-107 


88209 


26198073 


297 


17-233 


6-671 


129600 


46656000 


360 


18-973 


7-113 


88804 


26463592 


298 


17-262 


6-679 


130321 


47045831 


361 


19-000 


7-120 


89401 


26730899 


299 


17-291 


6-686 


131044 


47437928 


362 


19-026 


7-126 


90000 


27000000 


300 


17-320 


6-694 


131769 


47832147 


363 


19-052 


7-133 


90601 


27270901 


301 


17-349 


6-701 


132496 


48228544 


364 


19-078 


7140 


91204 


27543608 


302 


17-378 


6-709 


133225 


48627125 


365 


19-104 


7146 


91809 


27818127 


303 


17-406 


6-716 


133956 


49027896 


366 


19131 


7-153 


92416 


28094464 


304 


17-435 


6-723 


134689 


49430863 


367 


19-167 


7-159 


93025 


28372625 


305 


17-464 


6-731 


135424 


49836032 


368 


19-183 


7-166 


93636 


28652616 


306 


17-492 


6-738 


136161 


50243409 


369 


19-209 


7-172 


94249 


28934443 


307 


17-521 


6-745 


136900 


50653000 


370 


19-235 


7179 


94864 


29218112 


308 


17-549 


6-753 


137641 


51064811 


371 


19-261 


7-185 


9.5481 


29503609 


309 


17-578 


6-760 


138384 


51478848 


372 


19-287 


7-191 


96100 


29791000 


310 


17-606 


6-767 


1391-29 


51895117 


373 


19-313 


7-198 


98721 


30080231 


311 


17-635 


6-775 


139876 


52313624 


374 


19-339 


7-204 


97344 


30371328 


312 


17-663 


6-782 


140625 


52734375 


375 


19-364 


7-211 


97969 


30664297 


313 


17-691 


6-789 


141376 


53157376 


376 


19-390 


7-217 


98596 


30959144 


314 


17-720 


6-796 


142129 


53582633 


377 


19-416 


7-224 


99225 


31255875 


315 


17-748 


6-804 


1 142884 


54010152 


378 


19-442 


7-230 



APPENDIX. 



823 



TABLE OF SQUAKES, CUBES, SQUARE AND CUBE ROOTS OF NUMBERS— ( Cbw^wwei). 



Squares. 


Cubes. 


No. 


Square 
roots. 


Cube 
roots. 


Squares. 


Cubes. 


No. 


Square 
roots. 


Cube 
roots. 


143641 


54439939 


379 


19-467 


7-236 


195364 


86350888 


442 


21-023 


7-617 


144400 


54872000 


380 


19-493 


7-243 


196249 


86938307 


443 


21-047 


7-623 


145161 


55306341 


381 


19-519 


7-249 


197136 


87528384 


444 


21-071 


7-628 


145924 


55742968 


382 


19-544 


7-255 


198025 


88121125 


445 


21-095 


7-634 


146689 


56181887 


383 


19-570 


7-262 


198916 


88716536 


446 


21-118 


7-640 


147456 


56623104 


384 


19-595 


7-268 


199809 


89314623 


447 


21-142 


7-646 


148225 


57066625 


385 


19621 


7-274 


200704 


89915392 


448 


21-166 


7-651 


148996 


57512456 


386 


19-646 


7-281 


201601 


90518849 


449 


21-189 


7-657 


149769 


57960603 


387 


19-672 


7-287 


202500 


91125000 


450 


21-213 


7-663 


150544 


58411072 


388 


19-697 


7-293 


203401 


91733851 


451 


21-236 


7-668 


151321 


68863869 


389 


19-723 


7-299 


204304 


92345408 


452 


21-260 


7-674 


152100 


59319000 


390 


19-748 


7-306 


205209 


92959677 


453 


21-283 


7-680 


152881 


59776471 


391 


19-773 


7-312 


206116 


93576664 


454 


21-307 


7-685 


153664 


60236288 


392 


19-798 


7-318 


207025 


94196375 


455 


21-330 


7-691 


154449 


60698457 


393 


19-824 


7-324 


207936 


94818816 


456 


21-354 


7-697 


155236 


61162984 


394 


19-849 


7-331 


208849 


95443993 


457 


21-377 


7-702 


156025 


61629875 


395 


19-874 


7-337 


209764 


96071912 


458 


21-400 


7-708 


156816 


62099136 


396 


19-899 


7-343 


210681 


96702579 


459 


21-424 


7-713 


157609 


62570773 


397 


19-924 


7-349 


211600 


97336000 


460 


21-447 


7-719 


158404 


63044792 


398 


19-949 


7-355 


212521 


97972181 


461 


21-470 


7-725 


159201 


63521199 


399 


19-974 


7-361 


213444 


98611128 


462 


21-494 


7-730 


160000 


64000000 


400 


20-000 


7-368 


214369 


99252847 


463 


21-517 


7-736 


160801 


64481201 


401 


20-024 


7-374 


215296 


99897344 


464 


21-540 


7-741 


161604 


64964808 


402 


20-049 


7-380 


216225 


100544625 


465 


21-563 


7-747 


162409 


65450827 


403 


20-074 


7-386 


217156 


101194696 


466 


21-587 


7-752 


163216 


65939264 


404 


20-099 


7-392 


218089 


101847563 


467 


21-610 


7-758 


164025 


66430125 


405 


20-124 


7-398 


219024 


102503232 


468 


21-633 


7-763 


164836 


66923416 


406 


20-149 


7-404 


219961 


103161709 


469 


21-656 


7-769 


165649 


67419143 


407 


20-174 


7-410 


220900 


103823000 


470 


21-679 


7-774 


166464 


67917312 


408 


20-199 


7-416 


221841 


104487111 


471 


21-702 


7-780 


167281 


68417929 


409 


20-223 


7-422 


222784 


105154048 


472 


21-725 


7-785 


168100 


68921000 


410 


20-248 


7-428 


223729 


105823817 


478 


21-748 


7-791 


168921 


69426531 


411 


20-273 


7-434 


224676 


106496424 


474 


21-771 


7-796 


169744 


69934528 


412 


20-297 


7-441 


225625 


107171875 


475 


21-794 


7-802 


170569 


70444997 


413 


20-322 


7-447 


226576 


107850176 


476 


21-817 


7-807 


171396 


70957944 


414 


20-346 


7-453 


227529 


108531333 


477 


21-840 


7-813 . 


172225 


71473375 


415 


20-371 


7-459 


228484 


109215352 


478 


21-863 


7-818 


173056 


71991296 


416 


20-396 


7-465 


229441 


109902239 


479 


21-886 


7-824 


173889 


72511713 


417 


20-420 


7-470 


230400 


110592000 


480 


21-908 


7-829 


174724 


73034632 


418 


20-445 


7-476 


231361 


111284641 


481 


21-931 


7-835 - 


175561 


73560059 


419 


20-469 


7-482 


232324 


111980168 


482 


21-954 


7-840 


176400 


74088000 


420 


20-493 


7-488 


233289 


112678587 


483 


21-977 


7-846 


177241 


74618461 


421 


20-518 


7-494 


234256 


113379904 


484 


22-000 


7-851 


178084 


75151448 


422 


20-542 


7-500 


235225 


114084125 


485 


22-022 


7-856 


178929 


75686967 


423 


20-566 


7-506 


236196 


114791256 


486 


22-045 


7-862 


179776 


76225024 


424 


20-591 


7-512 


237169 


115501303 


487 


22-068 


7-867 


180625 


76765625 


425 


20-615 


7-518 


238144 


116214272 


488 


22-090 


7-872 


181476 


77308776 


426 


20-639 


7-524 


239121 


116930169 


489 


22-113 


7-878 


182329 


77854483 


427 


20-663 


7-530 


240100 


117649000 


490 


22-135 


7-883 


183184 


78402752 


428 


20-688 


7-536 


241081 


118370771 


491 


22-158 


7-889 


184041 


78953589 


429 


20-712 


7-541 


242064 


119095488 


492 


22-181 


7-894 


184900 


79507000 


430 


20-736 


7-547 


243049 


119823157 


493 


22-203 


7-899 


185761 


80062991 


431 


20-760 


7-553 


244036 


120553784 


494 


22-226 


7-905 


186624 


80621568 


432 


20-784 


7-559 


245025 


121287375 


495 


22-248 


7-910 


187489 


81182737 


433 


20-808 


7-565 


246016 


122023936 


496 


22-271 


7-915 


188356 


81746504 


434 


20-832 


7-571 . 


247009 


122763473 


497 


22-293 


7-921 


189225 


82312875 


435 


20-856 


7-576 


248004 


128505992 


498 


22-315 


7-926 


190096 


82881856 


436 


20-880 


7-582 


249001 


124251499 


499 


22-338 


7-931 


190969 


83453453 


437 


20-904 


7-588 


250000 


125000000 


500 


22-360 


7-937 


191844 


84027672 


438 


20-928 


7-594 


251001 


125751501 


501 


22-383 


7-942 


192721 


84604519 


439 


20-952 


7-600 


252004 


126506008 


502 


22-405 


7-947 


193600 


85184000 


440 


20-976 


7-605 


253009 


127263527 


503 


22-427 


7-952 


194481 


85766121 


441 


21-000 


7-611 


254016 


128024064 


504 


22-449 


7-958 



824: 



APPENDIX. 



TABLE OF SQUARES, CUBES, SQUAEE AND CUBE EOOTS OF l^^TJKBEHQ— (Continued). 



Squares. 


Cubes. 


No. 


Square 
roots. 


Cube 
roots. 


Squares. 


Cubes. 


No. 


Square 
roots. 


Cube 
roots. 


255025 


128787625 


505 


22-472 


7-963 


322624 


183250432 


568 


23-832 


8-281 


256036 


129554216 


506 


22-494 


7-968 


323761 


184220009 


569 


23-853 


8-286 


257049 


130323843 


507 


22-516 


7-973 


324900 


185193000 


670 


23-874 


8-291 


258064 


131096512 


508 


22-538 


7-979 


326041 


186169411 


571 


23-895 


8-296 


259081 


131872229 


509 


22-561 


7-984 


327184 


187149248 


572 


23-916 


8-301 


260100 


132651000 


510 


2-2-583 


7-989 


328329 


188132517 


573 


23-937 


8-305 


261121 


133432831 


511 


22-605 


7-994 


329476 


189119224 


674 


23-958 


8-310 


262144 


134217728 


512 


22-627 


8-000 


330625 


190109375 


675 


23-979 


8-315 


263169 


135005697 


513 


22-649 


8-005 


331776 


191102976 


576 


24-000 


8-320 


264196 


135796744 


514 


22-671 


8-010 


332929 


192100033 


577 


24-020 


8-325 


265225 


136590875 


515 


22-693 


8-015 


334084 


193100552 


578 


24-041 


8-329 


266256 


137388096 


516 


22-715 


8-020 


335241 


194104539 


679 


24-062 


8-334 


267289 


138188413 


517 


22-737 


8-025 


336400 


195112000 


680 


24-083 


8-339 


268324 


138991832 


518 


22-759 


8-031 


337561 


196122941 


681 


24-103 


8-344 


269361 


139798359 


519 


22-781 


8-U36 


338724 


197187368 


682 


24-124 


8-349 


270400 


140608000 


520 


22-803 


8-041 


339889 


198155287 


583 


24-146 


8-353 


271441 


141420761 


521 


22-825 


8-046 


341056 


199176704 


584 


24-166 


8-358 


272484 


142236648 


522 


22-847 


8-051 


342225 


200201625 


685 


24-186 


8-363 


273529 


143055667 


523 


22-869 


8-056 


343396 


201230056 


586 


24-207 


8-368 


274576 


143877824 


524 


22-891 


8-062 


344569 


202262003 


687 


24-228 


8-372 


275625 


144703125 


525 


22-912 


8-067 


345744 


203297472 


588 


24-248 


8-377 


276676 


145531576 


526 


22-934 


8-072 


346921 


204336469 


589 


24-269 


8-382 


277729 


146363183 


527 


22-956 


8-077 


348100 


205379000 


590 


24-289 


8-387 


278784 


147197952 


528 


22-978 


8-082 


349281 


206425071 


691 


24-310 


8-391 


279841 


148035889 


529 


23-000 


8-087 


350464 


2^07474688 


692 


24-331 


. 8-396 


280900 


148877000 


530 


23-021 


8-092 


351649 


208527857 


593 


24-351 


8-401 


281961 


149721291 


531 


23-043 


8-097 


352836 


209584584 


694 


24-372 


8-406 


283024 


150568768 


532 


23-065 


8-102 


354025 


210644875 


695 


24-392 


8-410 


284089 


151419437 


533 


23-086 


8-107 


355216 


211708736 


596 


24-413 


8-415 


285156 


152273304 


534 


23-108 


8-112 


356409 


212776173 


697 


24-433 


8-420 


286225 


153130375 


535 


23-130 


8-118 


357604 


213847192 


698 


24-454 


8-424 


287296 


153990656 


636 


23-151 


8-123 


358801 


214921799 


599 


24-474 


8-429 


288369 


154854153 


537 


23-173 


8-128 


360000 


216000000 


600 


24-494 


8-434 


289444 


155720872 


538 


23-194 


8-133 


361201 


217081801 


601 


24-516 


8439 


290521 


156590819 


539 


23-216 


8-138 


362404 


218167208 


602 


24-636 


8-443 


291600 


157464000 


540 


23-237 


8-143 


363609 


219256227 


603 


24-556 


8-448 


292681 


158340421 


541 


23-259 


8-148 


364816 


220348864 


604 


24-576 


8-453 


293764 


159220088 


542 


23-280 


8-153 


366025 


221445125 


605 


24-596 


8-457 


294849 


160103007 


543 


23-302 


8-158 


367236 


222545016 


606 


24-617 


8-462 


295936 


160989184 


544 


23-323 


8-163 


368449 


223648543 


607 


24-637 


8-467 


297025 


161878625 


545 


23-345 


8-168 


369664 


224755712 


608 


24-657 


8-471 


298116 


162771336 


546 


23-366 


8-173 


370881 


225866529 


609 


24-677 


8-476 


299209 


163667323 


547 


23-388 


8-178 


372100 


226981000 


610 


24-698 


8-480 


300304 


164566592 


548 


23-409 


8-183 


373321 


228099131 


611 


24-718 


8-485 


301401 


165469149 


549 


23-430 


8-188 


374544 


229220928 


612 


24-738 


8-490 


302500 


166375000 


550 


23-452 


8-193 


375769 


230346397 


613 


24-758 


8-494 


303601 


167284151 


551 


23-473 


8-198 


376996 


231475544 


614 


24-779 


8-499 


304704 


168196608 


652 


23-494 


8-203 


378225 


232608375 


615 


24-799 


8-504 


305809 


169112377 


553 


23-515 


8-208 


379456 


233744896 


616 


24-819 


8-508 


306916 


170031464 


554 


23-537 


8-213 


380689 


234885113 


617 


24-839 


8-513 


308025 


170953875 


555 


23-558 


8-217 


381924 


236029032 


618 


24-859 


8-517 


309136 


171879616 


556 


23-579 


8-222 


383161 


237176659 


619 


24-879 


8-622 


310249 


172808693 


557 


23-600 


8-227 


384400 


238328000 


620 


24-899 


8-527 


311364 


173741112 


558 


23-622 


8-232 


385641 


239483061 


621 


24-919 


8-531 


312481 


174676879 


559 


23-643 


8-237 


386884 


240641848 


622 


24-939 


8-536 


313600 


175616000 


560 


23-664 


8-242 


388129 


241804367 


623 


24-959 


8-540 


314721 


176558481 


561 


23-685 


8-247 


389376 


242970624 


624 


24-979 


8-545. 


315844 


177504328 


562 


23-706 


8-252 


390625 


244140625 


625 


26-000 


8-549 


316969 


178453547 


563 


23-727 


8-257 


391876 


245314376 


626 


25-019 


8-554 


318096 


179406144 


564 


23-748 


8-262 


393129 


246491883 


627 


25-039 


8-568 


319225 


180362125 


565 


23-769 


8-267 


394384 


247673152 


628 


25-059 


8-563 


320356 


, 181321496 


566 


23-790 


8-271 


395641 


248858189 


629 


25-079 


8-568 


321489 


182284263 


567 


23-811 


8-276 1 


396900 


250047000 


630 


25-099 


8-572 



APPENDIX, 



825 



TABLE 


OF SQUAE 


ES, CUBES, SQUAEE A^ 


D CUBE 


EOOTS OF '^U'SIBE^S— (Continued). 


Squares. 


Cubes. 


No. 


Square 
I roots. 


Cube 
roots. 


i 
Squares. 


Cubes. 


No. 


Square 
roots. 


Cube 
roots. 


398161 


251239591 


631 


25-119 


8-577 


481636 


334255384 


694 


26-343 


8-853 


399424 


252435968 


632 


25-139 


8-581 


483025 


335702375 


695 


26-362 


8-857 


400689 


253636137 


633 


25159 


8-586 


484416 


337153536 


696_ 


26-381 


8-862 


401956 


254840104 


634 


25179 


8-590 


485809 


338608873 


697 


26-400 


8-866 


403225 


256047875 


635 


25-199 


8-595 


487204 


340068392 


698 


26-419 


8-870 


404496 


257259456 


636 


25-219 


8-599 


488601 


341532099 


699 


26-438 


8-874 


405769 


258474853 


637 


25-238 


8-604 


490000 


343000000 


700 


26-457 


8-879 


407044 


259694072 


638 


25-258 


8-608 


491401 


344472101 


701 


26-476 


8-883 


408321 


260917119 


639 


25-278 


8-613 


492804 


345948408 


702 


26-495 


6-887 


409600 


262144000 


640 


25-298 


8-617 


494209 


347428927 


703 


26-514 


8-891 


410881 


263374721 


641 


25-317 


8-622 


: 495616 


348913664 


i 704 


26-532 


8-895 


412164 


264609288 


642 


25-337 


8-626 


! 497025 


35041)2625 


; 705 


26-551 


8-900 


413449 


265847707 


643 


25-357 


8-631 


498436 


351895816 


706 


26-570 


8-904 


414736 


267089984 


644 


25-377 


3-635 


499849 


353393243 


707 


26-589 


8-908 


416025 


268336125 


645 


25-396 


8-640 


501264 


354894912 


708 


26-608 


8-912 


417316 


269586136 


646 


25-416 


8-644 


502681 


356400829 


709 


26-627 


8-916 


418609 


270840023 


647 


25-436 


8-649 


504100 


357911000 


710 


26-645 


8-921 


419904 


272097792 


648 


25-455 


8-653 


505521 


359425431 


711* 


26-664 


8-925 


421201 


273359449 


649 


25-475 


8-657 


506944 


360944128 


712 


26-683 


8-929 


422500 


274625000 


650 


25-495 


8-662 


508369 


362467097 


713 


26-702 


8-938 


423801 


275894451 


651 


25-514 


8-666 


509796 


363994344 


714 


26-720 


8-937 


425104 


277167808 


652 


25-534 


8-671 


511225 


365525875 


715 


26-739 


8-942 


426409 


278445077 


653 


25-553 


8-675 


512656 


367061696 


716 


26-758 


8-946 


427716 


279726264 


654 


25-573 


8-680 


514089 


368601813 


717 


26-776 


8-950 


429025 


281011375 


655 


25-592 


8-684 


515524 


370146232 


718 


26-795 


8-954 


430336 


282300416 


656 


25-612 


8-688 


516961 


371694959 


719 


26-814 


8-958 


431649 


283593393 


657 


25-632 


8-693 


618400 


373248000 


720 


26-832 


8-962 


432964 


284890312 


658 


25-651 


8-697 


1 519841 


374805361 


721 


26-851 


8-966 


434281 


286191179 


659 


25-670 


8-702 


521284 


£76367048 


722 


26-870 


8-971 


435600 


287496000 


660 


25-690 


8-706 


522729 


377933067 


723 


26-888 


8-975 


436921 


288804781 


661 


25-709 


8-710 


524176 


379503424 


724 


26-907 


8-979 


438244 


290117528 


662 


25-729 


8-715 


, 525625 


381078125 


725 


26-925 


8-983 


439569 


291434247 


663 


25-748 


8-719 


527076 


382657176 


726 


26-944 


8-987 


440896 


292754944 


664 


25-768 


8-724 


1 528529 


384240583 


727 


26-962 


8991 


442225 


294079625 


665 


25-787 


8-728 


529984 


385828352 


728 


26-981 


8-995 


443556 


295408296 


666 


25-806 


8-732 


531441 


387420489 


729 


27-000 


9-000 


444889 


296740963 


667 


25-826 


8-737 


532900 


389017000 


730 


27-018 


9-004 


446224 


298077632 


668 


25-845 


8-741 


534361 


390617891 


731 


27-037 


9-008 


447561 


299418309 


669 


25-865 


8-745 


535824 


392223168 


732 


27-055 


9-012 


448900 


300763000 


670 


25-884 


8-750 


537289 


393832837 


738 


27-073 


9-016' 


450241 


302111711 


671 


25-903 


8-754 


538756 


395446904 


734 


27-092 


9-020 


451584 


303464448 


672 


25-922 


8-759 


540225 


397065375 


735 


27-110 


9-024 


452929 


304821217 


673 


25-942 


8-763 


541696 


398688256 


736 


27-129 


9-028 


454276 


306182024 


674 


25-961 


8-767 j 


543169 


400315553 


737 


27-147 


9-032 


455625 


307546875 


675 


25-980 


8-772 


544644 


401947272 


738 


27-166 


9-036 


456976 


308915776 


676 


26-000 


8-776 ! 


546121 


403583419 


739 


27-184 


9040 


458329 


310288733 


677 


26-019 


8-780 i 


547600 


405224000 


740 


27-202 


9-045 


459684 


311665752 


678 


26-038 


8-785 i 


549081 


406869021 


741 


27-221 


9-049 


461041 


313046839 


679 


26-057 


8-789 


550564 


408518488 


742 


27-239 


9-058 


462400 


314432000 


680 


26-076 


8-793 : 


552049 


410172407 


743 


27-258 


9-057 


463761 


315821241 


681 


26-095 


8-797 


553536 


411830784 


744 


27-276 


9-061 


465124 


317214568 


682 


26-115 


8-802 1 


555025 


413493625 


745 


27-294 


9-065 


466489 


318611987 1 


683 


26-134 


8-806 i 


556516 


415160936 


746 


27-313 


9-069 


467856 


320013504 


684 


26-153 


8-810 j 


558009 


416832723 


747 


27-331 


9-073 


469225 


321419125 


685 


26-172 


8-815 


559504 


418508992 


748 


27-349 


9-077 


470596 


322828856 


686 


26-191 


8-819, 


561001 


420189749 


749 


27-367 


9-081 


471969 


324242703 


687 


26-210 


8-823 


562500 


421875000 


750 


27-386 


9-085 


473344 


325660672 


688 


26-22y 


8-828 


564001 


423564751 


751 


27-404 


9089 


474721 


327082769 


689 


26-248 


8-832 


565504 1 


425259008 


752 


27-422 


9-093 


476100 


328509000 


690 


26-267 


8-836 


567009 1 


426957777 


753 


27-440 


9-097 


477481 


329939371 


691 


26-286 


8-840 


568516 


428661064 


754 


27-459 


9-101 


478864 


331373888 


692 


26-305 


8-845 


570025 


430368875 


755 


27-477 


9-105 


480249 


332812557 


693 


26-324 


8-849 . 


571536 


432081216 


756 


27-495 


9-109 



826 



APPENDIX. 



TABLE OF SQUARES, CUBES, SQUAEE AND CUBE BOOTS OF '^VMBEES— (Continued). 



Squares. 


Cubes. 


No. 


Square 
roots. 


Cube 
roots. 


Squares. 


Cubes. 


No. 


Square 
roots.* 


Cube 
roots. 


573049 


433798093 


757 


27-513 


9-113 


672400 


551368000 


820 


28-635 


9-359 


574564 


435519512 


758 


27-531 


9-117 


674041 


553387661 


821 


28-653 


9-363 


576081 


437245479 


759 


27-549 


9-121 


675684 


555412248 


822 


28-670 


9-367 


577600 


438976000 


760 


27-568 


9-125 


677329 


557441767 


823 


28-687 


9-371 


579121 


440711081 


761 


27-586 


9-129 


678976 


559476224 


824 


28-705 


9-375 


580644 


442450728 


762 


27-604 


9-133 


680625 


561515625 


825 


28-722 


9-378 


582169 


444194947 


763 


27-622 


9-137 


682276 


563559976 


826 


28-740 


9-382 


583696 


445943744 


764 


27-640 


9-141 


683929 


565609283 


827 


28-757 


9-386 


585225 


447697125 


765 


27-658 


9-145 


685584 


567663552 


828 


28-774 


9-390 


586756 


449455096 


766 


27-676 


9-149 


687241 


569722789 


829 


28-792 


9-394 


588289 


451217663 


767 


27-694 


9-153 


688900 


571787000 


830 


28-809 


9-397 


589824 


452984832 


768 


27-712 


9157 


690561 


573856191 


831 


28-827 


9-401 


591361 


454756609 


769 


27-730 


9-161 


692224 


575930368 


832 


28-844 


9-405 


592900 


456533000 


770 


27-748 


9-165 


693889 


578009537 


833 


28-861 


9-409 


594441 


458314011 


771 


27-766 


9-169 


695556 


580093704 


834 


28-879 


9-412 


595984 


460099648 


772 


27-784 


9-173 


697225 


582182875 


835 


28-896 


9-416 


597529 


461889917 


773 


27-802 


9-177 


698896 


584277056 


836 


28-913 


9-420 


599076 


463684824 


774 


27-820 


9-181 


700569 


586376253 


837 


28-930 


9-424 


600625 


465484375 


775 


27-838 


9-185 


702244 


588480472 


838 


28-948 


9-427 


602176 


467288576 


776 


27-856 


9-189 


703921 


590589719 


839 


28-965 


9-431 


603729 


469097433 


777 


27-874 


9-193 


705600 


592704000 


840 


28-982 


9-435 


605284 


470910952 


778 


27-892 


9-197 


707281 


594823321 


841 


29-000 


9-439 


606841 


472729139 


779 


27-910 


9-201 


708964 


596947688 


842 


29-017 


9-442 


608400 


474552000 


780 


27-928 


9-205 


710649 


599077107 


843 


29-034 


9-446 


609961 


476379541 


781 


27-946 


9-209 


712336 


601211584 


844 


29-051 


9-450 


611524 


478211768 


782 


27-964 


9-213 


714025 


603351125 


845 


29-068 


9-454 


613089 


480048687 


783 


27-982 


9-216 


715716 


605495736 


846 


29-086 


9-457 


614656 


481890304 


784 


28-000 


9-220 


717409 


607645423 


847 


29-103 


9-461 


616225 


483736625 


785 


28-017 


9-224 


719104 


609800192 


848 


29-120 


9-465 


617796 


485587656 


786 


28-035 


9-228 


720801 


611960049 


849 


29-137 


9-468 


619369 


487443403 


787 


28-053 


9-232 


722500 


614125000 


850 


29-154 


9-472 


620944 


489303872 


788 


28-071 


9-236 


724201 


616295051 


851 


29-171 


9-476 


622521 


491169069 


789 


28-089 


9-240 


725904 


618470208 


852 


29-189 


9-480 


624100 


493039000 


790 


28-106 


9-244 


727609 


620650477 


853 


29-206 


9-483 


625681 


494913671 


791 


28-124 


9-248 


729316 


622835864 


854 


29-223 


9-487 


627264 


496793088 


792 


28-142 


9-252 


731025 


625026375 


855 


29-240 


9-491 


628849 


498677257 


793 


28-160 


9-256 


732736 


627222016 


856 


29-257 


9 494 


630436 


500566184 


794 


28-178 


9-259 


734449 


629422793 


857 


29-274 


9-498 


632025 


502459875 


795 


28-195 


9-263 


736164 


631628712 


858 


29-291 


9-502 


633616 


504358336 


796 


28-213 


9-267 


737881 


633839779 


859 


29-308 


9-505 


635209 


506261573 


•797 


28-231 


9-271 


739600 


636056000 


860 


29-325 


9-509 


636804 


508169592 


798 


28-248 


9-275 


741321 


638-277381 


861 


29-342 


9-513 


638401 


510082399 


799 


28-266 


9-279 


743044 


640503928 


862 


29-359 


9-517 


640000 


512000000 


800 


28-284 


9-283 


744769 


642735647 


863 


29-376 


9-520 


641601 


513922401 


801 


28-301 


9-287 


746496 


644972544 


864 


29-393 


9-524 


643204 


515849608 


802 


28-319 


9-290 


748225 


647214625 


865 


29-410 


9-528 


644809 


517781627 


803 


28-337 


9-294 


749956 


649461896 


866 


29-427 


9-531 


.646416 


519718464 


804 


28-354 


9-298 


751689 


651714363 


867 


29-444 


9-535 


648025 


521660125 


805 


28-372 


9-302 


753424 


653972032 


868 


29-461 


9-539 


649636 


523606616 


806 


28-390 


9-306 


755161 


656234909 


869 


29-478 


9-542 


651249 


525557943 


807 


28-407 


9-310 


756900 


658503000 


.870 


29-495 


9-546 


652864 


527514112 


808 


28-425 


9-314 


758641 


660776311 


871 


29-512 


9-550 


654481 


529475129 


809 


28-442 


9-317 


760384 


663054848 


872 


29-529 


9-553 


656100 


531441000 


810 


28-460 


9-321 


762129 


665338617 


873 


29-546 


9-557 


657721 


533411731 


811 


28-478 


9-325 


763876 


667627624 


874 


29-563 


9-561 


659344 


535387328 


812 


28-495 


9-329 


■'765625 


669921875 


875 


29-580 


9-564 


660969 


537367797 


813 


28-513 


9-333 


767376 


672221376 


876 


29-597 


9-568 


662596 


539353144 


814 


28-530 


9-337 


769129 


674526133 


877 


29-614 


9-571 


664225 


541343375 


815 


28-548 


9-340 


770884 


676836152 


878 


29-631 


9-575 


665856 


543338496 


816 


28-565 


9-344 


772641 


679151439 


879 


29-647 


9-579 


667489 


545338513 


817 


28-583 


9-348 


774400 


681472000 


880 


29-664 


9-582 


669124 


547343432 


818 


28-600 


9-352 


776161 


683797841 


881 


29-681 


9-586 


670761 


549353259 


819 


28-618 


9-356 


777924 


686128968 


882 


29-698 


9-590 



APPENDIX. 



827 



TABLE OF SQUARES, CUBES, SQUARE AND CUBE ROOTS OF NVUBER8— (Continued). 



Squares. 


Cubes. 


No. 


Square 
roots. 


Cube 
roots. 


Squares. 
894916 


Cubes. 


No. 


Square 
roots. 


Cube 
roots. 


779689 


688465387 


883 


29-715 


9-593 


846590536 


946 


30-757 


9-816 


781456 


690807104 


884 


29-732 


9-597 


896808 


849278123 


947 


30-773 


9-820 


783225 


693154125 


885 


29-748 


9-600 


898704 


851971392 


948 


30-789 


9-823 


784996 


695506456 


886 


29-765 


9-604 


900601 


854670349 


949 


30-805 


9-827 


786769 


697864103 


887 


29-782 


9-608 


902500 


857375000 


9r>0 


30-822 


9-830 


788544 


700227072 


888 


29-799 


9-611 


904401 


860085351 


951 


30-838 


9-833 


790321 


702595369 


889 


29-816 


9-615 


906304 


862801408 


952 


30-854 


9-837 


792100 


704969000 


890 


29-832 


9-619 


908209 


865523177 


953 


30-870 


9-840 


793881 


707347971 


891 


29-849 


9-622 


910116 


868250664 


954 


30-886 


9-844 


795664 


709732288 


892 


29-866 


9-626 


91-2025 


870983875 


955 


30-903 


9-847 


797449 


712121957 


893 


29-883 


9-629 


913936 


873722816 


956 


30-919 


9-851 


799236 


714516984 


894 


29-899 


9-633 


915849 


876467493 


957 


30-935 


9-854 


SOI 025 


716917375 


895 


29-916 


9-636 


917764 


879217912 


958 


30-951 


9-857 


802816 


719323136 


896 


29-933 


9-640 


919681 


881974079 


959 


30-967 


9-861 


S04609 


721734273 


897 


29-949 


9-644 


921600 


884736000 


960 


30-983 


9-864 


€06404 


724150792 


898 


29-966 


9-647 


923521 


887503681 


961 


31-000 


9-868 


808201 


726572699 


899 


29-983 


9-651 


925444 


890277128 


962 


31-016 


9-871 


810000 


729000000 


900 


30-000 


9-654 


927369 


893056347 


963 


31-032 


9-875 


S11801 


731432701 


901 


30-016 


9-658 


929296 


895841344 


964 


31-048 


9-878 


813604 


733870808 


902 


30-033 


9-662 


931225 


898632125 


965 


31-064 


9-881 


815409 


736314327 


903 


30-049 


9-665 


933156 


901428696 


966 


31-080 


9-885 


817216 


738763264 


904 


30-066 


9-669 


935089 


904231063 


967 


31-096 


9-888 


819025 


741217625 


905 


30083 


9-672 


937024 


907039232 


968 


31-112 


9-892 


820836 


743677416 


906 


30-099 


9-676 


938961 


909853209 


969 


31-128 


9-895 


822649 


746142643 


907 


30-116 


9-679 


940900 


912673000 


970 


31-144 


9-898 


824464 


748613312 


908 


30-133 


9-683 


942841 


915498611 


971 


31-160 


9-902 


826281 


751089429 


909 


30-149 


9-686 


944784 


918330048 


972 


31-176 


9-905 


828100 


753571000 


910 


30-166 


9-690 


946729 


921167317 


973 


31-192 


9-909 


829921 


756058031 


911 


30-182 


9-694 


948676 


924010424 


974 


31-208 


9-912 


831744 


758550528 


912 


30-199 


9-697 


950625 


926859375 


975 


31-224 


9-915 


833569 


761048497 


913 


30-215 


9-701 


952576 


929714176 


976 


31-240 


9-919 


835396 


763551944 


914 


30-232 


9-704 


954529 


932574833 


977 


31-256 


9-922 


837225 


766060875 


915 


30-248 


9-708 


956484 


935441352 


978 


31-272 


9-926 


839056 


768575296 


916 


30-265 


9-711 


958441 


938313739 


979 


31-288 


9-929 


840889 


771095213 


917 


30-282 


9-715 


960400 


941192000 


980 


31-304 


9-932 


842724 


773620632 


918 


30-298 


9-718 


962361 


944076141 


981 


31-320 


9-936 


844561 


776151559 


919 


30-315 


9-722 


964324 


946966168 


982 


31-336 


9939 


846400 


778688000 


920 


30-331 


9-725 


966289 


949862087 


983 


31-352 


9-943 


848241 


781229961 


921 


30-347 


9 729 


968256 


952763904 


984 


31-368 


9-946 


850084 


783777448 


922 


30-364 


9-732 


970225 


955671626 


985 


31-384 


9-949' 


851929 


786330467 


923 


30-380 


9-736 


972196 


958585256 


986 


31-400 


9-953 


853776 


788889024 


924 


30-397 


9-739 


974169 


961504803 


987 


31-416 


9-956 


855625 


791453125 


925 


30-413 


9-743 


976144 


964430272 


988 


31-432 


9-959 


857476 


794022776 


926 


30-430 


9-746 


978121 


967361669 


989 


31-448 


9-963 


859329 


796597983 


927 


30-446 


9-750 


980100 


970299000 


990 


31-464 


9-966 


861184 


799178752 


928 


30-463 


9-753 


982081 


973242271 


991 


31-480 


9-969 


863041 


801765089 


929 


30-479 


9-757 


984064 


976191488 


992 


31-496 


9-973 


864900 


804357000 


930 


30-495 


9-761 


986049 


979146657 


993 


31-511 


9-976 


866761 


806954491 


931 


30-512 


9-764 


988036 


982107784 


994 


31-527 


9-979 


868624 


809557568 


932 


30-528 


9-767 


990025 


985074875 


995 


31-543 


9-983 


870489 


812166237 


933 


30-545 


9-771 


992016 


988047936 


996 


31-559 


9-986 


872356 


814780504 


934 


30-561 


9-774 


994009 


991026973 


997 


31-575 


9989 


874225 


817400375 


935 


30-577 


9-778 


996004 


994011992 


998 


31-591 


9-993 


876096 


820025856 


936 


30-594 


9-782 


998001 


997002999 


999 


31-606 


9-996 


877969 


822656953 


937 


30-610 


9-785 


1000000 


1000000000 


1000 


31-622 


10-000 


879844 


825293672 


938 


30-626 


9-788 . 


1000201 


1003003001 


1001 


31-638 


10-003 


881721 


827936019 


939 


30-643 


9-792 


1004004 


1006012008 


1002 


31-654 


10-006 


883600 


830584000 


940 


30-659 


9-795 


1006009 


1009027027 


1003 


31-670 


10-009 


885481 


833237621 


941 


30-675 


9-799 


1008016 


1012048064 


1004 


31-685 


10-013 


-887364 


835896888 


942 


30-692 


9-802 


1010025 


1015075125 


1005 


31-701 


10-016 


889249 


838561807 


943 


30-708 


9-806 


101-2036 


1018108216 


1006 


31-717 


10-019 


891136 


841232384 


944 


30-724 


9-809 


1014049 


1021147343 


1007 


31-733 


10-023 


893025 


843908625 


945 


30-740 


9-813 


1016064 


1024192512 


1008 


31-749 


10-026 



828 



APPENDIX. 
TABLE OP RECIPROCALS. 









1 


•2 


3 


•4 


5 


6 


•7 


•8 


•9 





00 


10^000 


5-0000 


3 3333 


2^5000 


2^0000 


1^6667 


1^4286 


1^2500 


Mill 


1 


1-00000 


•90909 


•83333 


•76923 


•71428 


•66667 


•62500 


•58823 


•55555 


•52631 


2 


•50000 


•47619 


•45454 


•43478 


•41667 


•40000 


•38461 


•37037 


•35714 


•34483 


3 


•33333 


•32258 


•31250 


•30303 


•29412 


•28571 


•27778 


•27027 


•26316 


•25641 


4 


•25000 


24390 


•23810 


•23256 


•22727 


•22222 


•21739 


21277 


•20833 


•20408 


5 


•20000 


19608 


•19231 


•18868 


•18519 


•18182 


•17857 


•17544 


•17241 


•16949 


6 


•16667 


16393 


•16129 


•15873 


• 15625 


•15385 


•15152 


• 14925 


• 14706 


•14493 


7 


• 14286 


14085 


•13889 


•13699 


•13514 


•13333 


•13158 


•12987 


•12821 


•12658 


8 


•12500 


12346 


•12195 


• 12048 


•11905 


•11765 


11628 


•11494 


•11364 


•11236 


9 


•11111 


10989 


-10870 


•10753 


•10638 


• 10526 


10417 


•10309 


•10204 


•10101 


10 


•10000 


09901 


•09804 


•09709 


•09615 


•09524 


09434 


•09346 


09259 


09174 


11 


•09091 


09009 


•08929 


•08850 


•08772 


•08696 


08621 


'08547 


08475 


08403 


12 


•08333 


08264 


•08197 


•08130 


•08065 


•08000 


07937 


•07874 


07813 


07752 


13 


•07693 


07634 


•07576 


•07519 


•07463 


•07407 


07353 


•07299 


•07246 


•07194 


14 


•07143 


07092 


•07042 


•06993 


•06944 


•06897 


06849 


•06803 


•06757 


06711 


15 


•06667 


06623 


•06579 


•06536 


•06494 


•06452 


06410 


•06369 


•06329 


06289 


16 


•06250 


06211 


•06173 


•06135 


•06098 


•06061 


06024 


•05988 


•05952 


•05917 


17 


•05882 


05848 


•05814 


•05780 


•05747 


•05714 


05682 


•05650 


•05618 


05587 


18 


•05556 


05525 


•05495 


•05464 


•05435 


•05405 


05376 


•05348 


•05319 


05291 


19 


•05263 


05236 


•05208 


•05181 


•05155 


•05128 


05102 


•05076 


•05051 


05025 


20 


•05000 


04975 


•04950 


•04926 


•04902 


-04878 


04854 


•04831 


04808 


04785 


21 


•04762 


04739 


•04717 


•04695 


•04673 


•04651^ 


04630 


•04608 


04587 


04566 


22 


•04545 


04525 


•04505 


•04484 


•04464 


•04444 


04425 


•04405 


04386 


04367 


23 


•04348 


04329 


•04310 


•04292 


•04274 


•04255 


04237 


•04219 


04202 


04184 


24 


•04167 


04149 


•04132 


•04115 


•04098 


•04082 


04065 


•04049 


04032 


04016 


25 


•04000 


03984 


•03968 


•03953 


•03937 


•03922 


03906 


•03891 


03876 


03861 


26 


•03846 


03831 


•03817 


•03802 


•03788 


•03774 


03759 


•03745 


03731 


03717 


27 


•03704 


03690 


•03676 


•03663 


•03650 


•03636 


03623 


•03610 


03597 


03584 


28 


•03571 


03559 


•03546 


•03534 


•03521 


•03509 


03497 


•03484 


03472 


03460 


29 


•03448 


03436 


•03425 


•03413 


•03401 


•03390 


03378 


•03367 


03356 


03344 


30 


•03333 


03322 


•03311 


•03300 


•03289 


•03279 


03268 


•03257 


03247 


03236 


31 


•03226 


03215 


•03205 


•03195 


•03185 


•03175 


03165 


•03155 


03145 


03135 


32 


•03125 


03115 


•03106 


•03096 


•03086 


•03077 


03067 


•03058 


03049 


03040 


33 


•03030 


03021 


•03012 


•03003 


•02994 


•02985 


02976 


•02967 


02959 


02950 


34 


•02941 


02933 


•02924 


•02915 


•02907 


•02899 


02890 


•02882 


02874 


02865 


35 


•02857 


02849 


•02841 


•02833 


•02825 


•02817 


02809 


•02801 


02793 


02786 


36 


•02778 


02770 


•02762 


•02755 


•02747 


•02740 


02732 


•02725 


02717 


02710 


37 


•02703 


02695 


•02688 


•02681 


•02674 


•02667 


02660 


•02653 


02646 


02639 


38 


•02632 


02625 


•02618 


•02611 


•02604 


•02597 


02591 


•02584 


02577 


02571 


39 


•02564 


02558 


•02551 


•02545 


•02538 


•02532 


02525 


•02519 


02513 


02506 


40 


•02500 


02494 


•02488 


•02481 


•02475 


•02469 


02463 


•02457 • 


02451 


02445 


41 


•02439 


02433 


•02427 


•02421 


•02415 


•02410 


02404 


•02398 


02392 • 


02387 


42 


•02381 


02375 


•02370 


•02364 


•02358 


•02353 


02347 


•02342 


02336 


02331 


43 


•02326 


02320 


•02315 


•02309 


•02304 


•02299 


02294 


•02288 


02283 • 


02278 


44 


•02273 


02268 


•02262 


•02257 


•02252 


•02247 • 


02242 


•02237 


02232 


02227 


45 


•02222 


02217 


•02212 


•02208 


•02203 


•02198 


02193 


•02188 • 


02183 • 


02179 


46 


•02174 


02169 


•02165 


•02160 


•02155 


•02151 


02146 


•02141 


02137 • 


02132 


47 


•02128 


02123 


•02119 


•02114 


•02110 


•02105 


02101 


•02096 


02092 • 


02088 


48 


•02083 


02079 


•02075 


•02070 


•02066 


•02062 


02058 


•02053 


02049 • 


02045 


49 


•02041 


02037 


•02033 


•02028 


•02024 


•02020 


02016 


•02012 


02008 • 


02004 




•0 


•1 


•2 


•3 


4 


•5 


•G 


•7 


•8 


•9 



APPENDIX. 
TABLE OF RECIPROCALS— Con^mwed 



829 





•0 


•1 


•2 


•3 


•4 


•5 


•6 


•7 


•8 


•9 


50 


•02000 


01996 


01992 


•01988 


•01984 


•01980 


01976 


01972 


01969 


•01965 


51 


•01961 


01957 


01953 


•01949 


•01946 


•01942 


01938 


01934 


•01931 


•01927 


52 


•01923 


01919 


01916 


•01912 


•01908 


•01905 


01901 


01898 


01894 


•01890 


53 


•01887 


01883 


01880 


•01876 


01873 


•01869 


01866 


01862 


•01859 


•01855 


54 


•01852 


01848 


01845 


01842 


01838 


•01835 


01832 


•01828 


•01825 


•01821 


55 


•01818 


01815 


01812 


01808 


01805 


•01802 


•01799 


•01795 


•01792 


•01789 


56 


•01786 


01783 


01779 


01776 


01773 


•01770 


•01767 


•01764 


01761 


•01757 


57 


•01754 


01751 


01748 


01745 


01742 


•01739 


01736 


•01733 


01730 


•01727 


58 


•01724 


01721 


01718 


01715 


•01712 


•01709 


•01706 


•01704 


01701 


•01698 


59 


•01695 


01692 


01689 


01686 


•01684 


•01681 


•01678 


01675 


01672 


01669 


60 


•01667 


01664 


01661 


01658 


•01656 


•01653 


01650 


01647 


01645 


01642 


61 


•01639 


01637 


01634 


01631 


•01629 


•01626 


01623 


01621 


01618 


01616 


62 


•01613 


01610 


01608 


•01605 


•01603 


•01600 


01597 


01595 


01592 


01590 


63 


•01587 


01585 


01582 


01580 


01577 


•01575 


01572 


01570 


01567 


01565 


64 


•01563 


01560 


01558 


01555 


01553 


•01550 


01548 


01546 


01543 


01541 


65 


•01538 


01536 


01534 


•01531 


•01529 


•01527 


01524 


01522 


01520 


01517 


66 


•01515 


01513 


01511 


•01508 


•01506 


•01504 


01502 


01499 


01497 


01495 


67 


•01493 


01490 


01488 


•01486 


•01484 


•01481 


01479 


01477 


01475 


01473 


68 


•01471 


01468 


01466 


•01464 


•01462 


•01460 


01458 


01456 


01453 


01451 


69 


•01449 


01447 


•01445 


•01443 


•01441 


•01439 


01437 


01435 


01433 


01431 


70 


•01429 


01427 


01425 


•01422 


•01420 


•01418 


01416 


01414 


01412 


01410 


71 


•01408 


01406 


•01404 


•01403 


01401 


•01399 


01397 


01395 


01393 


01391 


72 


•01389 


01387 


01385 


•01383 


•01381 


•01379 


01377 


01376 


01374 


01372 


73 


•01370 


01368 


01366 


01364 


•01362 


•01361 


01359 


01357 


01355 


01353 


74 


•01351 


01350 


01348 


01346 


01344 


•01342 


01340 


01339 


01337 


01335 


75 


•01333 


01332 


01330 


•01328 


01326 


•01325 


01323 


01321 


01319 


01318 


76 


•01316 


01314 


01312 


•01311 


01309 


•01307 


01305 


01304 


01302 


01300 


77 


•01299 


01297 


•01295 


•01294 


•01292 


•01290 


01289 


01287 


01285 


01284 


78 


•01282 


01280 


01279 


•01277 


•01276 


•01274 


01272 


01271 


01269 


01267 


79 


•01266 


01264 


01263 


•01261 


01259 


•01258 


01256 


01255 


01253 


01252 


80 


•01250 


01248 


01247 


•01245 


•01244 


•01242 


01241 


01239 


01238 


01236 


81 


•01235 


01233 


01232 


•01230 


•01229 


•01227 


01225 


01224 


01222 


01221 


S2 


•01220 


01218 


•01217 


•01215 


•01214 


•01212 


01211 


01209 


01208 


01206 


83 


•01205 


01203 


•01202 


•01200 


•01199 


•01198 


01196 


01195 


01193 


01192 


84 


•01190 


01189 


•01188 


01186 


01185 


•01183 


01182 


01181 


01179 


01178 


85 


•01176 


01175 


01174 


•01172 


01171 


•01170 


01168 


01167 


01166 


01164 


86 


•01163 


01161 


01160 


01159 


•01157 


•01156 


01155 


01153 


01152 


01151 


87 


•01149 


01148 


01147 


•01145 


01144 


•01143 


01142 


01140 


01139 


01138 


88 


•01136 


01135 


01134 


01133 


01131 


•01130 


01129 


01127 


01126 


01125 


89 


•01124 


01122 


01121 


01120 


01119 


•01117 


01116 


01115 


01114 


01112 


90 


•01111 • 


OHIO 


01109 


01107 


01106 


•01105 


01104 


01103 


01101 


01100 


91 


•01099 


01098 


01096 


01095 


01094 


•01093 


01092 


01091 


01089 


01088 


92 


•01087 • 


01086 


01085 


01083 


01082 


•01081 


01080 


01079 


01078 


01076 


93 


•01075 • 


01074 


01073 


01072 


01071 


•01070 


01068 


01067 


01066 


01065 


94 


•01064 • 


01063 


01062 


01060 


01059 


•01058 


01057 


01056 


01055 


01054 


95 


•01053 • 


01052 • 


01050 • 


01049 • 


01048 


•01047 


01046 


01045 


01044 


01043 


96 


•01042 


01041 


01040 


01038 


01037 


•01036 


01035 


01034 


01033 


01032 


97 


•01031 


01030 


01029 


01028 


01027 


•01026 


01025 


01024 


01022 


01021 


98 


•01020 


01019 


01018 


01017 


01016 


•01015 


01014 


01013 


01012 


01011 


99 


•01010 • 


01009 


01008 


01007 


01006 


•01005 


01004 


01003 


01002 


01001 







•1 


2 


3 


•4 


•5 


•6 


*7 


•8 


•9 



830 



APPENDIX. 









I.ATITUDES AND 


DEPARTURES. 








^ 


1 


s 


3 


4L 


5 


^ 


A... 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 1 


Lat. 


Dep. 


Lat. 


1 


0° 


1-000 


0-000 


2-000 


0-000 


3-000 


0-000 i 


4-000 


0-000 


5-000 


90° 


oi 


rooo 


0-004 


2-000 


0-009 


3-000 


0-013 1 


4-000 


0-017 


5-000 


89| 


0^ 


1-000 


0-009 


2-000 


0-017 


3-000 


0-026 i 


4-000 


0-035 


5-000 


m 


0| 


1-000 


0-013 


2-000 


0-026 


3-000 


0-039 


4-000 


0-052 


5-000 


89i 


1° 


1-000 


0-017 


2-000 


0-035 


3-000 


0-052 1 


3-999 


0-070 


4-999 


89° 


H 


1-000 


0-022 


2-000 


0-044 


2-999 


0-065 ! 


3-999 


0-087 


4-999 


88f 


H 


1-000 


0-026 


1-999 


0-052 


2-999 


0-079 ' 


3-999 


0-105 


4-998 


88i 


If 


1-000 


0031 


1-999 


0-061 


2-999 


0-092 


3-998 


0-122 


4-998 


88i 


2° 


0-999 


0-035 


1-999 


0-070 


2-998 


0-105 


3-998 


0-140 


4-997 


88° 


H 


0-999 


0-039 


1-998 


0-079 


2-998 


0-118 


3-997 


0-167 


4-996 


87f 


H 


0-999 


0-044 


1-998 


0-087 


2-997 


0-131 


3-996 


0-174 


4-995 


87i 


2| 


0-999 


0-048 


1-998 


0-096 


2-997 


0-144 


3-995 


0-192 


4-994 


87ir 


3° 


0-999 


0-052 


1-997 


0-105 


2-996 


0-157 


3-995 


0-209 


4-993 


87° 


H 


0-998 


0-057 


1-997 


0-113 


2-995 


0-170 


3-994 


0-227 


4-992 


86|- 


H 


0-998 


0-061 


1-996 


0-122 


2-994 


0-183 


3-993 


0-244 


4-991 


86^ 


8| 


0-998 


0-065 


1-996 


0-131 


2-994 


0-196 


3-991 


0-262 


4-989 


86i 


4° 


0-998 


0-070 


1995 


0-140 


2-993 


0-209 


3-990 


0-279 


4-988 


86° 


4i 


0-997 


0-074 


1-995 


0-148 


2-992 


0-222 


3-989 


0-296 


4-986 


851- 


H 


0-997 


0-078 


1-994 


0-157 


2-991 


0-235 


3-988 


0-314 


4-985 


85i 


4f 


0-997 


0-083 


1-993 


0-166 


2-990 


0-248 


3-986 


0-331 


4-983 


85i 


5° 


0-996 


0-087 


1-992 


0174 


2-989 


0-261 


.3-985 


0-349 


4-981 


85° 


H 


0-996 


0-092 


1-992 


0-183 


2-987 


0-275 


3-983 


0-366 


4-979 


84f 


H 


0-995 


0-096 


1-991 


0-192 


2-986 


0-288 


3-982 


0-383 


4-977 


84i 


5f 


0-995 


0-100 


1-990 


0-200 


2-985 


0-301 


3-980 


0-401 


4-975 


84i 


6° 


0-995 


0105 


1-989 


0-209 


2-984 


0-3H 


3-978 


0-418 


4-973 


84° 


6i 


0-994 


0-109 


1-988 


0-218 


2-982 


0-327 


3-976 


0-435 


4-970 


83f 


H 


0-994 


0-113 


1-987 


0-226 


2-981 


0-340 


3-974 


0-453 


4-968 


83i 


6| 


0-993 


0-118 


1-986 


0-235 


2-979 


0-353 


3-972 


0-470 


4-965 


83^ 


7° 


0-993 


0-122 


1-985 


0-244 


2-978 


"0-366 


3-970 


0-487 


4-963 


83°- 


'7i 


0-99-2 


0-126 


1-984 


0-252 


2-976 


0-379 


3-968 


0-505 


4-960 


82|- 


'7i 


0-991 


0-131 


1-983 


0-261 


2-974 


0-392 


3-966 


0-622 


4-957 


82i 


n 


0-991 


0-135 


1-982 


0-270 


2-973 


0-405 


3-963 


0-539 


4-954 


82i 


8° 


0-990 


0-139 


1-981 


0-278 


2-971 


0-418 


3961 


0-657 


4-951 


82° 


8i 


0-990 


0-143 


1-979 


0-287 


2-969 


0-430 


3-959 


0-574 


4-948 


811- 


8i 


0-989 


0148 


1-978 


0-296 


2-967 


0-443 


3-956 


0-591 


4-945 


8H 


8| 


0-988 


0-152 


1-977 


0-304 


2-965 


0-456 


3-953 


0-608 


4-942 


81i 


9° 


0-988 


0-156 


1-975 


0-313 


2-963 


0-469 


3-951 


0-626 


4-938 


8r 


n 


0-987 


0-161 


1-974 


0-321 


2-961 


0-482 


3-948 


0-643 


4-935 


801- 


H 


0-986 


0-165 


1-973 


0-330 


2-959 


0-495 


3-945 


0-660 


4-931 


80i 


n 


0-986 


0-169 


1-971 


0-339 


2-957 


0-508 


3-942 


0-677 


4-928 


80i 


10° 


0-985 


0174 


1-970 


0-347 


2-954 


0-521 


3-939 


0-695 


4-924 


80° 


lOi 


0-984 


0-178 


1-968 


0-356 


2-952 


0-534 


3-936 


0-712 


4-920 


79f 


lOJ 


0-983 


0-182 


1-967 


0-364 


2-950 


0-547 


3-933 


0-729 


4-916 


1H 


lOf 


0-982 


0-187 


1-965 


0-373 


2-947 


0-560 


3 930 


0-746 


4-912 


79ir 


ir 


0-982 


0-191 


1-963 


0-382 


2-945 


0-572 


3-927 


0-763 


4-908 


79° 


Hi 


0-981 


0-195 


1-962 


0-390 


2-942 


0-585 


S-923 


0-780 


4-904 


781- 


IH 


0-980 


0-199 


1-960 


0-399 


2-940 


0-598 


3-920 


0-797 


4-900 


^78^- 


Hf 


0-979 


0-204 


1958 


0-407 


2-937 


0-611 


3916 


0-815 


4-895 


IS 


ir 


0-978 


0-208 


1-956 


0-416 


2-934 


0-624 


3-913 


0-832 


4-891 


78° 


12ir 


0-977 


0-212 


1-954 


0-424 


2-932 


0-637 


3-909 


0-849 


4-886 


771- 


12i 


0-976 


0-216 


1-953 


0-433 


2-929 


0-649 


3-905 


0-866 


4-881 


77i 


12| 


0-975 


0-221 


1-951 


0-441 


2-926 


0-662 { 


3-901 


0-883 


4-877 


Hi 


13° 


0-974 


0-225 


1-949 


0-450 


2-923 


0-675 1 


3-897 


0-900 


4-872 


77° 


13i 


0-973 


0-229 


1-947 


0-458 


2-920 


0-688 


3-894 


0-917 


4-867 


76f 


13i 


0-972 


0-233 


1-945 


0-467 


2-917 


0-700 1 


3-889 


0-934 


4-862 


76i 


13| 


0-971 


0-238 


1-943 


0-475 


2-914 


0-713 


3-885 


0-951 


4-857 


H 


14° 


0-970 


0-242 


1-941 


0-484 


2-911 


0-726 i 


3-881 


0-968 


4-851 


76° 


14i 


0-969 


0-246 


1-938 


0-492 


2-908 


0-738 j 


3-877 


0-985 


4-846 


75f 


14i 


0-968 


0-250 


1-936 


0-501 


2-904 


0-751 


3-873 


1-002 


4-841 


76i 


U| 


0-967 


0-255 


1-934 


0-509 


2-901 


0-764 


3-868 


1-018 


4-835 


?t 


15° 


0-966 


0-259 


1-932 


0-518 


2-898 


0-776 i 


3-864 


1-035 


4-830 


75° 


W) 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


■t 


1 


] 


1 


J 


i 


; 


t 


S. 


5 



APPENDIX. 



831 









I.ATITUDES 


AND DEPARTURES. 








.w 


5 

Dep. 


O 


7 


8 


» 


bis 


J 


Lat. 


Dep, 

0-000 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


1 


0° 


0-000 


6-000 


7-000 


0-000 


8-000 


0-000 


9-000 


0-000 


90° 


Oh 


0-022 


6-000 


0-026 


7-000 


0-031 


8-000 


0-035 


9-000 


0-039 


89f 


Oi 


0-044 


6-000 


0-052 


7-000 


0-061 


8-000 


0-070 


9-000 


0-079 


SH 


Of 


0065 


5-999 


0-079 


6-999 


0-092 


7-999 


0-105 


8-999 


0-118 


89i 


r 


0-087 


5-999 


0-105 


6-999 


0-122 


7-999 


0-140 


8-999 


0-157 


89° 


H 


0-109 


5-999 


0131 


6-998 


0-153 


7998 


0-175 


8-998 


0-196 


88f 


H 


0131 


5-998 


0-157 


6-998 


0-183 


7-997 


0-209 


8-997 


0-236 


88i 


If 


0-153 


5-997 


0-183 


6-997 


0-214 


7-996 


0-244 


8-996 


0-275 


88i 


2= 


0-174 


5-996 


0-209 


6-996 


0-244 


7-995 


0-279 


8-995 


0-314 


88° 


H 


0-196 


5-995 


0-236 


6-995 


0-275 


7-994 


0-314 


8-993 


0-353 


87f 


H 


0-218 


5-994 


0-262 


6-993 


0-305 


7-992 


0-349 


8-991 


0-393 


87i 


2f 


0-240 


5-993 


0-288 


6-992 


0-336 


7-991 


0-384 


8-990 


0-432 


87i 


3° 


0-262 


5-992 


0-314 


6-i^90 


0-366 


7-989 


0-419 


8-988 


0-471 


8T° 


H 


0-2S3 


5-990 


0-340 


6-989 


0-397 


7-987 


0-454 


8-986 


0-510 


86| 


H 


0-305 


5-9S9 


0-386 


6987 


0-427 


7-985 


0-488 


8-983 


0-549 


86i 


3| 


0-327 


5-9S7 


0-392 


6-985 


0-458 


7-983 


0-523 


8-981 


0-589 


86ir 


4° 


0-349 


5-985 


0-419 


6-983 


0-488 


7-981 


0-558 


8-978 


0-628 


86° 


H 


0-371 


5-984 


0-445 


6-981 


0-519 


7-978 


0-593 


8-975 


0-667 


85f 


H 


0-392 


5-982 


0-471 


6-978 


0-549 


7-975 


0-628 


8-972 


0-706 


85^ 


4| 


0-414 


5-979 


0-497 


6-976 


0-580 


7-973 


0-662 


8-969 


0-745 


85i 


5° 


0-436 


5-977 


0-523 


6-973 


0-610 


7-970 


0-697 


8-966 


0-784 


85° 


H 


0-458 


5-975 


0-549 


6-971 


0-641 


7-966 


0-732 


8-962 


0-824 


841- 


H 


0-479 


5-972 


0-575 


6-968 


0-671 


7-963 


0-767 


8-959 


0-863 


84i 


5f 


0-501 


5-970 


0-601 


6-965 


0-701 


7-960 


0-802 


8-955 


0-902 


84i 


6° 


0-523 


5-967 


0-627 


6-962 


0-732 


7-956 


0-836 


8-951 


0-941 


84° 


6i 


0-544 


5-964 


0653 


6-958 


0-762 


7-952 


0-871 


8-947 


0-980 


83f 


6i 


0-566 


5-961 


0-679 


6-955 


0-792 


7-949 


0-906 


8-942 


1-019 


83i 


6| 


0-588 


5-958 


0-705 


6-951 


0-823 


7-945 


0-940 


8-938 


1-058 


83i 


7° 


0-609 


5-955 


0-731 


6-948 


0-853 


7-940 


0-975 


8-933 


1-097 


83° 


7i 


0-631 


5-952 


0-757 


6-944 


0-883 


7-936 


1-010 


8-928 


1-136 


82| 


n 


0-653 


5-949 


0-783 


6-940 


0-914 


7-932 


1-044 


8-923 


1-175 


82i 


7f 


0-674 


5-945 


0-809 


6-936 


0-944 


7-927 


1-079 


8-918 


1-214 


82i 


8° 


0-696 


5-942 


0-855 


6-932 


0-974 


7-922 


1-113 


8-912 


1-253 


82° 


8i 


0-717 


5-938 


0-861 


6-928 


l-(i04 


7-917 


1-148 


8-907 


1-291 


81f 


8i 


0-739 


5-934 


0-887 


6-923 


1-036 


7-912 


1-182 


8-901 


1-330 


8H 


8| 


0-761 


5-930 


0-913 


6-919 


1-065 


7-907 


1-217 


8-895 


1-369 


81i 


9° 


0-782 


5-926 


0-939 


6-914 


1-095 


7-902 


1-251 


8-889 


1-408 


81° 


n 


0-804 


5-922 


0-964 


6-909 


1-125 


7-896 


1-286 


8-883 


1-447 


80f 


n 


0-825 


5-918 


0-990 


6-904 


1-155 


7-890 


1-320 


8-877 


1-485 


80i 


9| 


0-847 


5-913 


1-016 


6-899 


1-185 


7-884 


1-355 


8-870 


1-524 


80J 


10° 


0-868 


5-909 


1-042 


6-894 


1-216 


7-878 


1-389 


8863 


1-563 


80° 


m 


0-890 


5-904 


1-068 


6-888 


1-246 


7-872 


1-424 


8-856 


1-601 


79f 


10^ 


0-911 


5-900 


1-093 


6-883 


1-276 


7-866 


1-458 


8-849 


1-640 


79i 


10| 


0-933 1 


5-895 


1-119 


6-877 


1-306 


7-860 


1-492 


8-842 


1-679 


79i 




0-954 


5-890 


1-145 


6-871 


1-336 


7-853 


1-526 


8-835 


1-717 


T9° 


Hi 


0-975 


5-885' 


1-171 


6-866 


1-366 


7-846 


1-561 


8-827 


1-756 


78| 


Hi 


0-997 


5-880 


1-196 


6-859 


1-396 


7-839 


1-595 


8-819 


1-794 


78i 


iif 


1-018 


5-874 


1-222 


6-853 


1-425 


7-832 


1-629 


8-811 


1-833 


78i 


12° 


1-040 


5-869 


1-247 


6-847 


1-455 


7-825 


1-663 


. 8-803 


1-871 


78° 


m 


1-061 


5-863 


1-273 


6 841 


1-485 


7-818 


1-697 


8-795 


1-910 


77f 


12i 


1-082 


5-858 


1-299 


6-834 


1-515 


7-810 


1-732 


8-787 


1-948 


m 


12| 


1-103 


5-852 


1-324 


6-827 


1-545 


7-803 


1-766 


8-778 


1-986 


77i 


13° 


1-125 


5-846 


1-350 


6-821 


1-575 


7-795 


1-800 


8-769 


2-025 


77° 


18i 


1-146 


5-840 


1-375 


6-814 


1-604 


7-787 


1-834 


8-760 


2-063 


76f 


13^ 


1-167 I 


5-834 


1-401 


6 807 


1-634 


7-779 


1-868 


8-751 


2-101 


76i 


131 


1-188 


5-828 


1-426 


6-799 


1-664 


7-771 


1-902 


8-742 


2-139 


V6i 


14° 


1-210 


5-822 


1-452 


6-792 


1»693 


7-762 


1-935 


8-733 


2-177 


76° 


Ui 


1-231 


5-815 


1-477 


6-78i 


1-723 


7-754 


1-969 


8-723 


2-215 


m 


14i 


1-252 


5-809 


1-502 


6-777 


1-753 


7-745 


2-003 


8-713 


2-253 


75i 


14f 


1-273 


5-8fl2 


1-528 


6-769 


1-782 


7-736 


2-037 


8-703 


2-291 


V5i 


15° 


1-294 


5-796 


1-553 


6-761 


1-812 


7-727 


2-071 


8-693 


2-329 


75° 


be 


Lat. 
S 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


bc 


J 


e 


» ■ i 


S 1 


» 


J 



832 



APPENDIX. 









LATITUDES 


AND DEPARTURES. 








M 


1 


1 ^ 


3 


4 


5 


^ 


1 


Lat. 


Dep. 

0-259 


1 Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


M 


15° 


0-966 


1-932 


0-518 


2-898 


0-776 


3-864 


1-035 


4-830 


75° 


1-H 


0-965 


0-263 


1-930 


0-526 


2-894 


0-789 


3-859 


1-052 


4-824 


74| 


15i 


0-964 


0-267 


1-927 


0-534 


2-891 


0-802 


3-855 


1-069 


4-818 


74i 


15f 


0-962 


0-271 


1-925 


0-543 


2-887 


0-814 


3-850 


1-086 


4-812 


74i 


16° 


0-961 


0-276 


1-923 


0-551 


2-884 


0-827 


3-845 


1-103 


4-806 


74° 


16i 


0-960 


0-280 


1-920 


0-560 


2880 


0-839 


3-840 


1-119 


4-800 


73f 


16^ 


0-959 


0-284 


1-918 


0-568 


2-876 


0-852 


3-835 


1-136 


4-794 


73i 


16| 


0-958 


0-288 


1-915 


0-576 


2-873 


0-865 


3-830 


1-153 


4-788 


73i: 


17^ 


0-956 


0-292 


1-913 


0-585 


2-869 


0-877 


3-825 


1-169 


4-782 


73° 


m 


0-955 


0-297 


1-910 


0-593 


2-865 


0-890 


8-820 


1-186 


4-775 


72f 


in 


0-954 


0-301 


1-907 


0-601 


2-861 


0-902 


3-815 


1-203 


4-769 


72i 


171 


0-952 


0-305 


1-905 


0-610 


2-857 


0-915 


3-810 


1-220 


4-762 


72i 


18° 


0-951 


0-309 


1-902 


0-618 


2-853 


0-927 


3-804 


1-236 


4-755 


72° 


m 


0-950 


0-313 


1-899 


0-626 


2-849 


0-939 


3-799 


1-253 


4-748 


71f 


m 


0-948 


0-317 


1-897 


0-635 


2-845 


0-952 


3-793 


1-269 


4-742 


m 


181 


0-947 


0-321 


1-894 


0-643 


2-841 


0-964 


3-788 


1-286 


4-735 


71i 


19° 


0-946 


0-328 


1-891 


0-651 


2-837 


0-977 


3-782 


1-302 


4-728 


71° 


19i 


0-944 


0-330 


1-888 


0-659 


2-832 


0-989 


3-776 


1-319 


4-720 


1 70f 


19i 


0-943 


0-334 


1-885 


0-668 


2-828 


1-001 


3-771 


1-335 


4-713 


i 70i 


19| 


0-941 


0-338 


1-882 


0-676 


2-824 


1-014 


3-765 


1-352 


4-706 


70i 


20° 


0-940 


0-342 


1-879 


0-684 


2-819 


1026 


3-759 


1-368 


1 4-698 


! 70° 


20i 


0-938 


0-346 


1-876 


0-692 


2-815 


1-038 


. 3-753 


1-384 


4-691 


: 69f 


20i 


0-937 


0-350 


1-873 


0-700 


2-810 


1-051 


3-747 


1-401 


4-683 


1 69i 


20f 


0-935 


0-354 


1-870 


0-709 


2-805 


1-063 


3-741 


1-417 


4-676 


69i 


21° 


0-934 


0-358 


1-867 


0-717 


2-801 


1-075 


3-734 


1-433 


4-668 


69° 


21i 


0-932 


0-362 


1-864 


0-725 


2-796 


1-087 


3-728 


1-450 


4-660 


i 68f 


21i 


0-930 


0-367 


1-861 


0-733 


2-791 


1-100 


3-722 


1-466 


4-652 


1 68i 


21f 


0-929 


0-371 


1-858 


0-741 


2-786 


1-112 


3-715 


1-482 


4-644 


1 68J 


22° 


0-927 


0-375 


l-8o4 


0-749 


2-782 


1-124 


3-709 


1-498 


4-636 


1 68° 


22i 


0-926 


0-379 


1-851 


0-757 


2-777 


1-136 


3-702 


1-515 


4-628 


67f- 


22^ 


0-924 


0-383 


1-848 


0-765 


2-772 


1-148 


3-696 


1-531 


4-619 


67i 


22f 


0-922 


0-387 


1-844 


0-773 


2-767 


1-160 


3-689 


1-547 


4-611 


67i 


23° 


0-921 


0-391 


1-841 


0-781 


2-762 


1-172 


3-682 


1-563 


4-603 


67° 


23i 


0-919 


0-395 


1-838 


0-789 


2-756 


1-184 


3-675 


1-579 


4-594 


66f 


23i 


0-917 


0-399 


1-834 


0-797 


2-751 


1-196 


3-668 


1-595 


4-585 


66i 


23f 


0-915 


0-403 


1-831 


0-805 


2-746 


1-208 


3-661 


1-611 


4-577 


66i 


24° 


0-914 


0-407 


1-827 


0-813 


2-741 


1-220 


3-654 


1-627 


4-568 


66° 


24i 


0-912 


0-411 


1-824 


0-821 


2-735 


1-232 


3-647 


1-643 


4-559 


65f 


24i 


0-910 


0-415 


1-820 


0-829 


2-730 


1-244 


3-640 


1-659 


4-550 


65i 


241 


0-908 


0-419 


1-816 


0-837 


2-724 


1-256 


3-633 


1-675 


4-541 


65i 


25° 


0-906 


0-423 


1-813 


0-845 


2-719 


1-268 


3-625 


1-G90 


4-532 


65° 


25i 


0-904 


0-427 


1-809 


0-853 


2-713 


1-280 


3-618 


1-706 


4-522 


64f 


25i 


0-903 


0-431 


1-805 


0-861 


2-708 


1-292 


3610 


1-722 


4-513 


64i 


25f 


0-901 


0-434 


1-801 


0-869 


2-702 


1-303 


3-603 


1-738 


4-503 


64i 


26° 


0-899 


0-438 


1-798 


0-877 


2-696 


1-315 


3-595 


1-753 


4-494 


64° 


26i 


0-897 


0-442 


1-794 


0-885 


2-691 


1-327 


3-587 


1-769 


4-484 


63f 


26i 


0-895 


0-446 


1-790 


0-892 


2-685 


1-339 


3-580 


1-785 


4-475 


63^ 


26| 


0-893 


0-450 


1-786 


0-900 


2-679 


1-350 


3-572 


1-800 


4-465 


m 


27° 


0-891 


0-454 


1-782 


0-908 


2-673 


1-362 


3-564 


1-816 


4-455 


63° 


27i 


0-889 


0-458 


1-778 


0-916 


2-667 


1-374 


3-556 


1-831 


4-445 


62f 


27i 


0-887 


0-462 


1-774 


0-923 


2-661 


1-385 


3-548 


1-847 


4-435 


62i 


271 


0-885 


0-466 


1-770 


0-931 


2-655 


1-397 


3-c40 


1-862 


4-425 


^li 


28° 


0-883 


0-469 


1-766 


0-939 


2-649 


1-408 


3-532 


1-878 


4-415 


62° 


28i 


0-881 


0-473 


1-762 


0-947 


2-643 


1-420 


3-524 


1-893 


4-404 


61f 


28i 


0-879 


0-477 


1-758 


0-954 


2-636 


1-431 


3-515 


1-909 


4-394 


6H 


28| 


0-877 


0-481 


1-753 


0-962 


2-630 


1-443 


3-507 


1-924 


4-384 


^H 


29° 


0-875 


0-485 


1-749 


0-970 


2-624 


1-454 


3-498 


1-939 


4-373 


61° 


29J 


0-872 


0-489 


1-745 


0-977 


2-617 


1-466 


3 490 


1-954 


4-362 


60f 


29i 


0-870 


0-492 


1-741 


0-985 


2-611 


1-477 


3-481 


1-970 


4-352 


60^ 


29f 


0-868 


0-496 


1-736 


0-992 


2-605 


1-489 


3-473 


1-985 


4-341 


^^1 


30° 


0-866 


0-500 


1-732 


1000 


2-598 


1-500 


3-464 


2-000 


4-330 


60° 


bb 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


be 


i 


1 1 


2 


! 


4 


5 


1 



APPENDIX. 



833 



liA-TITUDES AND DEPARTURES. 



te 


S 


6 


^ _l 


8 


O 


^ 


1 


Dep. 


Lat. 


Dep. 


Lat. 


1 Dep. 


Lat. 

7-727 


Dep. 


Lat. 


Dep. 


1 


15° 


1294 


5-796 


1-553 


6-761 


1-812 


2-071 


8-693 


2-329 


^5° 


m 


1-315 


5-789 


1-578 


6-754 


1-841 


7-718 


2-104 


8-683 


2 367 


741 


15.i 


1-336 


5-782 


1-603 


6-745 


1-871 


7-709 


2-138 


8-673 


2-405 


m 


U'i 


1-357 


5-775 


1-629 


6737 


1-900 


7-700 


2-172 


8-662 


2-448 


741 


1«° 


1-378 


5-768 


1-654 


6-729 


1-929 


7-690 


2-205 


8-661 


2-481 


74° 


16ir 


1-399 


5-760 


1679 


6720 


r9;)9 


7-680 


2-239 


8-640 


2-518 


73f 


16.i 


1-420 


5-753 


1-704 


6-712 


1-988 


7-671 


2-272 


8-629 


2-556 


73i 


16^ 


1-441 


5-745 


1-729 


6-703 


2-017 


7-661 


2-306 


8-618 


2-594 


731 


17° 


1-462 


5-738 


1-754 


6-694 


2-('47 


7-650 


2-339 


8-607 


2-631 


73° 


17i 


1-483 


5-730 


1-779 


6-685 


2-076 


7-640 


2-372 


8-595 


2-669 


72f 


in 


1-504 


5-722 


1-804 


6-676 


2-105 


7-630 


2-406 


8-583 


2-706 


72i 


171 


1-524 


5-714 


1-829 


6-667 


2-134 


7-619 


2439 


8-572 


2-744 


721 


18° 


1-545 


5-706 


1-854 


6-657 


2-163 


7-608 


2-472 


8-560 


2-781 


72° 


m 


1-566 


5-698 


1-879 


6-648 


2-192 


7 598 


2-505 


8-547 


2-818 


71f 


m 


1-587 


5-690 


1-904 


6-638 


2-221 


7-587 


2-538 


8-636 


2-856 


ni 


m 


1-607 


5-6S2 


1929 


6-629 


2-250 


7-575 


2-572 


8-622 


2-893 


71^ 


19° 


1-628 


5-673 


1-953 


6-619 


2-279 


7-564 


2-605 


8-610 


2-930 


19i 


1-648 


5-665 


1-978 


6-609 


2-308 


1 7-553 


2-638 


8-497 


2-967 


70f 


19.} 


1-669 


5-656 


2-003 


6-598 


2-337 


I 7-541 


2-670 


8-484 


3-004 


70i 


19f 


1-690 


5-647 


2-028 


6-588 
6-578 


2-365 


7-529 


2-703 


8-471 


3-041 


'^01 


20° 


1 1-710 


5-638 


2-A52 


2 394 


7-518 


2-736 


8-457 


3-078 


70° 


20i- 


1-731 


5-629 


2-077 


6-567 


2-423 


1 7-506 


2-769 


8-444 


8-115 


' 69f 


20i 


1-751 


5-620 


2-101 


6-557 


2-451 


7-493 


2-802 


8-430 


3-152 


69i 


20| 


1-771 


5-611 


2-126 


6-546 


2-480 


7-481 


2-834 


8-416 


3-189 


69i 


21 


1-792 


5-601 


2-150 


6-535 


2-509 


7-469 


2-867 


8-402 


8-226 


69° 


21i 


1-812 


5-592 


2-175 


6-524 


2-537 


7-456 


2-900 


8-388 


8-262 


68f 


2H 


1-833 


5-582 


2-199 


6-513 


2-566 


7-443 


2-932 


8-374 


8-299 


68^ 


21f 


1-853 


5-573 


2-223 


6-502 


2-594 


7-430 


2-964 


8-869 


3-835 


681r 


22° 


1-873 


5-563 


2-248 


6-490 


2-622 


7-417 


2-997 


8-S46 


3-371 


68° 


221 


1-893 


5-553 


2-272 


6-479 


2-651 


7-404 


8-029 


8-830 


8-408 


67f 


22} 


1-913 


5-543 


2-296 


6-467 


2-679 


7-£91 


3 -(61 


8-315 


8-444 


67i 


22J 


1-934 


5-533 


2-320 


6-455 


2-707 


7-378 


3-094 


8-800 


8-480 


evi 


23° 


l-95i 


5-523 


2-344 


6-444 


2-735 


7-364 


8-126 


8-285 


3-517 


67° 


231 


1-974 


5-513 


2-368 


6-432 


2 763 


7-350 


3-158 


8-269 


8-6£3 


66f 


23.^ 


1-994 


5-502 


2-392 


6-419 


2-791 


7-336 


3-190 


8-254 


3-5S9 


66i 


231 


2-014 


5-492 


2-416 


6-407 


2-819 


7-322 


8-222 


8-288 


3-625 


661 


24° 


2-034 


5-481 


2-440 


6-395 


2-847 


7-308 


3-254 


8-222 


8-661 


66° 


241 


2-054 


5-471 


2-464 


6-382 


2-875 


7-294 


3-286 


8-206 


3-696 


65f 


m 


2-073 


5-460 


2-488 


6-370 


2-903 


7-280 


3-318 


8-190 


3-732 


65} 


241 


2-093 


5-449 


2-512 


6-357 


2-931 


7-265 


3-849 


8-173 


8-768 


! 651 


25° 


2-113 


5-438 


2-536 


6-344 


2-958 


7-250 


3-881 


8-157 


3-804 


"65°" 


251 


2-133 


6-427 


2-559 


6-331 


2-986 


7-236 


3-413 


8-140 


3-839 


64f 


25i 


2-153 


5-416 


2-583 


6-318 


3-014 


7-221 


3-444 


8-123 


3-876 


H4i 


25| 


2-172 


5-404 


2-607 


6-303 


3-041 


7-206 


S-476 


8-106 


3-910 


641 


26° 


2-192 


5-393 


2-630 


6-292 


3-069 


7-190 


8-507 


8-089 


3-945 


64° 


261 


2-211 


5-381 


2-654 


6-278 


3096 


7175 


3-588 


8-(i72 


8-981 


63f 


26} 


2-231 


5-370 


2-677 


6-265 


3-123 


7160 


8-670 


8-064 


4-016 


68i 


26| 


2250 


5-358 


2-701 


6-251 


3151 


7144 


3-601. 


8-087 


4-051 


631 


27° 


2-270 


5-346 


2-724 


6-237 


3-178 


7-128 


3-632 


8-019 


4086 


63° 


271 


2-289 


5-334 


2-747 


6-223 


3-205 


7-112 


8-663 


8-001 


4-121 


62f 


27i 


2-309 


5-322 


2-770 


6-209 


3-232 


7-096 


8-694 


7983 


4-156 


62i 


27| 


2-328 


5-310 


2-794 


6-195 


3-259 


7-080 


3-725 


7-965 


4190 


621 


28° 


2-347 


5-298 


2-817 


6-181 


3-286 


7-064 


3-756 


7-947 


4-226 


62° 


281 


2-367 


5-285 


2-840 


6-166 


3-313 * 


7-047 


3-787 


7-928 


4-260 


61f 


28i- 


2-386 


5-273 


2-863 


6-152 


3-340 


7-031 


3-817 


7-909 


4294 


61i 


281 


2-405 


5-260 


2-886 


6-137 


3-367 


7-014 


3-848 


7-891 


• 4-329 


611 


29° 


2-424 


5-248 


2-909 


6-122 


3-394 


6-997 


3-H78 


7-872 


4-363 


61° 


291 


2-443 


5-235 


2-932 


6-107 


3-420 


6-980 


3-909 


7-852 


4-398 


60| 


29.^ 


2-462 


5-222 


2-955 


6-093 


3-447 


6-963 


3-939 


7-833 


4-432 


60i 


29| 


2-481 


5-209 


2-977 


6-077 


3-474 


6-946 


3-970 


7-814 


4-466 


601 


30° 


2-500 


5-196 


3-000 


6-062 


S-500 


6-928 


4-000 


7-794 


4-600 


60° 




Lat. 
5 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


i 


• J 


1 


7 


S I 


9 


M 



54 



834 



APPENDIX. 









LATITUDES 


AND DEPAKTURES. 








^ 


1 


1 ^ 


3 


A 


Lat. 


^ 


1 


Lat. 

0-866 


Dep. 


1 Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


1 


30° 


0-500 


1 1-732 


1-000 


2-598 


1-500 


3-464 


2-000 


4-330 


60° 


30i 


0-864 


0-504 


! 1-728 


1-008 


2-592 


1-511 


3-455 


2-015 


4-319 


59| 


m 


0-862 


0-508 


1-723 


1-015 


2-585 


1-523 


3-447 


2-030 


4-308 


69i 


30f 


0-859 


0-511 


1-719 


1-023 


2-578 


1-534 


3-438 


2-045 


4-297 


59i 


31° 


0-857 


0-515 


1-714 


1-030 


2-572 


1-545 


3-429 


2-060 


4-286 


59° 


31i 


0-855 


0-519 


1-710 


1-038 


2-565 


1-556 


3-420 


2-075 


4-275 


o8f 


31i 


0-853 


0-522 


1-705 


1-045 


2-558 


1-567 


3-411 


2-090 


4-263 


68i 


31f 


0-850 


0-526 


1-701 


1-052 


2-551 


1-579 


3-401 


2-105 


4-252 


58i 


32° 


0-848 


0-530 


1-696 


1-060 


2-544 


1-590 


3-392 


2-120 


4-240 


58° 


32i 


0-846 


0534 


1-691 


1-067 


2-537 


1-601 


8-383 


2-134 


4-229 


57f 


32^ 


0-843 


0-537 


1-687 


1-075 


2-530 


1-612 


3-374 


2-149 


4-217 


67i 


32f 


0-841 


0-541 


1-682 


1-082 


2-523 


1-623 


3-364 


2-164 


4-205 


m 


33° 


0-839 


0-545 


1-677 


1-089 


2-516 


1-634 


3-355 


2-179 


4-193 


5T° 


33i 


0-836 


0-548 


1-673 


1-097 


2-509 


1-645 


8-345 


2-193 


4-181 


56f 


33^ 


0-834 


0-552 


1-668 


1-104 


2-502 


1-656 


3-336 


2-208 


4-169 


56i 


33| 


0-831 


0-556 


1-663 


1-111 


2-494 


1-667 


3-326 


2-222 


4-157 


56i 


34° 


0-829 


0-559 


1-658 


1-118 


2-487 


1-678 


3-316 


2-237 


4-145 


56° 


34J 


0-827 


0-563 


1-653 


1-126 


2-480 


1-688 


3-306 


2-251 


4-188 


66f 


34i 


0-824 


0-566 


1-648 


1-133 


2-472 


1-699 


3-297 


2-266 


4121 


66i 


341 


0-822 


0-570 


1-643 


1-140 


2-465 


1-710 


3-287 


2-280 


4-108 


55i 


35° 


0-819 


0-574 


1-638 


1-147 


2-457 


1721 


3-277 


2-294 


1 4-096 


55° 


35J 


0-817 


0-577 


1-633 


1-154 


2-450 


1-731 


3-267 


2-309 


4-083 


54f 


35i 


0-814 


0-581 


1-628 


1-161 


2-442 


1-742 


3-257 


2-323 


4-071 


64i 


35f 


0-812 


0-584 


1-623 


1-168 


2-435 


1-763 


3-246 


2-887 


4-068 


64i 


36° 


0-809 


0-588 


1-618 


1-176 


2-427 


1-763 


3-236 


2-851 


4-045 


54° 


36i 


0-806 


0-591 


1-613 


1-183 


2-419 


1-774 


3-226 


2-865 


4-032 


63f 


36^ 


0-804 


0-595 


1-608 


1-190 


2-412 


1-784 


3-215 


2-879 


4-019 


5H 


36| 


0-801 


0-598 


1-603 


1-197 


2-404 


1-795 


3-205 


2-893 


4-006 


53i 


31° 


0-799 


0-602 


1-597 


1-204 


2-396 


1-805 


3-195 


2-407 


3-993 


53° 


37i 


0-796 


0-605 


1-592 


1-211 


2-388 


1-816 


3-184 


2-421 


3-980 


62f 


3n 


0-793 


0-609 


1-587 


1-218 


2-380 


1-826 


3-173 


2-435 


3-967 


62i 


371 


0-791 


0-612 


1-581 


1-224 


2-372 


1-837 


3-163 


2-449 


3-953 


52i 


38° 


0-788 


0-616 


1-576 


1-231 


2-364 


1-847 


3-152 


2-463 


3-940 


52° 


381 


0-785 


0-619 


1-571 


1-238 


2-356 


1-857 


3-141 


2-476 


3-927 


61f 


38i 


0-783 


0-623 


1-565 


1-245 


2-348 


1-868 


3-130 


2-490 


3-913 


51i 


38| 


0-780 


0-626 


1-560 


1-252 


2-340 


1-878 


3-120 


2-504 


3-899 


51ir 


39° 


0-777 


0-629 


1-554 


1-259 


2-331 


1-888 


3-109 


2-517 


3-886 


51° 


39J 


0-774 


0-633 


1-549 


1-265 


2-323 


1-898 


3-098 


2-. 31 


3-872 


50f 


39i 


0-772 


0-636 


1-543 


1-272 


2-315 


1-908 


3-086 


2-544 


3-858 


60i 


39| 


0-769 


0-639 


1-538 


1-279 


2-307 


1-918 


3-075 


2-558 


3-844 


50i 


40° 


0-766 


0-643, 


1-532 


1-286 


2-298 


1-928 


3-064 


2-571 


3-830 


50° 


40^ 


0-763 


0-646 


1-526 


1-292 


2-290 


1-938 


3-053 


2-584 


3-816 


49f 


40J 


0-760 


0-649 


1-521 


1-299 


2-281 


1-948 


3042 


2-598 


3-802 


49i 


40| 


0-758 


0-653 


1-515 


1-306 


2-273 


1-958 


3-030 


2-611 


3-788 


49i 


41° 


0-755 


0-656 


1-509 


1-312 


2-264 


1-968 


3 019 


2-624 


8-774 


49° 


41i 


0-752 


0-659 


1-504 


1-319 


2-256 


1-978 


3-007 


2-637 


3-759 


48f 


41i 


0-749 


0-663 


1-498 


1-325 


2-247 


1-988 


2-996 


2-650 


3-745 


m 


41| 


0-746 


0-666 


1-492 


1-332 


2-238 


1-998 


2-984 


2-664 


3-730 


m 


42° 


0-743 


0-669 


1-486 


1-338 


2-229 


2-007 


2-973 


2-677 


3-716 


48° 


42i 


0-740 


0-672 


1-480 


1-345 


2-221 


2-017 


2-961 


2-689 


3-701 


47f 


42^ 


0-737 


0-676 


1-475 


1-351 


2-212 


.2-027 


2-949 


2-702 


8-686 


47i 


42f 


0-734 


0-679 


1-469 


1-358 


2-203 


2-036 


2-937 


2-715 


3-672 


47i 


43° 


0-731 


0-682 


1-463 


1-364 


2-194 


2-046 


2-925 


2-728 


3-657 


47° 


431 


0-728 


0-685 


1-457 


1-370 


2-185 


2-056 


2-918 


2-741 


3-642 


46f 


43i 


0-725 


0-688 


1-451 


1-377 


2-176 


2-065 


2-901 


2-753 


3-627 


46i 


43| 


0-722 


0-692 


1-445 


1-383 


2-167 


2-075 


2-889 


2-766 


3-612 


46i 


44° 


0-719 


0-695 


1-489 


1-389 


2-158 


2-084 


2-877 


2-779 


3-597 


46° 


44i 


0-716 


0-698 


1-433 


1-396 


2-149 


2-093 


2-865 


2-791 


8-582 


45f 


44i 


0-713 


0-701 


1-427 


1-402 


2-140 


2-103 


2-853 


2-804 


3-566 


45i 


44f 


0-710 


0-704 


1-420 


1-408 


2-131 


2-112 


2-841 


2-816 


8-551 


^^i 


45° 


0-707 


1707 


1-414 


1-414 


2-121 


2-121 


2 828 


2-828 


3-536 


45° 


tab 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 
5 


bo 

.s 


1 


1 


' ' 2 


3 1 


■ A 


J 



APPENDIX. 



835 









I.ATITUDES AND 


DEPARTURES. 








^ 


5 


6 


7 


! 8 


O 


t 


i 


Dep. 


Lat. 


\ Dep. 


Lat. 


Dep. 


! Lat. 


Dep. 1 


Lat. 


Dep. 


•c 

M 


30° 


2-500 


5-196 


1 3 000 


6-062 


3-500 


! 6-928 


4-000 


7-794 


4-500 


60° 


30i 


2-519 


5-183 


j 3-023 


i 6-047 


3-526 


6-911 


4-030 , 


7-775 


4534 


591 


80^ 


2-538 


5-170 


3-045 


6-031 


3-553 


6-893 


4-060 


7-755 


4-568 


59i 


30| 


2-556 


5-156 


3-068 


6016 


3-579 


1 6-875 


4-090 


7 735 


4-602 


69i 


31° 


2-575 


5-143 


3-090 


6-000 


3-605 


; 6-857 


4-120 


7-715 


4-635 


59° 


31i 


2-594 


5129 


3 113 


5-984 


3-631 


6-839 


4-150 i 


7-694 


4-669 


68f 


3H 


2-612 


5-116 


3-135 


5-968 


3-657 


6-821 


4-180 j 


7-674 


4-702 


58i 


31f 


2-631 


5-102 


3157 


5-952 


3-683 


6-803 


4-210 


7-653 


4-736 


58i 


32° 


2-650 


5-088 


3-180 


5-936 


3-709 


6-784 


4-239 


7-632 


4-769 j 


58° 


^2i 


2-668 


5074 


3-202 


5-920 


3-735 


6-766 


4-269 


7-612 


4-802 1 


57f 


32i 1 


1 2-686 


5-060 


3-224 


5-904 


3-761 


6-747 


4-298 


7-591 


4-836 


m 


32| i 


2-705 


5-046 


3-246 


5-887 


8-787 


6728 


1 4-328 


7-569 


4-869 


57i 


33° 


2-723 


5-032 


3-268 


5-871 


8-812 


6-709 


4-357 


7-548 


4-902 


57° 


33i j 


2-741 1 


5-018 


3-290 


5-854 


3-838 


6-690 


t 4-386 


7-527 


' 4-935 


56| 


33i 


2-760 


5-003 


3-312 


5-837 


8-864 


6-671 


4-416 


7-505 


4-967 


66i 


33f 1 


2-778 ! 


4-989 


3333 


5-820 


3-889 


6-652 


4-445 


7-483 


5-000 


56i 


34° 


2-796 i 


4-974 


3-355 


5-803 


8-914 


6-632 


, 4-474 


7-461 


5-033 


56° 


34i 


2-814 i 


4-960 


3-377 


5-786 


8-940 


6-613 


4-502 


7-439 


6-065 


65f 


34^ 


2-832 


4-945 


3-398 


5-769 


8-965 


'■ 6-593 


4-531 


7-41'? 


5-098 


55i 


34f 


2-850 


4-930 


3-420 


5-752 


8-990 


6-573 


4-560 


7-395 


5-130 


55i 


35° 


2-868 1 


4-915 


3-441 


5-734 


4-015 


6-653 


4-589 


1 7-372 


5-162 


1r 


35i 


2-886 


4-900 


3-463 


5-716 


4-040 


6-533 


4-617 


7-350 


5-194 


54f 


35i 


2-904 


4-885 


3-484 


5-699 


4-065 


6-513 


4-646 


7-327 


5-226 


54i 


35| 


2-921 


4-869 


3-505 


5-681 


4090 


6-493 


4-674 


7-304 


1 5-258 


54i 


36° 


2-939 


4-854 


3-527 


5-663 


4115 


6-472 


4-702 


7-281 


! 5-290 


54° 


36i 


2-957 


4-839 


3-548 


5-645 


4-139 


6-452 


4-730 


7-2E8 


5-322 


53f 


36i 


2 974 


4-823 


3-569 


5-627 


4164 


6-431 


4-759 


7-235 


5-353 


53^ 


36f 


2-992 


4-808 


3-590 


5-609 


4-188 


6-410 


4-787 


7-211 


j 5-385 


53i 


37° 


3-009 


4-792 


3-611 


5-590 


4-213 


6-389 


4-815 


7-188 


1 5-416 


53° 


37i 


3-026 


4-776 


3-632 


5-572 


4-237 


6-368 


4-842 


7-164 


5-448 


62f 


37i 


3044 


4-760 


3-653 


5-554 


4-261 


6-347 


4-870 


7-140 


5-479 


62i 


371 


3-061 


4-744 


3-673 


5-535 


4-286 


6-326 


4-898 


7-116 


5-510 


52i 


38° 


3-078 


4-728 


3-694 


5-516 


4-310 


6-304 


4-925 


7-092 


5-541 


52° 


38J 


3095 


4-712 


3-715 


5-497 


4-334 


6-283 


4-958 


7-068 


5-572 


51f 


38i 


3-113 


4-696 


3-735 


5-478 


4-358 


6-261 


4-980 


7-043 


5-603 


5H 


38| ! 


3-130 


4-679 


3-756 


5-459 


4-381 


6-239 


5-007 


7-019 


6-633 


51i 


39° i 


3-147 


4-663 


3-776 


5-440 


4-405 


6-217 


6-035 


6 994 


5-664 


51° 


39i 1 


3-164 j 


4-646 


3-796 


5-421 


4-429 


6-195 


5-062 ; 


6-970 


6-694 i 


50f 


39^ 1 


3-180 1 


4-630 


3-816 


5-401 


4-453 


6173 


6-089 


6-945 


5-725 


60^ 


391 1 


3-197 


4-613 


3-837 


5-382 


4-476 


6-151 


5-116 


6-920 


5-755 


60i 


40° 


3-214 


4-596 


3-857 


5-362 


4-500 


6-128 


5-142 


6-894 


5-785 i 


50° 


40ir 


3-231 j 


4-579 


3-877 


5-343 


4-523 


: 6-106 


5-169 


6-869 


6-815 


49f 


m 


3-247 1 


4-562 


3-897 


5-323 


4-546 


1 6-083 


5-196 


6-844 


5-845 


49i 


m 1 


3-264 


4-545 


3-917 


5-303 


4-569 


1 6-061 


5-222 


6-818 


5-875 


49i 


41° 


3-280 


4-528 


3-936 


5-283 


4-592 


6-038 


5-248 


6-792 


5-905 


49° 


41i 


3-297 I 


4-511 


3-956 


5-263 


4-615 


6-015 


5-275 


6-767 


6-934 


481 


4H 


3-313 


4-494 


3-976 1 


5-243 


4-638 


j 6-992 


5-301 


6-741 


5-964 ; 


48i 


41f 


3-329 j 


4-476 


3-995 


5-222 


4-661 


5-968 


5-327 1 


6-715 


5-993 


48i 


42° 


3-346 


4-459 


4-015 


5-202 


4-684 


5-945 


5-353 ' 


6-688 


6-022 1 


48° 


42i 


3-362 


4-441 


4-034 


5-182 


4-707 


5-922 


5-379 ' 


6-662 


6-051 


47f 


42^ 


3-378 


4-424 


4-054 


5-161 


4-729 


5-898 


5-405 i 


6-635 


6080 


m 


42| 


3-394 


4-406 


4-073 


5-140 


4-752 


5-875 


5-430 ' 


6-609 


6-109 i 


47i 


43° 


3-410 


4-388 


4-092 


5-119 


4-774 


5-851 


5-456 


6-582 


6-138 j 


47° 


43i 


3-426 ' 


4-370 


4-111 


5-099 


4-796 


5-827 


5-481 


6-555 


6-167 


461 


43i 


3-442 i 


4-352 


4-130 


5-078 


4-818 


5-803 


5-507 


6-528 


6-195 


46i 


43f 


3-458 


4-334 


4-149 


5-057 


4-^41 


5-779 


5-532 


6-501 


6-224 1 46ir 


44° 


3-473 ' 


4-316 


4-168 


5-035 


4-863 


5-755 


5-557 


6-474 


6-252 1 46° 


44i 


3-489 


4-298 


4-187 


5-014 


4-885 


5-730 


5-582 


6-447 


6-280 45| 


44^ 


3-505 


4-280 


4-206 


4-993 


4-906 


5-706 


5-607 


6-419 


6-308 : 45i 


44f 


3-520 


4-261 


4-224 


4-971 


4-928 


5-681 


5-632 


6-392 ! 


6-336 1 45i 


45° 


3-536 


4-243 


4-243 


4.950 


4-950 


5-657 


5-657 ! 


6-364 i 

1 


6-364 1 

1! 


45° 




Lat. 


Dep. 


Lat. 




Dep. 


Lat. 


Dep. 


Lat. 


Dep. 1 
S 


Lat. 1 


1 


J 


s 


•s 




® I 


M 



APPENDIX. 



NATURAL. SINES AND COSINES. 





o« 


1» 


3" 


3° 


4,0 




/ 


Sine. 


Cosine. 


Sine. 


Cosine. 


Sine. 


Cosine. 


Sine. 


Cosine. 


Sine. 


Cosine. 


/ 





00000 


Unit. 


01745 


99985 


03490 


99939 


05234 


99863 


06976 


99756 


60 


1 


00029 


Unit. 


01774 


99984 


03519 


99938 


05263 


99861 


07005 


99754 


59 


2 


00058 


Unit. 


01803 


99984 


03548 


99937 


05292 


99860 


07034 


99752 


58 


3 


00087 


Unit. 


01832 


99983 


03577 


99936 


05321 


99858 


07063 


99750 


57 


4 


00116 


Unit. 


01862 


99983 


03606 


99935 


05350 


99857 


07092 


99748 


56 


5 


00145 


Unit. 


01891 


99982 


03635 


99934 


05379 


99855 


07121 


99746 


55 


6 


00175 


Unit. 


01920 


99982 


03664 


99933 


05408 


99854 


07150 


99744 


54 


7 


00204 


Unit. 


01949 


99981 


03693 


99932 


05437 


99852 


07179 


99742 


53 


8 


00233 


Unit. 


01978 


99980 


03723 


99931 


05466 


99851 


07208 


99740 


52 


9 


00262 


Unit. 


02007 


99980 


03752 


99930 


05495 


99849 


07237 


99738 


51 


10 


00291 


Unit. 


02036 


99979 


03781 


99929 


05524 


99847 


07266 


99736 


50 


11 


00320 


99999 


02065 


99979 


03810 


99927 


05553 


99846 


07295 


99734 


49 


12 


00349 


99999 


02094 


99978 


03839 


99926 


05582* 


99844 


07324 


99731 


48 


13 


00378 


99999 


02123 


99977 


03868 


99925 


05611 


99842 


07353 


99729 


47 


14 


00407 


99999 


02152 


99977 


03897 


99924 


05640 


99841 


07382 


99727 


46 


15 


00436 


99999 


02181 


99976 


03926 


99923 


05669 


99839 


07411 


99725 


45 


16 


00465 


99999 


02211 


99976 


03955 


99922 


05698 


99838 


07440 


99723 


44 


17 


00495 


99999 


02240 


99975 


03984 


99921 


05727 


99836 


07469 


99721 


43 


18 


00524 


99999 


02269 


99974 


04013 


99919 


05756 


99834 


07498 


99719 


42 


19 


00553 


99998 


02298 


99974 


04042 


99918 


05785 


99833 


07527 


99716 


41 


20 


00582 


99998 


02327 


99973 


04071 


99917 


05814 


99831 


07556 


99714 


40 


21 


00611 


99998 


02356 


99972 


04100 


99916 


05844 


99829 


07585 


99712 


39 


22 


00640 


99998 


02385 


99972 


04129 


99915 


05873 


99827 


07614 


99710 


38 


23 


00669 


99998 


02414 


99971 


04159 


99913 


05902 


99826 


07643 


99708 


37 


24 


00698 


99998 


02443 


99970 


04188 


99912 


05931 


99824 


07672 


99705 


36 


25 


00727 


99997 


02472 


99969 


04217 


99911 


05960 


99822 


07701 


99703 


35 


26 


00756 


99997 


02501 


99969 


04246 


99910 


05989 


99821 


07730 


99701 


34 


27 


00785 


99997 


02530 


99968 


04275 


99909 


06018 


99819 


07759 


99699 


33 


28 


00814 


99997 


02560 


99967 


04304 


99907 


06047 


99817 


07788 


99696 


32 


29 


00844 


99996 


02589 


99966 


04333 


99906 


06076 


99815 


07817 


99694 


31 


30 


00873 


99996 


02618 


99966 


04362 


99905 


06105 


99813 


07846 


99692 


30 


31 


00902 


99996 


02647 


99965 


04391 


99904 


06134 


99812 


07875 


99689 


29 


32 


00931 


99996 


02676 


99964 


04420 


99902 


06163 


99810 


07904 


99687 


28 


33 


00960 


99995 


02705 


99963 


04449 


99901 


06192 


99808 


07933 


99685 


27 


34 


00989 


99995 


02734 


99963 


04478 


99900 


06221 


99806 


07962 


99683 


26 


35 


01018 


99995 


02763 


99962 


04507 


99898 


06250 


99804 


07991 


99680 


25 


36 


01047 


99995 


02792 


99961 


04536 


99897 


06279 


99803 


08020 


99678 


24 


37 


01076 


99994 


02821 


99960 


04565 


99896 


06308 


99801 


08049 


99676 


23 


38 


01105 


99994 


02850 


99959 


04594 


99894 


06337 


99799 


08078 


99673 


22 


39 


01134 


99994 


02879 


99959 


04623 


99893 


06366 


99797 


08107 


99671 


21 


40 


01164 


99993 


02908 


99958 


04653 


99892 


06395 


99795 


08136 


99668 


20 


41 


01193 


99993 


02938 


99957 


04682 


99890 


06424 


99793 


08165 


99666 


19 


42 


01222 


99993 


02967 


99956 


04711 


99889 


06453 


99792 


08194 


99664 


18 


43 


01251 


99992 


02996 


99955 


04740 


99888 


06482 


99790 


08223 


99661 


17 


44 


01280 


99992 


03025 


99954 


04769 


99886 


06511 


99788 


08252 


99659 


16 


45 


01309 


99991 


03054 


99953 


04798 


99885 


06540 


99786 


08281 


99657 


15 


46 


01338 


99991 


03083 


99952 


04827 


99883 


06569 


99784 


08310 


99654 


14 


47 


01367 


99991 


03112 


99952 


04856 


99882 


06598 


9.9782 


08339 


99652 


13 


48 


01396 


99990 


03141 


99951 


04885 


99881 


06627 


99780 


08368 


99649 


12 


49 


01425 


99990 


03170 


99950 


04914 


99879 


06656 


99778 


08397 


99647 


11 


50 


01454 


99989 


03199 


99949 


04943 


99878 


06685 


99776 


08426 


99644 


10 


51 


01483 


99989 


03228 


99948 


04972 


99876 


06714 


99774 


08455 


99642 


9 


52 


01513 


99989 


03257 


99947 


05001 


99875 


06743 


99772 


08484 


99639 


8 


53 


01542 


99988 


03286 


99946 


05030 


99873 


06773 


99770 


08513 


99637 


7 


54 


01571 


99988 


03316 


99945 


05059 


99872 


06802 


99768 


08542 


99635 


6 


55 


01600 


99987 


03345 


99944 


0.5088 


99870 


06831 


99766 


08571 


99632 


5 


56 


01629 


99987 


03374 


99943 


05117 


99869 


06860 


99764 


08600 


99630 


4 


57 


01658 


99986 


03403 


99942 


05146 


99867 


06889 


99762 


08629 


99627 


3 


58 


01687 


99986 


03432 


99941 


05175 


99866 


06918 


99760 


08658 


99625 


2 


59 


01716 


99985 


03461 


99940 


05205 


99864 


06947 


99758 


08687 


99622 


1 


60 


01745 


99985 


03490 


99939 


05234 


99863 


06976 


99756 


08716 


99619 







Cosine. 


Sine. 


Cosine. 


Sine. 


Cosine. 


Sino. 


Cosine. 


Sine. 


Cosine. 


Sine. 




f 


H 


[)° 


8. 


^o 1 


8' 


7^ 


8< 


3° 


8r 


5° 


/ 



APPENDIX. 



837 



NATURAL. SINES AND COSINBS. 





r.. I 


GO 


T-o 


8« 


9» 




/ 


Sine. 


Cosine. 


Bine. 


Cosine. 


Sine. 


Cosine. 


Sine. 


Cosine. 


Sine. 


Cosine. 


/ 





08716 


99619 


10453 


99452 


' 12187 


99255 


13917 


99027 


15643 


98769 


60 


1 


08745 


99617 


10482 


99449 


12216 


99251 


13946 


99023 


15672 


987G4 


59 


2 


08774 


99614 


10511 


99446 


12245 


99248 


13975 


99019 


15701 


98760 


58 


3 


08803 


99612 


10540 


99443 


12274 


99244 


14004 


99015 


15730 


98755 


57 


4 


08831 


99609 


10569 


99440 


12302 


99240 


14033 


99011 


15758 


98751 


56 


5 


08860 


99607 


10597 


99437 


12331 


99237 


14061 


99006 


15787 


98746 


55 


6 


08889 


99604 


10626 


99434 


12360 


99233 


14090 


99002 


15816 


98741 


54 


7 


08918 


99602 


10655 


99431 


12389 


99230 


14119 


98998 


15845 


98737 


53 


8 


08947 


99599 


10684 


99428 


12418 


99226 


14148 


98994 


15873 


98732 


52 


9 


08976 


99596 


10713 


99424 


12447 


99222 


14177 


98990 


15902 


98728 


51 


10 


09005 


99594 


10742 


99421 


12476 


99219 


14205 


98986 


15931 


98723 


50 


11 


09034 


99591 


10771 


99418 


12504 


99215 


14234 


98982 


15959 


98718 


49 


12 


09063 


99588 


10800 


99415 


12533 


99211 


14263 


98978 


15988 


98714 


48 


13 


09092 


99586 


10829 


99412 


12562 


99208 


14292 


98973 


16017 


98709 


47 


14 


09121 


99583 


10858 


99409 


12591 


99204 


14320 


98969 


16046 


98704 


46 


15 


09150 


99580 


10887 


99406 


12620 


99200 


14349 


98965 


16074 


98700 


45 


16 


09179 


99578 


10916 


99402 


12649 


99197 


14378 


98961 


16103 


98695 


44 


17 


09208 


99575 


10945 


99399 


12678 


99193 


14407 


98957 


16132 


98690 


43 


18 


09237 


99572 


10973 


99396 


12706 


99189 


14436 


98953 


16160 


98686 


42 


19 


09266 


99570 


11002 


99393 


12735 


99186 


14464 


98948 


16189 


98681 


41 


20 


09295 


99567 


11031 


99390 


12764 


99182 


14493 


98944 


16218 


98676 


40 


21 


09324 


99564 


11060 


99386 


12793 


99178 


14522 


98940 


16246 


98671 


39 


22 


09353 


99562 


11089 


99383 


12822 


99175 


14551 


98936 


16275 


98667 


38 


23 


09382 


99559 


11118 


99380 


12851 


99171 


14580 


98931 


16304 


98662 


37 


24 


09411 


99556 


11147 


99377 


12880 


99167 


14608 


98927 


16333 


98657 


36 


25 


09440 


99553 


11176 


99374 


12908 


99163 


14637 


98923 


16361 


98652 


35 


26 


09469 


99551 


11205 


99370 


12937 


99160 


14666 


98919 


16390 


98648 


34 


27 


09498 


99548 


11234 


99367 


12966 


99156 


14695 


98914 


16419 


98643 


33 


28 


09527 


99545 


11263 


99364 


12995 


99152 


14723 


98910 


16447 


98638 


32 


29 


09556 


99542 


11291 


99360 


13024 


99148 


14752 


98906 


16476 


98633 


31 


30 


09585 


99540 


11320 


99357 


13053 


99144 


14781 


98902 


16505 


98629 


30 


31 


09614 


99537 


11349 


99354 


13081 


99141 


14810 


98897 


16533 


98624 


29 


32 


09642 


99534 


11378 


99351 


13110 


99137 


14838 


98893 


16562 


98619 


28 


33 


09671 


99531 


11407 


99347 


13139 


99133 


14867 


98889 


16591 


98614 


27 


34 


09700 


99528 


11436 


99344 


13168 


99129 


14896 


98884 


16620 


98609 


26 


35 


09729 


99526 


11465 


99341 


13197 


99125 


14925 


98880 


16648 


98604 


25 


36 


09758 


99523 


11494 


99337 


13226 


99122 


14954 


98876 


16677 


98600 


24 


37 


09787 


99520 


11523 


99334 


13254 


99118 


14982 


98871 


16706 


98595 


23 


38 


09816 


99517 


11552 


99331 


13283 


99114 


15011 


98867 


16734 


98590 


22 


39 


09845 


99514 


11580 


99327 


13312 


99110 


15040 


98863 


16763 


98585 


21- 


40 


09874 


99511 


11609 


99324 


13341 


99106 


15069 


98858 


16792 


98580 


20 


41 


09903 


99508 


11638 


99320 


13370 


99102 


15097 


98854 


16820 


98575 


19 


42 


09932 


99506 


11667 


99317 


13399 


99098 


15126 


98849 


16849 


98570 


18 


43 


09961 


99503 


11696 


99314 


13427 


99094 


15155 


98845 


16878 


98565 


17 


44 


09990 


99500 


11725 


99310 


13456 


99091 


15184 


98841 


16906 


98561 


16 


45 


10019 


99497 


11754 


99307 


13485 


99087 


15212 


98836 


16935 


98556 


15 


46 


10048 


99494 


11783 


99303 


13514 


99083 


15241 


98832 


16964 


98551 


14 


47 


10077 


994«1 


11812 


99300 


13543 


99079 


15270 


98827 


16992 


98546 


13 


48 


10106 


99488 


11840 


99297 


13572 


99075 


15299 


98823 


17021 


98541 


12 


49 


10135 


99485 


11869 


99293 


13600 


99071 


15327 


98818 


17050 


98536 


11 


50 


10164 


99482 


11898 


99290 


13629 


99067 


15356 


98814 


17078 


98531 


10 


51 


10192 


99479 


11927 


99286 


13658 


99063 


15385 


98809 


17107 


98526 


9 


52 


10221 


99476 


11956 


99283 


13687 


99059 


15414 


98805 


17136 


98521 


8 


53 


10250 


99473 


11985 


99279 


13716 


99055 


15442 


98800 


17164 


98516 


7 


54 


10279 


99470 


12014 


99276 


13744 


99051 


15471 


98796 


17193 


98511 


6 


55 


10308 


99467 


12043 


99272 


13773, 


99047 


15500 


98791 


17222 


98506 


5 


56 


10337 


99464 


12071 


99269 


13802 


99043 


15529 


98787 


17250 


98501 


4 


57 


10366 


99461 


12100 


99265 


13831 


99039 


15557 


98782 


17279 


98496 


a 


58 


10395 


99458 


12129 


99262 


13860 


99035 


]5586 


98778 


17308 


98491 


2 


59 


10424 


99455 


12158 


99258 


13889 


99031 


15615 


98773 


17336 


98486 


1 


60 


10453 


99452 


12187 


99255 


13917 


99027 


15643 


98769 


17365 


98481 







Cosine. 


Sine. 


Cosine. 


Sine. 


Cosine. 


Sine. 


Cosine. 


Sine. 


Cosine. 


Sine. 




/ 


8 


4,0 


8 


30 


S 


^0 i 


8 


1° 


84 


{y° 


/ 



838 



APPENDIX. 



NATURAL. SINES AND COSINES. 





10<' 


11° 


13° 


13° 


14=° 




/ 


Sine. 


Cosine. 


Sine. 


Cosine. 


,Sine. 


Cosine. 


Sine. 


Cosine. 


Sine. 


Cosine. 


/ 





17365 


98481 


19081 


98163 


20791 


97815 


22495 


97437 


24192 


97030 


60 


1 


17393 


98476 


19109 


98157 


20820 


97809 


22523 


97430 


24220 


97023 


59 


2 


17422 


98471 


19138 


98152 


20848 


97803 


22552 


97424 


24249 


97015 


58 


3 


17451 


98466 


19167 


98146 


20877 


97797 


22580 


97417 


24277 


97008 


57 


4 


17479 


98461 


19195 


98140 


20905 


97791 


22608 


97411 


24305 


97001 


56 


5 


17508 


98455 


19224 


98135 


20933 


97784 


22637 


97404 


24333 


96994 


55 


6 


17537 


98450 


19252 


98129 


20962 


97778 


22665 


97398 


24362 


96987 


54 


7 


17565 


98445 


19281 


98124 


20990 


97772 


22693 


97391 


24390 


96980 


53 


8 


17594 


98440 


19309 


98118 


21019 


97766 


22722 


97384 


24418 


96973 


52 


9 


17623 


98435 


19338 


98112 


21047 


97760 


22750 


97378 


24446 


96966 


51 


10 


17651 


98430 


19366 


98107 


21076 


97754 


22778 


97371 


24474 


96959 


50 


11 


17680 


98425 


19395 


98101 


21104 


97748 


22807 


97365 


24503 


96952 


49 


12 


17708 


98420 


19423 


98096 


21132 


97742 


22835 


97358 


24531 


96945 


48 


13 


17737 


98414 


19452 


98090 


21161 


97735 


22863 


97351 


24559 


96937 


47 


14 


17766 


98409 


19481 


98084 


21189 


97729 


22892 


97345 


24587 


96930 


46 


15 


17794 


98404 


19509 


98079 


21218 


97723 


22920 


97338 


24615 


96923 


45 


16 


17823 


98399 


19538 


98073 


21246 


97717 


22948 


97331 


24644 


96916 


44 


17 


17852 


98394 


19566 


98067 


21275 


97711 


22977 


97325 


24672 


96909 


43 


18 


17880 


98389 


19595 


98061 


21303 


97705 


23005 


97318 


24700 


96902 


42 


19 


17909 


98383 


19623 


98056 


21331 


97698 


23033 


97311 


24728 


96894 


41 


20 


17937 


98378 


19652 


98050 


21360 


97692 


23062 


97304 


24756 


96887 


40 


21 


17966 


98373 


19680 


98044 


21388 


97686 


23090 


97298 


24784 


96880 


39 


22 


17995 


98368 


19709 


98039 


21417 


97680 


23118 


97291 


24813 


96873 


38 


23 


18023 


98362 


19737 


98033 


21445 


97673 


23146 


97284 


24841 


96866 


37 


24 


18052 


98357 


19766 


98027 


21474 


97667 


23175 


97278 


24869 


96858 


36 


25 


18081 


98352 


19794 


98021 


21502 


97661 


23203 


97271 


24897 


96851 


35 


26 


18109 


98347 


19823 


98016 


21530 


97655 


23231 


97264 


24925 


96844 


34 


27 


18138 


98341 


19851 


98010 


21559 


97648 


23260 


97257 


24954 


96837 


33 


28 


18166 


98336 


19880 


98004 


21587 


97642 


23288 


97251 


24982 


96829 


32 . 


29 


18195 


98331 


19908 


97998 


21616 


97636 


23316 


97244 


25010 


96822 


31 


30 


18224 


98325 


19937 


97992 


21644 


97630 


23345 


97237 


25038 


96815 


30 


31 


18252 


98320 


19965 


97987 


21672 


97623 


23373 


97230 


25066 


96807 


29 


32 


18281 


98315 


19994 


97981 


21701 


97617 


23401 


97223 


25094 


96800 


28 


33 


18309 


98310 


20022 


97975 . 


21729 


97611 


23429 


97217 


25122 


96793 


27 


34 


18338 


98304 


20051 


97969 


21758 


97604 


23458 


97210 


25151 


96786 


26 


35 


18367 


98299 


20079 


97963 


21786 


97598 


23486 


97203 


25179 


96778 


25 


36 


18395 


98294 


20108 


97958 


21814 


97592 


23514 


97196 


25207 


96771 


24 


37 


18424 


98288 


20136 


97952 


21843 


97585 


23542 


97189 


25235 


96764 


23 


38 


18452 


98283 


20165 


97946 


21871 


97579 


23571 


97182 


25263 


96756 


22 


39 


18481 


98277 


20193 


97940 


21899 


97573 


23599 


97176 


25291 


96749 


21 


40 


18509 


98272 


20222 


97934 


21928 


97566 


23627 


97169 


25320 


96742 


20 


41 


18538 


98267 


20250 


97928 


21956 


97560 


23656 


97162 


25348 


96734 


19 


42 


18567 


98261 


20279 


97922 


21985 


97553 


23684 


97155 


25376 


96727 


18 


43 


18595 


98256 


20307 


97916 


22013 


97547 


23712 


97148 


25404 


96719 


17 


44 


18624 


98250 


20336 


97910 


22041 


97541 


23740 


97141 


25432 


96712 


m 


45 


18652 


98245 


20364 


97905 


22070 


97534 


23769 


97134 


25460 


96705 


15 


46 


18681 


98240 


20393 


97899 


22098 


97528 


23797 


97127 


25488 


96697 


14 


47 


18710 


98234 


20421 


97893 


22126 


97521 


23825 


97120 


25516 


96690 


13 


48 


18738 


98229 


20450 


97887 


22155 


97515 


23853 


97113 


25545 


96682 


12 


49 


18767 


98223 


20478 


97881 


22183 


97508 


23882 


97106 


25573 


96675 


11 


50 


18795 


98218 


20507 


97875 


22212 


97502 - 


23910 


97100 


25601 


96667 


10 


51 


18824 


98212 


20535 


97869 


22240 


97496 


23938 


97093 


25629 


96660 


9 


52 


18852 


98207 


20563 


97863 


22268 


97489 


23966 


97086 


25657 


96653 


8 


53 


18881 


98201 


20592 


97857 


22297 


97483 


23995 


97079 


25685 


96645 


■7 


54 


18910 


98196 


20620 


97851 


22325 


97476 


24023 


97072 


25713 


96638 


6 


55 


18938 


98190 


20649 


97845 


22353 


97470 


24051 


97065 


25741 


96630 


5 


56 


18967 


98185 


20677 


97839 


22382 


97463 


24079 


97058 


25769 


96623 


. 4 


57 


18995 


98179 


20706 


97833 


22410 


97457 


24108 


97051 


25798 


96615 


3 


58 


19024 


98174 


20734 


97827 


22438 


97450 


24136 


97044 


25826 


96608 


, 2 


59 


19052 


98168 


20763 


97821 


22467 


97444 


24164 


97037 


25854 


96600 


1 


60 


19081 


98163 


20791 


97815 


22495 


97437 


24192 


97030 


25882 


96593 







Cosine. 


Sine. 


Cosine. 


Sine. 


Cosine. 


Sine. 


Cosine. 


Sine. 


Cosine. 


Sine. 




/ 


7 


9' 


T 


S» 


7 


7° 


7< 


S° 


7i 


5» 


f 



APPENDIX. 



839 



NATURAL, SINGS AND COSINES. 





15° 


16° 


17° 


18° 


10° 




/ 


Sine. 


Cosine. 


Sine. 


Cosine. 


Sine. 


Cosine. 


Sine. 


Cosine. 


Sine. 


Cosine. 


/ 





25882 


96593 


27564 


96126 


29237 


95630 


30902 


95106 


32557 


94552 


60 


1 


25910 


96585 


27592 


96118 


29265 


95622 


30929 


95097 


32584 


94542 


59 


2 


25938 


96578 


27620 


96110 


29293 


95613 


30957 


95088 


32612 


94533 


58 


3 


25966 


96570 


27648 


96102 


29321 


95605 


30985 


95079 


32639 


94523 


57 


4 


25994 


96562 


27676 


96094 


29348 


95596 


31012 


95070 


32667 


94514 


56 


5 


26022 


96555 


27704 


96086 


29376 


95588 


31040 


95061 


32694 


94504 


55 


6 


26050 


96547 


27731 


96078 


29404 


95579 


31068 


95052 


32722 


94495 


54 


7 


26079 


96540 


27759 


96070 


29432 


95571 


31095 


95043 


32749 


94485 


53 


8 


26107 


96532 


27787 


96062 


29460 


95562 


31123 


95033 


32777 


94476 


52 


9 


26135 


96524 


27815 


96054 


29487 


95554 


31151 


95024 


32804 


94466 


51 


10 


26163 


96517 


27843 


96046 


29515 


95545 


31178 


95015 


32832 


94457 


50 


11 


26191 


96509 


27871 


96037 


29543 


95536 


31206 


95006 


32859 


94447 


49 


12 


26219 


96502 


27899 


96029 


29571 


95528 


31233 


94997 


32887 


94438 


48 


13 


26247 


96494 


27927 


96021 


29599 


95519 


31261 


94988 


32914 


94428 


47 


14 


26275 


96486 


27955 


96013 


29626 


95511 


31289 


94979 


32942 


94418 


46 


15 


26303 


96479 


27983 


96005 


29654 


95502 


31316 


94970 


32969 


94409 


45 


16 


26331 


96471 


28011 


95997 


29682 


95493 


31344 


94961 


32997 


94399 


44 


17 


26359 


96463 


28039 


95989 


29710 


95485 


31372 


94952 


33024 


94390 


43 


18 


26387 


96456 


28067 


95981 


29737 


95476 


31399 


94943 


33051 


94380 


42 


19 


26415 


96448 


28095 


95972 


29765 


95467 


31427 


94933 


33079 


94370 


41 


20 


26443 


96440 


28123 


95964 


29793 


95459 


31454 


94924 


33106 


94361 


40 


21 


26471 


96433 


28150 


95956 


29821 


95450 


31482 


94915 


33134 


94351 


39 


22 


26500 


96425 


28178 


95948 


29849 


95441 


31510 


94906 


33161 


94342 


38 


23 


26528 


96417 


28206 


95940 


29876 


95433 


31537 


94897 


33189 


94332 


37 


24 


26556 


96410 


28234 


95931 


29904 


95424 


31565 


94888 


33216 


94322 


36 


25 


26584 


96402 


28262 


95923 


29932 


95415 


31593 


94878 


33244 


94313 


35 


26 


26612 


96394 


28290 


95915 


29960 


95407 


31620 


94869 


33271 


94303 


34 


27 


26640 


96386 


28318 


95907 


29987 


95398 


31648 


94860 


33298 


94293 


33 


28 


26668 


96379 


28346 


95898 


30015 


95389 


31675 


94851 


33326 


94284 


32 


29 


26696 


96371 


28374 


95890 


30043 


95380 


31703 


94842 


33353 


94274 


31 


30 


26724 


96363 


28402 


95882 


30071 


95372 


31730 


94832 


33381 


94264 


30 


31 


26752 


96355 


28429 


95874 


30098 


95363 


31758 


94823 


33408 


94254 


29 


32 


26780 


96347 


28457 


95865 


30126 


95354 


31786 


94814 


33436 


94245 


28 


33 


26808 


96340 


28485 


95857 


30154 


95345 


31813 


94805 


33463 


94235 


27 


34 


26836 


96332 


28513 


95849 


30182 


95337 


31841 


94795 


33490 


94225 


26 


35 


26864 


96324 


28541 


95841 


30209 


95328 


31868 


94786 


33518 


94215 


25 


36 


26892 


96316 


28569 


95832 


30237 


95319 


31896 


94777 


33545 


94206 


24 


37 


26920. 


96308 


28597 


95824 


30265 


95310 


31923 


94768 


33573 


94196 


23 


38 


26948 


96301 


28625 


95816 


30292 


95301 


31951 


94758 


33600 


94186 


22 


39 


26976 


96293 


28652 


95807 


30320 


95293 


31979 


94749 


33627 


94176 


21. 


40 


27004 


96285 


28680 


95799 


30348 


95284 


32006 


94740 


33655 


94167 


20 


41 


27032 


96277 


28708 


95791 


30376 


95275 


32034 


94730 


33682 


94157 


19 


42 


27060 


96269 


28736 


95782 


30403 


95266 


32061 


94721 


33710 


94147 


18 


43 


27088 


96261 


28764 


95774 


30431 


95257 


32089 


94712 


33737 


94137 


17 


44 


27116 


96253 


28792 


95766 


30459 


95248 


32116 


94702 


33764 


94127 


16 


45 


27144 


96246 


28820 


95757 


30486 


95240 


32144 


94693 


33792 


94118 


15 


46 


27172 


96238 


28847 


95749 


30514 


95231 


32171 


94684 


33819 


94108 


14 


47 


27200 


96230 


28875 


95740 


30542 


95222 


32199 


94674 


33846 


94098 


13 


48 


27228 


96222 


28903 


95732 


30570 


95213 


32227 


94665 


33874 


94088 


12 


49 


27256 


96214 


28931 


95724 


30597 


95204 


32254 


94656 


33901 


94078 


11 


50 


27284 


96206 


28959 


95715 


30625 


95195 


1 32282 


94646 


33929 


94068 


10 


51 


27312 


96198 


28987 


95707 


30653 


95186 


32309 


94637 


33956 


94058 


9 


52 


27340 


96190 


29015 


95698 


30680 


95177 


32337 


94627 


33983 


94049 


8 


53 


27368 


96182 


29042 


95690 


30708 


95168 


32364 


94618 


34011 


94039 


7 


54 


27396 


96174 


29070 


95681 


30736 


95159 


32392 


94609 


34038 


94029 


6 


55 


i 27424 


96166 


29098 


95673 


30763 


95150 


32419 


94599 


34065 


94019 


5 


56 


27452 


96158 


29126 


95664 


3079i 


95142 


32447 


94590 


34093 


94009 


4 


57 


27480 


96150 


29154 


95656 


30819 


95133 


32474 


94580 


34120 


93999 


3 


58 


27508 


96142 


29182 


95647 


30846 


95124 


1 32502 


94571 


34147 


93989 


2 


59 


27536 


96134 


29209 


95639 


1 30874 


95115 


32529 


94561 


34175 


93979 


1 


60 


27564 


96126 


29237 


95630 


1 30902 


95106 


32557 


94552 


34202 


93969 







Cosine. 


Sine. 


Cosine. 


Sine. 


! Cosine. 


Sine. 


Cosine. 


Sine. 


Cosine. 


Sine. 




1 


7- 


4° 


7 

1 


3° 


7 


3° 


7 


1° 


7 


o° 


f 



840 



APPENDIX. 



NATURAL. SINES AND COSINES. 





ao° 


SI" 


33<» 


33° 


340 




/ 


Sine. 


Cosine. 


Sine. 


Cosine. 


Sine. 


Cosine. 


Sine. 


Cosine. 


Sine. 


Cosine. 


f 





34202 


93969 


35837 


93358 


37461 


92718 


39073 


92050 


40674 


91355 


60 


1 


34229 


93959 


35864 


93348 


37488 


92707 


39100 


92039 


40700 


91343 


59 


2 


34257 


93949 


35891 


93337 


37515 


92697 


39127 


92028 


40727 


91331 


58 


3 


34284 


93939 


35918 


93327 


37542 


92686 


39153 


92016 


40753 


91319 


57 


4 


34311 


93929 


35945 


93316 


37569 


92675 


39180 


92005 


40780 


91307 


56 


5 


34339 


93919 


35973 


93306 


37595 


92664 


39207 


91994 


40806 


91295 


55 


6 


34366 


93909 


36000 


93295 


37622 


92653 


39234 


91982 


40833 


91283 


54 


7 


34393 


93899 


36027 


93285 


37649 


92642 


39260 


91971 


40860 


912/2 


53 


8 


34421 


93889 


36054 


93274 


37676 


92631 


39287 


91959 


40886 


91260 


52 


9 


34448 


93879 


36081 


93264 


37703 


92620 


39314 


91948 


40913 


91248 


51 


10 


34475 


93869 


36108 


93253 


37730 


92609 


39341 


91936 


40939 


91236 


50 


11 


34503 


93859 


36135 


93243 


37757 


92598 


39367 


91925 


40966 


91224 


49 


12 


34530 


93849 


36162 


93232 


37784 


92587 


39394 


91914 


40992 


91212 


48 


13 


34557 


93839 


36190 


93222 


37811 


92576 


39421 


91902 


41019 


91200 


47 


14 


34584 


93829 


36217 


93211 


37838 


92565 


39448 


91891 


41045 


91188 


46 


15 


34612 


93819 


36244 


93201 


37865 


92554 


39474 


91879 


41072 


91176 


45 


16 


34639 


93809 


36271 


93190 


37892 


92543 


39501 


91868 


41098 


91164 


44 


17 


34666 


93799 


36298 


93180 


37919 


92532 


39528 


91856 


41125 


91152 


43 


18 


34694 


93789 


36325 


93169 


37946 


92521 


39555 


91845 


41151 


91140 


42 


19 


34721 


93779 


36352 


93159 


37973 


92510 


39581 


91833 


41178 


91128 


41 


20 


34748 


93769 


36379 


93148 


37999 


92499 


39608 


91822 


41204 


91116 


40 


21 


34775 


93759 


36406 


93137 


38026 


92488 


39635 


91810 


41231 


91104 


39 


22 


34803 


93748 


36434 


93127 


38053 


92477 


39661 


91799 


41257 


91092 


38 


23 


34830 


93738 


36461 


93116 


38080 


92466 


39688 


91787 


41284 


91080 


37 


24 


34857 


93728 


36488 


93106 


38107 


92455 


39715 


91775 


41310 


91068 


36 


25 


34884 


93718 


36515 


93095 


38134 


92444 


39741 


91764 


41337 


91056 


35 


26 


34912 


93708 


36542 


93084 


38161 


92432 


39768 


91752 


41363 


91044 


34 


27 


34939 


93698 


36569 


93074 


38188 


92421 


39795 


91741 


41390 


91032 


33 


28 


34966 


93688 


36596 


93063 


38215 


92410 


39822 


91729 


41416 


91020 


32 


29 


34993 


93677 


36623 


93052 


38241 


92399 


39848 


91718 


41443 


91008 


31 


30 


35021 


93667 


36650 


93042 


38268 


92388 


39875 


91706 


41469 


90996 


30 


31 


35048 


93657 


36677 


93031 


38295 


92377 


39902 


91694 


41496 


90984 


29 


32 


35075 


93647 


36704 


93020 


38322 


92366 


39928 


91683 


41522 


90972 


28 


33 


35102 


93637 


36731 


93010 


38349 


92355 


39955 


91671 


41549 


90960 


27 


34 


35130 


93626 


36758 


92999 


38376 


92343 


39982 


91660 


41575 


90948 


26 


35 


35157 


93616 


36785 


92988 


38403 


92332 


40008 


91648 


41602 


90936 


25 


36 


35184 


93606 


36812 


92978 


38430 


92321 


40035 


91636 


41628 


90924 


24 


37 


35211 


93596 


36839 


92967 


38456 


92310 


40062 


91625 


41655 


90911 


23 


38 


35239 


93585 


36867 


92956 


38483 


92299 


40088 


91613 


41681 


90899 


22 


39 


35266 


93575 


36894 


92945 


38510 


92287 


40115 


91601 


41707 


90887 


21 


40 


35293 


93565 


36921 


92935 


38537 


92276 


40141 


91590 


41734 


90875 


20 


41 


35320 


93555 


36948 


92924 


38564 


92265 


40168 


91578 


41760 


90863 


19 


42 


35347 


93544 


36975 


929] 3 


38591 


92254 


40195 


91566 


41787 


90851 


18 


43 


35375 


93534 


37002 


92902 


38617 


92243 


40221 


91555 


41813 


90839 


17 


44 


35402 


93524 


37029 


92892 


38644 


92231 


40248 


91543 


41840 


90826 


16 


45 


35429 


93514 


37056 


92881 


38671 


92220 


40275 


91531 


4186q 


90814 


15 


46 


35456 


93503 


37083 


92870 


38698 


92209 


40301 


91519 


41892 


90802 


14 


47 


35484 


93493 


37110 


92859 


38725 


92198 


40328 


91508 


41919 


90790 


13 


48 


35511 


93483 


37137 


92849 


38752 


92186 


40355 


91496 


41945 


90778 


12 


49 


35538 


93472 


37164 


92838 


38778 


92175 


40381 


91484 


41972 


90766 


11 


50 


35565 


93462 


37191 


92827 


38805 


92164 


'40408 


91472 


41998 


90753 


10 


51 


35592 


93452 


37218 


92816 


38832 


92152 


40434 


91461 


42024 


90741 


9 


52 


35619 


93441 


37245 


92805 


38859 


92141 


40461 


91449 


42051 


90729 


8 


53 


35647 


93431 


37272 


92794 


38886 


92130 


40488 


91437 


42077 


90717 


7 


54 


35674 


93420 


37299 


92784 


38912 


92119 


40514 


91425 


42104 


90704 


6 


55 


35701 


93410 


37326 


92773 


38939 


92107 


40541 


91414 


42130 


90692 


5 


56 


35728 


93400 


37353 


92762 


38966 


92096 


40567 


91402 


42156 


90680 


4 


57 


35755 


93389 


37380 


92751 


38993 


92085 


40594 


91390 


42183 


90668 


3 


58 


35782 


93379 


37407 


92740 


39020 


92073 


40621 


91378 


42209 


90655 


2 


59 


35810 


93368 


37434 


92729 


39046 


92062 


40647 


91366 


42235 


90643 


1 


eo 


35837 


93358 


37461 


92718 


39073 


92050 


40674 


91355 


42262 


90631 







Cosine. 


Sine. 


Cosine. 


Sine. 


Cosine. 


Sine. 


Cosine. 


Sine. 


Cosine. 


Sine. 




/. 


G 


0° 


6 


8° 


6 


7" 


G< 


SO 


6 


5° 


f 



APPENDIX. 



841 



NATURAL. SINES AND COSINES. 





a 


5° 


3G° 


270 


3 


S« 


3 


O'' 




/ 


Sine. 


Cosine. 


Sine. 


Cosine. 


Sine. 


Cosine. 


Sine. 


Cosine. 


Sine. 


Cosine. 


/ 





42262 


90631 


43837 


89879 


45399 


89101 


46947 


88295 


48481 


87462 


60 


1 


42288 


90618 


43863 


89867 


45425 


89087 


46973 


88281 


48506 


87448 


59 


2 


42315 


90606 


43889 


89854 


45451 


89074 


46999 


88267 


48532 


87434 


58 


3 


42341 


90594 


43916 


89841 


45477 


89061 


47024 


88254 


48557 


87420 


57 


4 


42:567 


90582 


43942 


89828 


45503 


89048 


47050 


88240 


48.^83 


87406 


56 


5 


42394 


90569 


43968 


89816 


45529 


89035 


47076 


88226 


48608 


87391 


55 


6 


42420 


90557 


43994 


89803 


45554 


89021 


47101 


88213 


48634 


87377 


54 


7 


42446 


90545 


44020 


89790 


45580 


89008 


47127 


88199 


48659 


87363 


53 


8 


42473 


90532 


44046 


89777 


45606 


88995 


47153 


88185 


48684 


87349 


52 


9 


42499 


90520 


44072 


89764 


45632 


88981 


47178 


88172 


48710 


87335 


51 


10 


42525 


90507 


44098 


89752 


45658 


88968 


47204 


88158 


48735 


87321 


50 


11 


42552 


90495 


44124 


89739 


45684 


88955 


47229 


88144 


48761 


87306 


49 


12 


42578 


90483 


44151 


89726 


45710 


88942 


47255 


88130 


48786 


87292 


48 


13 


42604 


90470 


44177 


89713 


45736 


88928 


47281 


88117 


48811 


87278 


47 


14 


42631 


90458 


44203 


89700 


45762 


88915 


47306 


88103 


48837 


87264 


46 


15 


42657 


90446 


44229 


89687 


45787 


88902 


47332 


88089 


48862 


87250 


45 


16 


42683 


90433 


44255 


89674 


45813 


88888 


47358 


88075 


48888 


87235 


44 


17 


42709 


90421 


44281 


89662 


45839 


88875 


47383 


88062 


48913 


87221 


43 


18 


42736 


90408 


44307 


89649 


45865 


88862 


47409 


88048 


48938 


87207 


42 


19 


42762 


90396 


44333 


89636 


45891 


88848 


47434 


88034 


48964 


87193 


41 


20 


42788 


90383 


44359 


89623 


45917 


88835 


47460 


88020 


48989 


87178 


40 


21 


42815 


90371 


44385 


89610 


45942 


88822 


47486 


88006 


49014 


87164 


39 


22 


42841 


90358 


44411 


89597 


45968 


88808 


47511 


87993 


49040 


87150 


38 


23 


42867 


90346 


44437 


89584 


45994 


88795 


47537 


87979 


49065 


87136 


37 


24 


42894 


90334 


44464 


89571 


46020 


88782 


47562 


87965 


49090 


87121 


36 


25 


42920 


90321 


44490 


89558 


46046 


88768 


47588 


87951 


49116 


87107 


35 


26 


42946 


90309 


44516 


89545 


46072 


88755 


47614 


87937 


49141 


87093 


34 


27 


42972 


90296 


44542 


89532 


46097 


88741 


47639 


87923 


49166 


87079 


33 


28 


42999 


90284 


44568 


89519 


46123 


88728 


47665 


87909 


49192 


87064 


32 


29 


43025 


90271 


44594 


89506 


46149 


88715 


47690 


87896 


49217 


87050 


31 


80 


43051 


90259 


44620 


89493 


46175 


88701 


47716 


87882 


49242 


87036 


30 


31 


43077 


90246 


44646 


89480 


46201 


88688 


47741 


87868 


49268 


87021 


29 


32 


43104 


90233 


44672 


89467 


46226 


88674 


47767 


87854 


49293 


87007 


28 


33 


43130 


90221 


44698 


89454 


46252 


88661 


47793 


87840 


49318 


86993 


27 


34 


43156 


90208 


44724 


89441 


46278 


88647 


47818 


87826 


49344 


86978 


26 


35 


43182 


90196 


44750 


89428 


46304 


88634 


47844 


87812 


49369 


86964 


25 


36 


43209 


90183 


44776 


89415 


46330 


88620 


47869 


87798 


49394 


86949 


24 


37 


43235 


90171 


44802 


89402 


46355 


88607 


47895 


87784 


49419 


86935 


23 


38 


43261 


90158 


44828 


89389 


46381 


88593 


47920 


87770 


49445 


86921 


22 


39 


43287 


90146 


44854 


89376 


46407 


88580 


47946 


87756 


49470 


86906 


21 ' 


40 


43313 


90133 


44880 


89363 


46433 


88566 


47971 


87743 


49495 


86892 


20 


41 


43340 


90120 


44906 


89350 


46458 


88553 


47997 


87729 


49521 


86878 


19 


42 


43366 


90108 


44932 


89337 


46484 


88539 


48022 


87715 


49546 


86863 


18 


43 


43392 


90095 


44958 


89324 


46510 


88526 


48048 


87701 


49571 


86849 


17 


44 


43418 


90082 


44984 


89311 


46536 


88512 


48073 


87687 


49596 


86834 


16 


45 


43445 


90070 


45010 


89298 


46561 


88499 


48099 


87673 


49622 


86820 


15 


46 


43471 


90057 


45036 


89285 


46587 


88485 


48124 


87659 


49647 


86805 


14 


47 


43497 


90045 


45062 


89272 


46613 


88472 


48150 


87645 


49672 


86791 


13 


48 


43523 


90032 


45088 


89259 


46639 


88458 


48175 


87631 


49697 


86777 


12 


49 


43549 


90019 


45114 


89245 


46664 


88445 


48201 


87617 


49723 


86762 


11 


50 


43575 


90007 


45140 


89232 


46690 


88431 


48226 


87603 


49748 


86748 


10 


51 


43602 


89994 


451G6 


89219 


46716 


88417 


48252 


87589 


49773 


86733 


9 


52 


43628 


89981 


45192 


89206 


46742 


88404 


48277 


87575 


49798 


86719 


8 


53 


43654 


89968 


45218 


89193 


46767 


88390 


48303 


87561 


49824 


86704 


7 


54 


43680 


89956 


45243 


89180 


46793 


88377 


48328 


87546 


49849 


86690 


6 


55 


43706 


89943 


45269 


89167 


46819' 


88363 


48354 


87532 


49874 


86675 


5 


56 


43733 


89930 


45295 


89153 


46844 


88349 


48379 


87518 


49899 


86661 


4 


57 


43759 


89918 


45321 


89140 


46870 


88336 


48405 


87504 


49924 


86646 


3 


58 


43785 


89905 


45347 


89127 


46896 


88322 


48430 


87490 


49950 


86632 


2 


59 


43811 


89892 


45373 


89114 


46921 


88308 


48456 


87476 


49975 


86617 


1 


60 


43837 


89879 


45399 


89101 


46947 


88295 


48481 


87462 


50000 


86603 







Cosine. 


Sine. 


Cosine. 


Sine. 


Cosine. 


Sine. 


Cosine, 


Sine. 


Cosine. 


Sine. 




/ 


6 


4° 


G 


J° 


Gt 


2° 


G] 


L" 


G( 


>» 


/ 



84:2 



APPENDIX. 



NATURAL, SINES AND COSINES. 





SO"* 


31" 


33° 


33° 


34=° 




/ 


Sine. 


Cosine. 


Sine. 


Cosine. 


Sine. 


Cosine. 


Sine. 


Cosine. 


Sine. 


Cosine. 


/ 





50000 


86603 


51504 


85717 


52992 


84805 


54464 


83867 


55919 


82904 


60 


1 


50025 


86588 


51529 


85702 


53017 


84789 


54488 


83851 


55943 


82887 


59 


2 


50050 


86573 


51554 


85687 


53041 


84774 


54513 


83835 


55968 


82871 


58 


3 


50076 


86559 


51579 


85672 


53066 


84759 


54537 


83819 


55992 


82855 


57 


4 


50101 


86544 


51604 


85657 


53091 


84743 


54561 


83804 


56016 


82839 


56 


5 


50126 


86530 


51628 


85642 


53115 


84728 


54586 


83788 


56040 


82822 


55 


6 


50151 


86515 


51653 


85627 


53140 


84712 


54610 


83772 


56064 


82806 


54 


7 


50176 


86501 


51678 


85612 


53164 


84697 


54635 


83756 


56088 


82790 


53 


8 


50201 


86486 


51703 


85597 


53189 


84681 


54659 


83740 


56112 


82773 


52 


9 


50227 


86471 


51728 


85582 


53214 


84666 


54683 


83724 


56136 


82757 


51 


10 


50252 


86457 


51753 


85567 


53238 


84650 


54708 


83708 


56160 


82741 


50 


11 


50277 


86442 


51778 


85551 


53263 


84635 


54732 


83692 


56184 


82724 


49 


12 


50302 


86427 


51803 


85536 


53288 


84619 


54756 


83676 


56208 


82708 


48 


13 


50327 


86413 


51828 


85521 


53312 


84604 


54781 


83660 


56232 


82692 


47 


14 


50352 


86398 


51852 


85506 


53337 


84588 


54805 


83645 


56256 


82675 


46 


15 


50377 


86384 


51877 


85491 


53361 


84573 


54829 


83629 


56280 


82659 


45 


16 


50403 


86369 


51902 


85476 


53386 


84557 


54854 


83613 


56305 


82643 


44 


17 


50428 


86354 


51927 


85461 


53411 


84542 


54878 


83597 


56329 


82626 


43 


18 


50453 


86340 


51952 


85446 


53435 


84526 


54902 


83581 


56353 


82610 


42 


19 


50478 


86325 


51977 


85431 


53460 


84511 


54927 


83565 


56377 


82593 


41 


20 


50503 


86310 


52002 


85416 


53484 


84495 


54951 


83549 


56401 


82577 


40 


21 


50528 


86295 


52026 


85401 


53509 


84480 


54975 


83533 


56425 


82561 


39 


22 


50553 


86281 


52051 


85385 


53534 


84464 


54999 


83517 


56449 


82544 


38 


23 


50578 


86266 


52076 


85370 


53558 


84448 


55024 


83501 


56473 


82528 


37 


24 


50603 


86251 


52101 


85355 


53583 


84433 


55048 


83485 


56497 


82511 


36 


25 


50628 


86237 


52126 


85340 


53607 


84417 


55072 


83469 


56521 


82495 


35 


26 


50654 


86222 


52151 


85325 


53632 


84402 


55097 


83453 


56545 


82478 


34 


27 


50679 


86207 


52175 


85310 


53656 


84386 


55121 


83437 


56569 


82462 


33 


28 


50704 


86192 


52200 


85294 


53681 


84370 


55145 


83421 


56593 


82446 


32- 


29 


50729 


86178 


52225 


85279 


53705 


84355 


55169 


83405 


56617 


82429 


31 


30 


50754 


86163 


52250 


85264 


53730 


84339 


55194 


83389 


56641 


82413 


30 


31 


50779 


86148 


52275 


85249 


53754 


84324 


55218 


83373 


56665 


82396 


29 


32 


50804 


86133 


52299 


85234 


53779 


84308 


55242 


83356 


56689 


82380 


28 


33 


50829 


86119 


52324 


85218 


53804 


84292 


55266 


83340 


56713 


82363 


27 


34 


50854 


86104 


52349 


85203 


53828 


84277 


55291 


83324 


56736 


82347 


26 


35 


50879 


86089 


52374 


85188 


53853 


84261 


55315 


83308 


56760 


82330 


25 


36 


50904 


86074 


52399 


85173 


53877 


84245 


55339 


83292 


56784 


82314 


24 


37 


50929 


86059 


52423 


85157 


53902 


84230 


55363 


83276 


56808 


82297 


23 


38 


50954 


86045 


52448 


85142 


53926 


84214 


55388 


83260 


56832 


82281 


22 


39 


50979 


86030 


52473 


85127 


53951 


84198 


55412 


83244 


56856 


82264 


21 


40 


51004 


86015 


52498 


85112 


53975 


84182 


55436 


83228 


56880 


82248 


20 


41 


51029 


86000 


52522 


85096 


54000 


84167 


55460 


83212 


56904 


82231 


19 


42 


51054 


85985 


52547 


85081 


54024 


84151 


55484 


83195 


56928 


82214 


18 


43 


51079 


85970 


52572 


85066 


54049 


84135 


55509 


83179 


56952 


82198 


17 


44 


51104 


85956 


52597 


85051 


54073 


84120 


55533 


83163 


56976 


82181 


16 


45 


51129 


85941 


52621 


85035 


54097 


84104 


55557 


83147 


57000 


82165 


15 


46 


51154 


85926 


52646 


85020 


54122 


84088 


55581 


83131 


57024 


82148 


14 


47 


51179 


85911 


52671 


85005 


54146 


84072 


55605 


83115 


57047 


82132 


13 


48 


51204 


85896 


52696 


84989 


54171 


84057 


55630 


83098 


57071 


82115 


12 


49 


51229 


85881 


52720 


84974 


54195 


84041 


55654 


83082 


57095 


82098 


11 


50 


51254 


85866 


52745 


84959 


54220 


84025 ' 


55678 


83066 


57119 


82082 


10 


51 


51279 


85851 


52770 


84943 


54244 


84009 


55702 


83050 


57143 


82065 


9 


52 


51304 


85836 


52794 


84928 


54269 


83994 


55726 


83034 


57167 


82048 


8 


53 


51329 


85821 


52819 


84913 


54293 


83978 


55750 


83017 


57191 


82032 


7 


54 


51354 


85806 


52844 


84897 


54317 


83962 


^5775 


83001 


57215 


82015 


6 


55 


51379 


85792 


52869 


84882 


54342 


83946 


55799 


82985 


57238 


81999 


5 


56 


51404 


85777 


52893 


84866 


54366 


83930 


55823 


82969 


57262 


81982 


4 


57 


51429 


85762 


52918 


84851 


54391 


83915 


55847 


82953 


57286 


81965 


3 


58 


51454 


85747 


52943 


84836 


54415 


83899 


55871 


82936 


57310 


81949 


2 


59 


51479 


85732 


52967 


84820 


54440 


83883 


55895 


82920 


57334 


81932 


1 


60 


51504 


85717 


52992 


84805 


54464 


83867 


55919 


82904 


57358 


81915 







Cosine. 


Sine. 


Cosine. 


Sine. 


Cosine. 


Sine. 


Cosine. 


Sine. 


Cosine. 


Sine. 




/ 


5 


9° 


5 


8° 


5 


70 


5< 


3" 


5 


5° 


/ 



APPENDIX. 



843 



NATURAL. SIXKS AND COSINES. 





3 


1 


30° 


37° 


3SO 


30' 




/ 


Sine. 


Cosine. 


1 

Sine. 


Cosine. 


Sine. 


Cosine. 


Sine. 


Cosine. 


Sine. 


Cosine. 


/ 





57358 


81915 


58779 


80902 


60182 


79864 


61566 


78801 


62932 


77715 


60 


1 


57381 


81899 


58802 


80885 


! 60205 


79846 


i 61589 


78783 


62955 


77696 


59 


2 


57405 


81882 


58826 


80867 


i 60228 


79829 


61612 


78765 


62977 


77678 


58 


3 


57429 


81865 


58849 


80850 


= 60251 


79811 


61635 


78747 


63000 


77660 


57 


4 


57453 


81848 


58873 


80833 


60274 


79793 


61658 


78729 


63022 


77641 


56 


5 


57477 


81832 


58896 


80816 


60298 


79776 


61681 


78711 


63045 


77623 


55 


6 


57501 


81815 


58920 


80799 


' 60321 


79758 


61704 


78694 


63068 


77605 


54 


7 


57524 


81798 


58943 


80782 


' 60344 


79741 


61726 


78676 


63090 


77586 


53 


8 


57548 


81782 


58967 


80765 


60367 


79723 


61749 


78658 


63113 


77568 


52 


9 


57572 


81765 


58990 


80748 


60390 


79706 


61772 


78640 


63135 


77550 


51 


10 


57596 


81748 


59014 


80730 


60414 


79688 


61795 


78622 


63158 


77531 


50 


11 


57619 


81731 


59037 


80713 


! 60437 


79671 ■ 


61818 


78604 


63180 


77513 


49 


12 


57643 


81714 


59061 


80696 


60460 


79653 ! 


61841 


78586 


63203 


77494 


48 


13 


57667 


81698 


59084 


80679 


60483 


79635 


61864 


78568 


63225 


77476 


47 


14 


57691 


81681 


59108 


80662 


, 60506 


79618 


61887 


78550 


: 63248 


77458 


46 


15 


57715 


81664 


59131 


80644 


60529 


79600 1 


61909 


78532 


1 63271 


77439 


45 


16 


57738 


81647 


59154 


80627 


60553 


79583 


61932 


78514 


63293 


77421 


44 


17 


57762 


81631 


59178 


80610 


60576 


79565 i 


61955 


78496 


! 63316 


77402 


43 


18 


57786 


81614 


59201 


80593 


60599 


79547 i 


61978 


78478 


1 63338 


77384 


42 


19 


57810 


81597 


59225 


80576 


60622 


79530 ' 


62001 


78460 


63361 


77366 


41 


20 


57833 


81580 


59248 


80558 


60645 


79512 1 


62024 


78442 


63383 


77347 


40 


21 


57857 


81563 


59272 


80541 


60668 


79494 1 


62046 


78424 


63406 


77329 


39 


22 


57881 


81546 1 


59295 


80524 


60691 


79477 ' 


62069 


78405 


63428 


77310 


38 


23 


57904 


81530 


59318 


80507 


60714 


79459 i 


62092 


78387 


63451 


77292 


37 


24 


57928 


81513 1 


59342 


80489 


60738 


79441 I 


62115 


78369 


63473 


77273 


36 


25 


57952 


81496 j 


59365 


80472 


60761 


79424 : 


62138 


78351 


63496 


77255 


35 


26 


57976 


81479 i 


59389 


80455 


60784 


79406 


62160 


78333 


63518 


77236 


34 


27 


57999 


81462 1 


59412 


80438 


60807 


79388 


62183 


78315 


63540 


77218 


33 


28 


5802-3 


81445 i 


59436 


80420 


60830 


79371 


62206 


78297 


63563 


77199 


32 


29 


58047 


81428 


59459 


80403 


60853 


79353 


62229 


78279 


63585 


77181 


31 


30 


58070 


81412 j 


59482 


80386 


60876 


79335 


62251 


78261 


63608 


77162 


30 


31 


58094 


81395 


59506 


80368 


60899 


79318 


62274 


78243 


63630 


77144 


29 


32 


58118 


81378 


59529 


80351 


60922 


79300 


62297 


78225 


63653 


77125 


28 


33 


58141 


81361 j 


59552 


80334 


60945 


79282 


62320 


78206 


63675 


77107 


27 


34 


58165 


81344 j 


59576 


80316 


60968 


79264 


62342 


78188 


63698 


77088 


26 


35 


58189 


81327 1 


59599 


80299 


60991 


79247 ; 


62365 


78170 


63720 


77070 


25 


36 


58212 


81310 j 


59622 


80282 


61015 


79229 j 


62388 


781.52 


63742 


77051 


24 


37 


58236 


81293 1 


59646 


80264 


61038 


79211 i 


62411 


78134 


63765 


77033 


23 


38 


58260 


81276 ! 


59669 


80247 


61061 


79193 ^ 


62433 


78116 


63787 


77014 


22 


39 


58283 


81259 : 


59693 


80230 


61084 


79176 


62456 


78098 i 


63810 


76996 


21- 


40 


58307 


81242 


59716 


80212 


61107 


791.58 I 


62479 


78079 


i 63832 


76977 


20 


41 


58330 


81225 ' 


59739 


80195 


61130 


79140 i 


62502 


78061 


63854 


76959 


19 


42 


58354 


81208 [ 


59763 


80178 


61153 


79122 


62524 


78043 


63877 


76940 


18 


43 


58378 


81191 1 


59786 


80160 


61176 


79105 


62547 


78025 


63899 


76921 


17 


44 


58401 


81174 i 


59809 


80143 


61199 


79087 i 


62570 


78007 


63922 


76903 


16 


45 


58425 


81157 


59832 


80125 


61222 


79069 


62592 


77988 


63944 


76884 


15 


46 


58449 


81140 


59856 


80108 


61245 


79051 


62615 


77970 


63966 


76866 


U 


47 


58472 


81123 i 


59879 


80091 


61268 


79033 


62638 


77952 


63989 


76847 


13 


48 


58496 


81106 


59902 


80073 


61291 


79016 


62660 


77934 


64011 


76828 


12 


49 


58519 


81089 : 


59926 


80056 


61314 


78998 


62683 


77916 


64033 


76810 


11 


50 


58543 


81072 i 


59949 


80038 I 


61337 


78980 


62706 


77897 


64056 


76791 


10 


51 


58567 


81055 ! 


59972 


80021 ! 


61360 


78962 


62728 


77879 


64078 


76772 


9 


52 


58590 


81038 


59995 


80003 , 


61383 


78944 


62751 


77861 


64100 


76754 


8 


53 


58614 


81021 


60019 


79986 1 


61406 


78926 


62774 


77843 1 


64123 


76735 


7 


54 


58637 


81004 1 


60042 


79968 


61429 


78908 i 


62796 


77824 ! 


64145 


76717 


6 


55 


58661 


80987 


60065 


79951 


61451. 


78891 ; 


62819 


77806 ; 


64167 


76698 


5 


56 


58684 


80970 


60089 


79934 


61474 


78873 ! 


62842 


77788 


64190 


76679 


4 


57 


58708 


80953 


60112 


79916 i 


61497 


78855 1 


62864 


77769 


64212 


76661 


3 


58 


58731 


80936 , 


60135 


79899 1 


61520 


78837 ' 


62887 


77751 


64234 


76642 I 


2 


59 


58755 


80919 


60158 


79881 i 


61543 


78819 


62909 


77733 


64256 


76623 


1 


60 


58779 


80902 ; 


60182 


79864 1 


61566 


78801 


62932 


77715 
Sine. 


64279 


76604 







Cosine. 


Sine. 


Cosine. 


Sine. 


Cosine. 


Sine. 


Cosine. 


Cosine. 


Sine. 




/ 


.3 


4.' 


5 


3° i 


5 


30 


5 


l" 


5C 


>o 


/ 



844 



APPENDIX. 



STATURAL. SINKS AND COSINBS. 





4.0« 


^l* 


4.3<» 


43« 


440 




/ 


Sine. 


Cosine. 


Sine. 


Cosine. 


Sine. 


Cosine. 


Sine. 


Cosine. 


Sine. 
69466 


Cosine. 


/ 





64279 


76604 


65606 


'lun 


66913 


74314 


68200 


73135 


71934 


60 


1 


64301 


76586 


65628 


75452 


66935 


74295 


68221 


73116 


69487 


71914 


59 


2 


64323 


76567 


65650 


75433 


66956 


74276 


68242 


73096 


69508 


71894 


58 


3 


64346 


76548 


65672 


75414 


66978 


74256 


68264 


73076 


69529 


71873 


57 


4 


64368 


76530 


65694 


75395 


66999 


74237 


68285 


73056 


69549 


71853 


56 


5 


64390 


76511 


65716 


75375 


67021 


74217 


68306 


73036 


69570 


71833 


55 


6 


64412 


76492 


65738 


75356 


67043 


74198 


68327 


73016 


69591 


71813 


54 


7 


64435 


76473 


65759 


75337 


67064 


74178 


68349 


72996 


69612 


71792 


53 


8 


64457 


76455 


65781 


75318 


67086 


74159 


68370 


72976 


69633 


71772 


52 


9 


64479 


76436 


65803 


76299 


67107 


74139 


68391 


72957 


69654 


71752 


51 


10 


64501 


76417 


65825 


75280 


67129 


74120 


68412 


72937 


69675 


71732 


50 


11 


64524 


76398 


65847 


75261 


67151 


74100 


68434 


72917 


69696 


71711 


49 


12 


64546 


76380 


65869 


75241 


67172 


74080 


68455 


72897 


69717 


71691 


48 


13 


64568 


76361 


65891 


75222 


67194 


74061 


68476 


72877 


69737 


71671 


47 


14 


64590 


76342 


65913 


75203 


67216 


74041 


68497 


72857 


69758 


71650 


46 


15 


64612 


76323 


65935 


75184 


67237 


74022 


68518 


72837 


69779 


71630 


45 


16 


64635 


76304 


65956 


75165 


67258 


74002 


68539 


72817 


69800 


71610 


44 


17 


64657 


76286 


65978 


75146 


67280 


73983 


68561 


72797 


69821 


71590 


43 


18 


64679 


76267 


66000 


75126 


67301 


73963 


68582 


72777 


69842 


71569 


42 


IP 


64701 


76248 


66022 


75107 


67323 


73944 


68603 


72757 


69862 


71549 


41 


20 


64723 


76229 


66044 


75088 


67344 


73924 


68624 


72737 


69883 


71529 


40 


21 


64746 


76210 


m^^^ 


75069 


67366 


73904 


68645 


72717 


69904 


71508 


39 


22 


64768 


76192 


66088 


75050 


67387 


73885 


^%m^ 


72697 


69925 


71488 


38 


23 


64790 


76173 


66109 


75030 


67409 


73865 


68688 


72677 


69946 


71468 


37 


24 


64812 


76154 


66131 


75011 


67430 


73846 


68709 


72657 


69966 


71447 


36 


25 


64834 


76135 


66153 


74992 


67452 


73826 


68730 


72637 


69987 


71427 


35 


26 


64856 


76116 


66175 


74973 


67473 


73806 


68751 


72617 


70008 


71407 


34 


27 


64878 


76097 


66197 


74953 


67495 


73787 


68772 


72597 


70029 


71386 


33 


28 


64901 


76078 


66218 


74934 


67516 


73767 


68793 


72577 


70049 


71366 


32 


29 


64923 


76059 


66240 


74915 


67538 


73747 


68814 


72557 


70070 


71345 


31 


30 


64945 


76041 


66262 


74896 


67559 


73728 


68835 


72537 


70091 


71325 


30 


31 


64967 


76022 


66284 


74876 


67580 


73708 


68857 


72517 


70112 


71305 


29 


32 


64989 


76003 


66306 


74857 


67602 


73688 


68878 


72497 


70132 


71284 


28 


33 


65011 


75984 


66327 


74838 


67623 


73669 


68899 


72477 


70153 


71264 


27 


34 


65033 


75965 


66349 


74818 


67645 


73649 


68920 


72457 


70174 


71243 


26 


35 


65055 


75946 


66371 


74799 


m^^^ 


73629 


68941 


72437 


70195 


71223 


25 


36 


65077 


75927 


66393 


74780 


67688 


73610 


68962 


72417 


70215 


71203 


24 


37 


65100 


75908 


66414 


74760 


67709 


73590 


68983 


72397 


70236 


71182 


23 


38 


65122 


75889 


66436 


74741 


67730 


73570 


69004 


72377 


70257 


71162 


22 


39 


65144 


75870 


66458 


74722 


67752 


73551 


69025 


72357 


70277 


71141 


21 


40 


65166 


75851 


66480 


74703 


67773 


73531 


69046 


72337 


70298 


71121 


20 


41 


65188 


75832 


66501 


74683 


67795 


73511 


69067 


72317 


70319 


71100 


19 


42 


65210 


75813 


66523 


74664 


67816 


73491 


69088 


72297 


70339 


71080 


18 


43 


65232 


75794 


66545 


74644 


67837 


73472 


69109 


72277 


70360 


71059 


17 


44 


65254 


75775 


^^^m 


74625 


67859 


73452 


69130 


72257 


70381 


71039 


16 


45 


65276 


75756 


66588 


74606 


67880 


73432 


69151 


72236 


70401 


71019 


15 


46 


65298' 


75738 


66610 


74586 


67901 


73413 


69172 


72216 


70422 


70998 


14 


47 


65320 


75719 


66632 


74567 


67923 


73393 


69193 


72196 


70443 


70978 


13 


48 


65342 


75700 


66653 


74548 


67944 


73373 


69214 


72176 


70463 


70957 


12 


49 


65364 


75680 


66675 


74528 


67965 


73353 


69235 


72156 


70484 


70937 


11 


50 


65386 


75661 


66697 


74509 


67987 


73333 


69256 


72136 


70505 


70916 


10 


51 


65408 


75642 


66718 


74489 


68008 


73314 


69277 


72116 


70525 


70896 


9 


52 


65430 


75623 


66740 


74470 


68029 


73294 


69298 


72095 


70546 


70875 


8 


53 


65452 


75604 


66762 


74451 


68051 


73274 


69319 


72075 


70567 


70855 


7 


54 


65474 


75585 


66783 


74431 


68072 


73254 


69340 


72055 


70587 


70834 


6 


55 


65496 


75566 


66805 


74412 


68093 


73234 


69361 


72035 


70608 


70813 


5 


56 


65518 


75547 


66827 


74392 


68115 


73215 


69382 


72015 


70628 


70793 


4 


57 


65540 


75528 


66848 


74373 


68136 


73195 


69403 


71995 


70649 


70772 


3 


58 


65562 


75509 


66870 


74353 


68157 


73175 


69424 


71974 


70670 


70752 


2 


59 


65584 


75490 


66891 


74334 


68179 


73155 


69445 


71954 


70690 


70731 


1 


60 


65606 


75471 


66913 


74314 


68200 


73135 


69466 


71934 


70711 


70711 







Cosine. 


Sine. 


Cosine. 


Sine. 


Cosine. 


Sine. 


Cosine. 


Sine. 


Cosine. 


Sine. 




t 


4* 


9° 


'A.i 


§0 


4-: 


7'^ 


4< 


5« 


4? 


%^ 


f 



APPENDIX. 



845 



LOGARITHMS OP NUMBERS. 



iv. 


o 


1 


3 


3 


4r 


O 


e 


7 


8 


3891 


I>. 


100 


GO 0000 


0434 


0868 


1301 


1734 


2166 


2598 


3029 


3461 


432 


101 


4321 


4751 


5181 


5609 


6038 


6466 


6894 


7321 


7748 


8174 


428 


102 


* 8600 


9026 


9451 


9876 


♦300 


0724 


1147 


1570 


1993 


2415 


424 


103 


01 2837 


3259 


3680 


4100 


4521 


4940 


5360 


5779 


6197 


6616 


419 


104 


*7033 


7451 


7868 


8284 


8700 


9116 


9532 


9947 


♦361 


0775 


416 


105 


02 1189 


1603 


2016 


2428 


2841 


3252 


3664 


4075 


4486 


4896 


412 


106 


5306 


5715 


6125 


6533 


6942 


7350 


7757 


8164 


8571 


8978 


408 


107 


* 9384 


9789 


♦195 


0600 


1004 


1408 


1812 


2216 


2619 


3021 


404 


108 


03 3424 


3826 


4227 


4628 


5029 


5430 


5830 


6230 


6629 


7028 


400 


109 


*7426 


7825 


8223 


8620 


9017 


9414 


9811 


♦207 


0602 


0998 


396 


110 


04 1393 


1787 


2182 


2576 


2969 


3362 


3755 


4148 


4540 


4932 


'393 


111 


5323 


5714 


6105 


6495 


6885 


7275 


7664 


8053 


8442 


8830 


389 


112 


*9218 


9606 


9993 


♦380 


0766 


1153 


1538 


1924 


2309 


2694 


386 


113 


05 3078 


3463 


3846 


4230 


4613 


4996 


5378 


5760 


6142 


6524 


382 


114 


* 6905 


7286 


7666 


8046 


8426 


8805 


9185 


9563 


9942 


♦320 


379 


115 


06 0698 


1075 


1452 


1829 


2206 


2582 


2958 


3333 


3709 


4083 


376 


116 


4458 


4832 


5206 


5580 


5953 


6326 


6699 


7071 


7443 


7815 


372 


117 


*8186 


8557 


8928 


9298 


9668 


♦038 


0407 


0776 


1145 


1514 


369 


118 


07 1882 


2250 


2617 


2985 


3352 


3718 


4085 


4451 


4816 


5182 


366 


119 


5547 


5912 


6276 


6640 


7004 


7368 


7731 


8094 


8457 


8819 


363 


120 


*9181 


9543 


9904 


♦266 


0626 


0987 


1347 


1707 


2067 


2426 


360 


121 


08 2785 


3144 


3503 


3861 


4219 


4576 


4934 


5291 


5647 


6004 


357 


122 


6360 


6716 


7071 


7426 


7781 


8136 


8490 


8845 


9198 


9552 


355 


123 


*9905 


♦258 


0611 


0963 


1315 


1667 


2018 


2370 


2721 


3071 


351 


124 


09 3422 


3772 


4122 


4471 


4820 


5169 


5518 


5866 


6215 


6562 


349 


125 


*6910 


7257 


7604 


7951 


8298 


8644 


8990 


9335 


9681 


♦026 


346 


126 


10 0371 


0715 


1059 


1403 


1747 


2091 


2434 


2777 


3119 


3462 


343 


127 


3804 


4146 


4487 


4828 


5169 


5510 


5851 


6191 


6531 


6871 


340 


128 


*7210 


7549 


7888 


8227 


8565 


8903 


9241 


9579 


9916 


♦253 


338 


129 


11 0590 


0926 


1263 


1599 


1934 


2270 


2605 


2940 


3275 


3609 


335 


130 


3943 


4277 


4611 


4944 


5278 


5611 


5943 


6276 


6608 


6940 


333 


131 


*7271 


7603 


7934 


8265 


8595 


8926 


9256 


9586 


9915 


♦245 


330 


132 


12 0574 


0903 


1231 


1560 


1888 


2216 


2544 


2871 


3198 


3525 


328 


133 


3852 


4178 


4504 


4830 


5156 


5481 


5806 


6131 


6456 


6781 


325 


134 


*7105 


7429 


7753 


8076 


8399 


8722 


9045 


9368 


9690 


♦012 


323 


135 


13 0334 


0655 


0977 


1298 


1619 


1939 


2260 


2580 


2900 


3219 


321 


136 


3539 


3858 


4177 


4496 


4814 


5133 


5451 


5769 


6086 


6403 


318 


137 


6721 


7037 


7354 


7671 


7987 


8303 


8618 


8934 


9249 


9564 


315 


138 


*9879 


♦194 


0508 


0822 


1136 


1450 


1763 


2076 


2389 


2702 


314. 


139 


14 3015 


3327 


3639 


3951 


4263 


4574 


4885 


5196 


5507 


5818 


311 


140 


6128 


6438 


6748 


7058 


7367 


7676 


7985 


8294 


8603 


8911 


309 


141 


* 9219 


9527 


9835 


♦142 


0449 


0756 


1063 


1370 


1676 


1982 


307 


142 


15 2288 


2594 


2900 


3205 


3510 


3815 


4120 


4424 


4728 


5032 


305 


143 


5336 


5640 


5943 


6246 


6549 


6852 


7154 


7457 


7759 


8061 


303 


144 


* 8362 


8664 


8965 


9266 


9567 


9868 


♦168 


0469 


0769 


1068 


301 


145 


16 1368 


1667 


1967 


2266 


2564 


2863 


3161 


3460 


3758 


4055 


299 


146 


4353 


4650 


4947 


5244 


5541 


5838 


6134 


6430 


6726 


7022 


297 


147 


7317 


7613 


7908 


8203 


8497 


8792 


9086 


9380 


9674 


9968 


295 


148 


17 0262 


0555 


0848 


1141 


1434 


1726 


2019 


2311 


2603 


2895 


293 


149 


3186 


3478 


3769 


4060 


4351 


4641 


4932 


5222 


5512 


5802 


291 


150 


6091 


6381 


6670 


6959 


7248 


7536 


7825 


8113 


8401 


8689 


289 


151 


*8977 


9264 


9552 


9839 


♦126 


0413 


0699 


0985 


1272 


1558 


287 


152 


18 1844 


2129 


2415 


2700 


2985 


3270 


3555 


3839 


4123 


4407 


285 


153 


4691 


4975 


5259 


5542 


5825, 


6108 


6391 


6674 


6956 


7239 


283 


154 


*7521 


7803 


8084 


8366 


8647 


8928 


9209 


9490 


9771 


♦051 


281 


155 


19 0332 


0612 


0892 


1171 


1451 


1730 


2010 


2289 


2567 


2846 


279 


156 


3125 


3403 


3681 


3959 


4237 


4514 


4792 


5069 


5346 


5623 


278 


157 


5900 


6176 


6453 


6729 


7005 


7281 


7556 


7832 


8107 


8382 


276 


158 


* 8657 


8932 


9206 


9481 


9755 


♦029 


0303 


0577 


0850 


1124 


274 


159 


20 1397 


1670 


1943 


2216 


2488 


2761 


3033 


3305 


3577 


3848 


272 


IV. 


O 


1 


3 


3 


4 


5 


e 


7 


8 


O 


». 



84:6 










APPENDIX. 


















LOQARITHMS OF NUMBERS. 










]V. 


o 


1 


3 


3 


4. 


5 


G 


7 


8 


9 


r>. 


160 


20 4120 


4391 


4663 


4934 


5204 


5475 


5746 


6016 


6286 


6556 


271 


161 


6826 


7096 


7365 


7634 


7904 


8173 


8441 


8710 


8979 


9247 


269 


162 


*9515 


9783 


♦051 


0319 


0586 


0853 


1121 


1388 


1654 


1921 


267 


163 


21 2188 


2454 


2720 


2986 


3252 


3518 


3783 


4049 


4314 


4579 


266 


164 


4844 


5109 


5373 


5638 


5902 


6166 


6430 


6694 


6957 


7221 


264 


165 


7484 


7747 


8010 


8273 


8536 


8798 


9060 


9323 


9585 


9846 


262 


166 


22 0108 


0370 


0631 


0892 


1153 


1414 


1675 


1936 


2196 


2456 


261 


167 


2716 


2976 


3236 


3496 


3755 


4015 


4274 


4533 


4792 


5051 


259 


168 


5309 


5568 


5826 


6084 


6342 


6600 


6858 


7115 


7372 


7630 


258 


169 


*7887 


8144 


8400 


8657 


8913 


9170 


9426 


9682 


9938 


♦193 


256 


170 


23 0449 


0704 


0960 


1215 


1470 


1724 


1979 


2234 


2488 


2742 


254 


171 


2996 


3250 


3504 


3757 


4011 


4264 


4517 


4770 


5023 


5276 


253 


172 


5528 


5781 


6033 


6285 


6537 


6789 


7041 


7292 


7544 


7795 


252 


173 


*8046 


8297 


8548 


8799 


9049 


9299 


9550 


9800 


♦050 


0300 


250 


174 


24 0549 


0799 


1048 


1297 


1546 


1795 


2044 


2293 


2541 


2790 


249 


175 


3038 


3286 


3534 


3782 


4030 


4277 


4525 


4772 


5019 


5266 


248 


176 


5513 


5759 


6006 


6252 


6499 


6745 


6991 


7237 


7482 


7728 


246 


177 


*7973 


8219 


8464 


8709 


8954 


9198 


9443 


9687 


9932 


♦176 


245 


178 


25 0420 


0664 


0908 


1151 


1395 


1638 


1881 


2125 


2368 


2610 


243 


179 


2853 


3096 


3338 


3580 


3822 


4064 


4306 


4548 


4790 


5031 


242 


180 


5273 


5514 


5755 


5996 


6237 


6477 


6718 


6958 


7198 


7439 


241 


181 


7679 


7918 


8158 


8398 


8637 


8877 


9116 


9355 


9594 


9833 


239 


182 


26 0071 


0310 


0548 


0787 


1025 


1263 


1501 


1739 


1976 


2214 


238 


183 


2451 


2688 


2925 


3162 


3399 


3636 


3873 


4109 


4346 


4582 


237 


184 


4818 


5054 


5290 


5525 


5761 


5996 


6232 


6467 


6702 


6937 


235 


185 


7172 


7406 


7641 


7875 


8110 


8344 


8578 


8812 


9046 


9279 


234 


186 


*9513 


9746 


9980 


♦213 


0446 


0679 


0912 


1144 


1377 


1609 


233 


187 


27 1842 


2074 


2306 


2538 


2770 


3001 


3233 


3464 


3696 


3927 


232 


188 


4158 


4389 


4620 


4850 


5081 


5311 


5542 


5772 


6002 


6232 


230 


189 


6462 


6692 


6921 


7151 


7380 


7609 


7838 


8067 


8296 


8525 


229 


190. 


*8754 


8982 


9211 


9439 


9667 


9895 


♦123 


0351 


0578 


0806 


228 


191 


28 1033 


1261 


1488 


1715 


1942 


2169 


2396 


2622 


2849 


3075 


227 


192 


3301 


3527 


3753 


3979 


4205 


4431 


4656 


4882 


5107 


5332 


226 


193 


5557 


5782 


6007 


6232 


6456 


6681 


6905 


7130 


7354 


7578 


225 


194 


7802 


8026 


8249 


8473 


8696 


8920 


9143 


9366 


9589 


9812 


223 


195 


29 0035 


0257 


0480 


0702 


0925 


1147 


1369 


1591 


1813 


2034 


222 


196 


2256 


2478 


2699 


2920 


3141 


3363 


3584 


3804 


4025 


4246 


221 


197 


4466 


4687 


4907 


5127 


5347 


5567 


5787 


6007 


6226 


6446 


220 


198 


6665 


6884 


7104 


7323 


7542 


7761 


7979 


8198 


8416 


8635 


219 


199 


*8853 


9071 


9289 


9507 


9725 


9943 


♦161 


0378 


0595 


0813 


218 


200 


30 1030 


1247 


1464 


1681 


1898 


2114 


2331 


2547 


2764 


2980 


217 


201 


3196 


3412 


3628 


3844 


4059 


4275 


4491 


4706 


4921 


5136 


216 


202 


5351 


5566 


5781 


5996 


6211 


6425 


6639 


6854 


7068 


7282 


215 


203 


7496 


7710 


7924 


8137 


8351 


8564 


8778 


8991 


9204 


9417 


213 


204 


*9630 


9843 


♦056 


0268 


0481 


0693 


0906 


1118 


1330 


1542 


212 


205 


31 1754 


1966 


2177 


2389 


2600 


2812 


3023 


3234 


3445 


3656 


211 


206 


3867 


4078 


4289 


4499 


4710 


4920 


5130 


5340 


5551 


5760 


210 


207 


5970 


6180 


6390 


6599 


6809 


7018 


7227 


7436 


7646 


7854 


209 


208 


8063 


8272 


8481 


8689 


8898 


9106 . 


9314 


9522 


9730 


9938 


208 


209 


32 0146 


0354 


0562 


0769 


0977 


1184 


1391 


1598 


1805 


2012 


207 


210 


2219 


2426 


2633 


2839 


3046 


3252 


3458 


3665 


3871 


4077 


206 


211 


4282 


4488 


4694 


4899 


5105 


5310 


5516 


5721 


5926 


6131 


205 


212 


6336 


6541 


6745 


6950 


7155 


7359 


7563 


7767 


7972 


8176 


204 


213 


*8380 


8583 


8787 


8991 


9194 


9398 


9601 


9805 


♦008 


0211 


203 


214 


33 0414 


0617 


0819 


1022 


1225 


1427 


1630 


1832 


2034 


2236 


202 


215 


2438 


2640 


2842 


3044 


3246 


3447 


3649 


3850 


4051 


4253 


202 


216 


4454 


4655 


4856 


5057 


5257 


5458 


5658 


5859 


6059 


6260 


201 


217 


6460 


6660 


6860 


7060 


7260 


7459 


7659 


7858 


8058 


8257 


200 


218 


* 8456 


8656 


8855 


9054 


9253 


9451 


9650 


9849 


♦047 


0246 


199 


219 


34 0444 


0642 


0841 


1039 


1237 


]435 


1632 


1830 


2028 


2225 


198 


3V. 


O 


1 


3 


3 


4 


5 


G 


! ^ 


« 


9 


r>. 



APPENDIX. 



847 



LOGARITHMS OP NUMBERS. 



]V. 





1 


3 


3 


4 


5 





7I 


8 


9 


I>. 


220 


34 2423 


2620 


2817 


3014 


3212 


3409 


3606 


3802 


3999 


4196 


197 


221 


4392 


4589 


4785 


4981 


5178 


5374 


5570 


5766 


5962 


6157 


196 


222 


6353 


6549 


6744 


6939 


7135 


7330 


7525 


7720 


7915 


8110 


195 


223 


* 8305 


8500 


8694 


8889 


9083 


9278 


9472 


9666 


9860 


♦054 


194 


224 


35 0248 


0442 


0636 


0829 


1023 


1216 


1410 


1603 


1796 


1989 


193 


225 


2183 


2375 


2568 


2761 


2954 


3147 


3339 


3532 


3724 


3916 


193 


226 


4108 


4301 


4493 


4685 


4876 


5068 


5260 


5452 


5643 


5834 


192 


227 


6026 


6217 


6408 


6599 


6790 


6981 


7172 


7363 


7554 


7744 


191 


228 


7935 


8125 


8316 


8506 


8696 


8886 


9076 


9266 


9456 


9646 


190 


229 


* 9835 


♦025 


0215 


0404 


0593 


0783 


0972 


1161 


1350 


1539 


189 


230 


36 1728 


1917 


2105 


2294 


2482 


2671 


2859 


3048 


3236 


3424 


188 


231 


3612 


3800 


3988 


4176 


4363 


4551 


4739 


4926 


5113 


5301 


188 


232 


5488 


5675 


5862 


6049 


6236 


6423 


6610 


6796 


6983 


7169 


187 


233 


7356 


7542 


7729 


7915 


8101 


8287 


8473 


8659 


8845 


9030 


186 


234 


*9216 


9401 


9587 


9772 


9958 


♦143 


0328 


0513 


0698 


0883 


185 


235 


37 1068 


1253 


1437 


1622 


1806 


1991 


2175 


2360 


2544 


2728 


184 


236 


2912 


3096 


3280 


3464 


3647 


3831 


4015 


4198 


4382 


4565 


184 


237 


4748 


4932 


5115 


5298 


5481 


5664 


5846 


6029 


6212 


6394 


183 


238 


6577 


6759 


6942 


7124 


7306 


7488 


7670 


7852 


8034 


8216 


182 


239 


*8398 


8580 


8761 


8943 


9124 


9306 


9487 


9668 


9849 


♦030 


181 


240 


38 0211 


0392 


0573 


0754 


0934 


1115 


1296 


1476 


1656 


1837 


181 


241 


2017 


2197 


2377 


2557 


2737 


2917 


3097 


3277 


3456 


3636 


180 


242 


3815 


3995 


4174 


4353 


4533 


4712 


4891 


5070 


5249 


5428 


179 


243 


5606 


5785 


5964 


6142 


6321 


6499 


6677 


6856 


7034 


7212 


178 


244 


7390 


7568 


7746 


7923 


8101 


8279 


8456 


8634 


8811 


8989 


178 


245 


*9166 


9343 


9520 


9698 


9875 


♦051 


0228 


0405 


0582 


0759 


177 


246 


39 0935 


1112 


1288 


1464 


1641 


1817 


1993 


2169 


2345 


2521 


176 


247 


2697 


2873 


3048 


3224 


3400 


3575 


3751 


3926 


4101 


4277 


176 


248 


4452 


4627 


4802 


4977 


5152 


5326 


5501 


5676 


5850 


6025 


175 


249 


6199 


6374 


6548 


6722 


6896 


7071 


7245 


7419 


7592 


7766 


174 


250 


7940 


8114 


8287 


8461 


8634 


8808 


8981 


9154 


9328 


9501 


173 


251 


*9674 


9847 


♦020 


0192 


0365 


0538 


0711 


0883 


1056 


1228 


173 


252 


40 1401 


1573 


1745 


1917 


2089 


2261 


2433 


2605 


2777 


2949 


172 


253 


3121 


3292 


3464 


3635 


3807 


3978 


4149 


4320 


4492 


4663 


171 


254 


4834 


5005 


5176 


5346 


5517 


5688 


5858 


6029 


6199 


6370 


171 


255 


6540 


6710 


6881 


7051 


7221 


7391 


7561 


7731 


7901 


8070 


170 


256 


8240 


'8410 


8579 


8749 


8918 


9087 


9257 


9426 


9595 


9764 


169 


257 


*9933 


♦102 


0271 


0440 


0609 


0777 


0946 


1114 


1283 


1451 


169 


258 


41 1620 


1788 


1956 


2124 


2293 


2461 


2629 


2796 


2964 


3132 


168 


259 


3300 


3467 


3635 


3803 


3970 


4137 


4305 


4472 


4639 


4806 


167 


260 


4973 


5140 


5307 


5474 


5641 


5808 


5974 


6141 


6308 


6474 


167 


261 


6641 


6807 


6973 


7139 


7306 


7472 


7638 


7804 


7970 


8135 


166 


262 


8301 


8467 


8633 


8798 


8964 


9129 


9295 


9460 


9625 


9791 


165 


263 


*9956 


♦121 


0286 


0451 


0616 


0781 


0945 


1110 


1275 


1439 


165 


264 


42 1604 


1768 


1933 


2097 


2261 


2426 


2590 


2754 


2918 


3082 


164 


265 


3246 


3410 


3574 


3737 


3901 


4065 


4228 


4392 


4555 


4718 


164 


266 


4882 


5045 


5208 


5371 


5534 


5697 


5860 


6023 


6186 


6349 


163 


267 


6511 


6674 


6836 


6999 


7161 


7324 


7486 


7648 


7811 


7973 


162 


268 


8135 


8297 


8459 


8621 


8783 


8944 


9106 


9268 


9429 


9591 


162 


269 


*9752 


9914 


♦075 


0236 


0398 


0559 


0720 


0881 


1042 


1203 


161 


270 


43 1364 


1525 


1685 


1846 


2007 


2167 


2328 


2488 


2649 


2809 


161 


271 


2969 


3130 


3290 


3450 


3610 


3770 


3930 


4090 


4249 


4409 


160 


272 


4569 


4729 


4888 


5048 


5207 


5367 


5526 


5685 


5844 


6004 


159 


273 


6163 


6322 


6481 


6640 


6799 , 


6957 


7116 


7275 


7433 


7592 


159 


274 


7751 


7909 


8067 


8226 


8384 


8542 


8701 


8859 


9017 


9175 


158 


275 


* 9333 


9491 


1 9648 


9806 


9964 


♦122 


0279 


0437 


0594 


0752 


158 


276 


44 0909 


1066 


; 1224 


1381 


1538 


1695 


, 1852 


2009 


2166 


2323 


157 


277 


2480 


2637 


1 2793 


' 2950 


3106 


3263 


' 3419 


3576 


3732 


3889 


157 


278 


4045 


! 4201 


1 4357 


1 4513 


. 4669 


, 4825 


i 4981 


5137 


5293 


5449 


156 


279 


5604 


j 5760 


; 5915 


! 6071 


1 6226 

1 


6382 

t 


6537 


6692 


6848 


7003 


155 


]V. 





1 


3 


3 


1' ■ 
4. 


5 


c 


7 


8 


9 





84:8 










APPENDIX. 


















IXJGARITHMS OP NUMBSRS. 










3V. 


O 


X 


3 


3 


4. 


5 


e 


7 


s 


9 


I>. 


280 


44 7158 


7313 


7468 


7623 


7778 


7933 


8088 


8242 


8397 


8552 


155 


281 


*8706 


8861 


9015 


9170 


9324 


9478 


9633 


9787 


9941 


♦095 


154 


282 


45 0249 


0403 


0557 


0711 


0865 


1018 


1172 


1326 


1479 


1633 


154 


283 


1786 


1940 


2093 


2247 


2400 


2553 


2706 


2859 


3012 


3165 


153 


284 


3318 


3471 


3624 


3777 


3930 


4082 


4235 


4387 


4540 


4692 


153 


285 


4845 


4997 


515P 


5302 


5454 


5606 


5758 


5910 


6062 


6214 


152 


286 


6366 


6518 


6670 


6821 


6973 


7125 


7276 


7428 


7579 


7731 


152 


287 


7882 


8033 


8184 


8336 


8487 


8638 


8789 


8940 


9091 


9242 


151 


288 


* 9392 


9543 


9694 


9845 


9995 


♦146 


0296 


0447 


0597 


0748 


151 


289 


46 0898 


1048 


1198 


1348 


1499 


1649 


1799 


1948 


2098 


2248 


150 


290 


2398 


2548 


2697 


2847 


2997 


3146 


3296 


3445 


3594 


3744 


150 


291 


3893 


4042 


4191 


4340 


4490 


4639 


4788 


4936 


5085 


5234 


149 


292 


5383 


5532 


5680 


5829 


5977 


6126 


6274 


6423 


6571 


6719 


149 


293 


6868 


7016 


7164 


7312 


7460 


7608 


7756 


7904 


8052 


8200 


148 


294 


8347 


8495 


8643 


8790 


8938 


9085 


9233 


9380 


9527 


9675 


148 


295 


*9822 


9969 


♦116 


0263 


0410 


0557 


0704 


0851 


0998 


1145 


147 


296 


47 1292 


1438 


1585 


1732 


1878 


2025 ■ 


2171 


2318 


2464 


2610 


146 


297 


2756 


2903 


3049 


3195 


3341 


3487 


3633 


3779 


3925 


4071 


146 


298 


4216 


4362 


4508 


4653 


4799 


4944 


5090 


5235 


5381 


5526 


146 


299 


5671 


5816 


5962 


6107 


6252 


6397 


6542 


6687 


6832 


6976 


145 


300 


7121 


7266 


7411 


7555 


7700 


7844 


7989 


8133 


8278 


8422 


145 


301 


8566 


8711 


8855 


8999 


9143 


9287 


9431 


9575 


9719 


9863 


144 


302 


48 0007 


0151 


0294 


0438 


0582 


0725 


0869 


1012 


1156 


1299 


144 


303 


1443 


1586 


1729 


1872 


2016 


2159 


2302 


2445 


2588 


2731 


143 


304 


2874 


3016 


3159 


3302 


3445 


3587 


^3730 


3872 


4015 


4157 


143 


305 


4300 


4442 


4585 


4727 


4869 


5011 


5153 


5295 


5437 


5579 


142 


306 


5721 


5863 


6005 


6147 


6289 


6430 


6572 


6714 


6855 


6997 


142 


307 


7138 


7280 


7421 


7563 


7704 


7845 


7986 


8127 


8269 


8410 


141 


308 


8551 


8692 


8833 


8974 


9114 


9255 


9396 


9537 


9677 


9818 


141 


309 


* 9958 


♦099 


0239 


0380 


0520 


0661 


0801 


0941 


1081 


1222 


140 


310 


49 1362 


1502 


1642 


1782 


1922 


2062 


2201 


2341 


2481 


2621 


140 


311 


2760 


2900 


3040 


3179 


3319 


3458 


3597 


3737 


3876 


4015 


139 


312 


4155 


4294 


4433 


4572 


4711 


4850 


4989 


5128 


5267 


5406 


139 


313 


5544 


5683 


5822 


5960 


6099 


6238 


6376 


6515 


6653 


6791 


139 


314 


6930 


7068 


7206 


7344 


7483 


7621 


7759 


7897 


8035 


8173 


138 


315 


8311 


8448 


8586 


8724 


8862 


8999 


9137 


9275 


9412 


9550 


138 


316 


*9687 


9824 


9962 


♦099 


0236 


0374 


0511 


0648 


0785 


0922 


137 


317 


50 1059 


1196 


1333 


1470 


1607 


1744 


1880 


2017 


2154 


2291 


137 


318 


2427 


2564 


2700 


2837 


2973 


3109 


3246 


3382 


3518 


3655 


136 


319 


3791 


3927 


4063 


4199 


4335 


4471 


4607 


4743 


4878 


5014 


136 


320 


5150 


5286 


5421 


5557 


5693 


5828 


5964 


6099 


6234 


6370 


136 


321 


6505 


6640 


6776 


6911 


7046 


7181 


7316 


7451 


7586 


7721 


135 


322 


7856 


7991 


8126 


8260 


8395 


8530 


8664 


8799 


8934 


9068 


135 


323 


*9203 


9337 


9471 


9606 


9740 


9874 


♦009 


0143 


0277 


0411 


134 


324 


51 0545 


0679 


0813 


0947 


1081 


1215 


1349 


1482 


1616 


1750 


134 


325 


1883 


2017 


2151 


2284 


2418 


2551 


2684 


2818 


2951 


3084 


133 


326 


3218 


3351 


3484 


3617 


3750 


3883 


4016 


■ 4149 


4282 


4414 


133 


327 


4548 


4681 


4813 


4946 


5079 


5211 


5344 


5476 


5609 


5741 


133 


328 


5874 


6006 


6139 


6271 


6403 


6535 


6668 


6800 


6932 


7064 


132 


329 


7196 


7328 


7460 


7592 


7724 


7855 


7987 


8119 


8251 


8382 


132 


330 


8514 


8646 


8777 


8909 


9040 


9171 


9303 


9434 


9566 


9697 


131 


331 


*9828 


9959 


♦090 


0221 


0353 


0484 


0615 


0745 


0876 


1007 


131 


332 


52 1138 


1269 


1400 


1530 


1661 


1792 


1922 


2053 


2183 


2314 


131 


333 


2444 


2575 


2705 


2835 


2966 


3096 


3226 


3356 


3486 


3616 


130 


334 


3746 


3876 


4006 


4136 


4266 


4396 


4526 


4656 


4785 


4915 


130 


335 


. 5045 


5174 


5304 


5434 


5563 


5693 


5822 


5951 


6081 


6210 


129 


336 


6339 


6469 


6598 


6727 


6856 


6985 


7114 


7243 


7372 


7501 


129 


337 


7630 


7759 


7888 


8016 


8145 


8274 


8402 


8531 


8660 


8788 


129 


338 


*8917 


9045 


9174 


9302 


9430 


9559 


9687 


9815 


9943 


♦072 


128 


339 


53 0200 


0328 


0456 


0584 


0712 


0840 


0968 


1096 


1223 


1351 


128 


N, 


o 


1 


3 


.3 


4 


5 


G 


•7 


8 


9 


I>. 



APPENDIX. 



849 



LOGARITHMS OP NU3IBERS. 



IV. 


O 


1 


3 


3 


4. 


5 


O 


7 


8 


O 


r>. 


340 


53 1479 


1607 


1734 


1862 


1990 


2117 


2245 


2372 


2500 


2627 


128 


341 


2754 


2882 


3009 


3136 


3264 


3391 


3518 


3645 


3772 


3899 


127 


342 


4026 


4153 


4280 


4407 


4534 


4661 


4787 


4914 


5041 


5167 


127 


343 


5294 


5421 


5547 


5674 


5800 


5927 


6053 


6180 


6306 


6432 


126 


344 


6558 


6685 


6811 


6937 


7063 


7189 


7315 


7441 


7567 


7693 


126 


345 


7819 


7945 


8071 


8197 


8322 


8448 


8574 


8699 


8825 


8951 


126 


346 


*9076 


9202 


9327 


9452 


9578 


9703 


9829 


9954 


♦079 


0204 


125 


347 


54 0329 


0455 


0580 


0705 


0830 


0955 


1080 


1205 


1330 


1454 


125 


348 


1579 


1704 


1829 


1953 


2078 


2203 


2327 


2452 


2576 


2701 


125 


349 


2825 


2950 


3074 


3199 


3323 


3447 


3571 


3696 


3820 


3944 


124 


350 


4068 


4192 


4316 


4440 


4564 


4688 


4812 


4936 


5060 


5183 


124 


351 


5307 


5431 


5555 


5678 


5802 


5925 


6049 


6172 


6296 


6419 


124 


352 


6543 


6Q66 


6789 


6913 


7036 


7159 


7282 


7405 


7529 


7652 


123 


353 


7775 


7898 


8021 


8144 


8267 


8389 


8512 


8635 


8758 


8881 


123 


354 


*9003 


9126 


9249 


9371 


9494 


9616 


9739 


9861 


9984 


♦106 


123 


355 


55 0228 


0351 


0473 


0595 


0717 


0840 


0962 


1084 


1206 


1328 


122 


356 


1450 


1572 


1694 


1816 


1938 


2060 


2181 


2303 


2425 


2547 


122 


357 


2668 


2790 


2911 


3033 


3155 


3276 


3398 


3519 


3640 


3762 


121 


358 


3883 


4004 


4126 


4247 


4368 


4489 


4610 


4731 


4852 


4973 


121 


359 


5094 


5215 


5336 


5457 


5578 


5699 


5820 


5940 


6061 


6182 


121 


360 


6303 


6423 


6544 


6664 


6785 


6905 


7026 


7146 


7267 


7387 


120 


361 


7507 


7627 


7748 


7868 


7988 


8108 


8228 


8349 


8469 


8589 


120 


362 


8709 


8829 


8948 


9068 


9188 


9308 


9428 


9548 


9667 


9787 


120 


363 


*9907 


♦026 


0146 


0265 


0385 


0504 


0624 


0743 


0863 


0982 


119 


364 


56 1101 


1221 


1340 


1459 


1578 


1698 


1817 


1936 


2055 


2174 


119 


365 


2293 


2412 


2531 


2650 


2769 


2887 


3006 


3125 


3244 


3362 


119 


366 


3481 


3600 


3718 


3837 


3955 


4074 


4192 


4311 


4429 


4548 


119 


367 


4666 


4784 


4903 


5021 


5139 


5257 


5376 


5494 


5612 


5730, 


118 


368 


5848 


5966 


6084 


6202 


6320 


6437 


6555 


6673 


6791 


6909 


118 


369 


7026 


7144 


7262 


7379 


7497 


7614 


7732 


7849 


7967 


8084 


118 


370 


8202 


8319 


8436 


8554 


8671 


8788 


8905 


9023 


9140 


9257 


117 


371 


*9374 


9491 


9608 


9725 


9842 


9959 


♦076 


0193 


0309 


0426 


117 


372 


57 0543 


0660 


0776 


0893 


1010 


1126 


1243 


1359 


1476 


1592 


117 


373 


1709 


1825 


1942 


2058 


2174 


2291 


2407 


2523 


2639 


2755 


116 


374 


2872 


2988 


3104 


3220 


3336 


3452 


3568 


3684 


3800 


3915 


116 


375 


4031 


4147 


4263 


4379 


4494 


4610 


4726 


4841 


4957 


5072 


116 


376 


5188 


5303 


5419 


5534 


5650 


5765 


5880 


5996 


6111 


6226 


115 


377 


6341 


6457 


6572 


6687 


6802 


6917 


7032 


7147 


7262 


7377 


115 


378 


7492 


7607 


7722 


7836 


7951 


8066 


8181 


8295 


8410 


8525 


115 


379 


8639 


8754 


8868 


8983 


9097 


9212 


9326 


9441 


9555 


9669 


114 


380 


*9784 


9898 


♦012 


0126 


0241 


0355 


0469 


0583 


0697 


0811 


114 


381 


58 0925 


1039 


1153 


1267 


1381 


1495 


1608 


1722 


1836 


1950 


114 


382 


2063 


2177 


2291 


2404 


2518 


2631 


2745 


2858 


2972 


3085 


114 


383 


3199 


3312 


3426 


3539 


3652 


3765 


3879 


3992 


4105 


4218 


113 


384 


4331 


4444 


4557 


4670 


4783 


4896 


5009 


5122 


5235 


5348 


113 


385 


5461 


5574 


5686 


5799 


5912 


6024 


6137 


6250 


6362 


6475 


113 


386 


6587 


6700 


6812 


6925 


7037 


7149 


7262 


7374 


7486 


7599 


112 


387 


7711 


7823 


7935 


8047 


8160 


8272 


8384 


8496 


8608 


8720 


112 


388 


8832 


8944 


9056 


9167 


9279 


9391 


9503 


9615 


9726 


9838 


112 


389 


*9950 


♦061 


0173 


0284 


0396 


0507 


0619 


0730 


0842 


0953 


112 


390 


59 1065 


1176 


1287 


1399 


1510 


1621 


1732 


1843 


1955 


2066 


111 


391 


2177 


2288 


2399 


2510 


2621 


2732 


2843 


2954 


3064 


3175 


111 


392 


3286 


3397 


3508 


3618 


3729 


3840 


3950 


4061 


4171 


4282 


111 


393 


4393 


4503 


4614 


4724 


4834 


4945 


5055 


5165 


5276 


5386 


110 


394 


5496 


5606 


5717 


5827 


5937 


6047 


6157 


6267 


6377 


6487 


110 


395 


6597 


6707 


6817 


6927 


7037 


7146 


7256 


7366 


7476 


7586 


110 


396 


7695 


7805 


7914 


8024 


8134 


8243 


8353 


8462 


8572 


8681 


110 


397 


8791 


8900 


9009 


9119 


9228 


9337 


9446 


9556 


9665 


9774 


109 


398 


*9883 


9992 


♦101 


0210 


0319 


0428 


0537 


0646 


0755 


0864 


109 


399 


60 0973 


1082 


1191 


1299 


1408 


1517 


1625 


1734 


1843 


1951 


109 


N. 


O 


1 


3 


3 


4. 


5 


G 


7 


8 


9 


I>. 



55 



850 



APPENDIX. 



LOGARITHMS OF NUMBERS. 



]V. 


o 


X 


3 


3 


4. 


5 


e 


7 


8 


O 


r>. 


400 


60 2060 


2169 


2277 


2386 


2494 


2603 


2711 


2819 


2928 


3036 


108 


401 


3144 


3253 


3361 


3469 


3577 


3686 


3794 


3902 


4010 


4118 


108 


402 


4226 


4334 


4442 


4550 


4658 


4766 


4874 


4982 


5089 


5197 


108 


403 


5305 


5413 


5521 


5628 


5736 


5844 


5951 


6059 


6166 


6274 


108 


404 


6381 


6489 


6596 


6704 


6811 


6919 


7026 


7133 


7241 


7348 


107 


405 


7455 


7562 


7669 


7777 


7884 


7991 


8098 


8205 


8312 


8419 


107 


406 


8526 


8633 


8740 


8847 


8954 


9061 


9167 


9274 


9381 


9488 


107 


407 


*9594 


9701 


9808 


9914 


♦021 


0128 


0234 


0341 


0447 


0554 


107 


408 


61 0660 


0767 


0873 


0979 


1086 


1192 


1298 


1405 


1511 


1617 


106 


409 


1723 


1829 


1936 


2042 


2148 


2254 


2360 


2466 


2572 


2678 


106 


410 


2784 


2890 


2996 


3102 


3207 


3313 


3419 


3525 


3630 


3736 


106 


411 


3842 


3947 


4053 


4159 


4264 


4370 


4475 


4581 


4686 


4792 


106 


412 


4897 


5003 


5108 


5213 


5319 


5424 


5529 


5634 


5740 


5845 


105 


413 


5950 


6055 


6160 


6265 


6370 


6476 


6581 


6686 


6790 


6895 


105 


414 


7000 


7105 


7210 


7315 


7420 


7525 


7629 


7734 


7839 


7943 


105 


415 


8048 


8153 


8257 


8362 


8466 


8571 


8676 


8780 


8884 


8989 


105 


416 


*9093 


9198 


9302 


9406 


9511 


9615 


9719 


9824 


9928 


♦032 


104 


417 


62 0136 


0240 


0344 


0448 


0552 


0656 


0760 


0864 


0968 


1072 


104 


418 


1176 


1280 


1384 


1488 


1592 


1695 


1799 


1903 


2007 


2110 


104 


419 


2214 


2318 


2421 


2525 


2628 


2732 


2835 


2939 


3042 


3146 


104 


420 


3249 


3353 


3456 


3559 


3663 


3766 


3869 


3973 


4076 


4179 


103 


421 


4282 


4385 


4488 


4591 


4695 


4798 


4901 


5004 


5107 


5210 


103 


422 


5312 


5415 


5518 


5621 


5724 


5827 


5929 


6032 


6135 


6238 


103 


423 


6340 


6443 


6546 


6648 


6751 


6853 


6956 


7058 


7161 


7263 


103 


424 


7366 


7468 


7571 


7673 


7775 


7878 


7980 


8082 


8185 


8287 


102 


425 


8389 


8491 


8593 


8695 


8797 


8900 


9002 


9104 


9206 


9308 


102 


426 


*9410 


9512 


9613 


9715 


9817 


9919 


♦021 


0123 


0224 


0326 


102 


427 


63 0428 


0530 


0631 


0733 


0835 


0936 


1038 


1139 


1241 


1342 


102 


428 


1444 


1545 


1647 


1748 


1849 


1951 


2052 


2153 


2255 


2356 


101 


429 


2457 


2559 


2660 


2761 


2862 


2963 


3064 


3165 


3266 


3367 


101 


430 


3468 


3569 


3670 


3771 


3872 


3973 


4074 


4175 


4276 


4376 


100 


431 


4477 


4578 


4679 


4779 


4880 


4981 


5081 


5182 


5283 


5383 


100 


432 


5484 


5584 


5685 


5785 


5886 


5986 


6087 


6187 


6287 


6388 


100 


433 


6488 


6588 


6688 


6789 


6889 


6989 


7089 


7189 


7290 


7390 


100 


434 


7490 


7590 


7690 


7790 


7890 


7990 


8090 


8190 


8290 


8389 


99 


435 


8489 


8589 


8689 


8789 


8888 


8988 


9088 


9188 


9287 


9387 


99 


436 


*9486 


9586 


9686 


9785 


9885 


9984 


♦084 


0183 


0283 


0382 


99 


437 


64 0481 


0581 


0680 


0779 


0879 


0978 


1077 


1177 


1276 


1375 


99 


438 


1474 


1573 


1672 


1771 


1871 


1970 


2069 


2168 


2267 


2366 


99 


439 


2465 


2563 


2662 


2761 


2860 


2959 


3058 


3156 


3255 


3354 


99 


440 


3453 


3551 


3650 


3749 


3847 


3946 


4044 


4143 


4242 


4340 


98 


441 


4439 


4537 


4636 


4734 


4832 


4931 


5029 


5127 


5226 


5324 


98 


442 


5422 


5521 


5619 


5717 


5815 


5913 


6011 


6110 


6208 


6306 


98 


443 


6404 


6502 


6600 


6698 


6796 


6894 


6992 


7089 


7187 


7285 


98 


444 


7383 


7481 


7579 


7676 


7774 


7872 


7969 


8067 


8165 


8262 


98 


445 


8360 


8458 


8555 


8653 


8750 


8848 


8945 


9043 


9140 


9237 


97 


446 


* 9335 


9432 


9530 


9627 


9724 


9821 


9919 


. ^016 


0113 


0210 


97 


447 


65 0308 


0405 


0502 


0599 


0696 


0793 


0890 


0987 


1084 


1181 


97 


448 


1278 


1375 


1472 


1569 


1666 


1762 


1859 


1956 


2053 


2150 


97 


449 


2246 


2343 


2440 


2536 


2633 


2730 


2826 


2923 


3019 


3116 


97 


450 


3213 


3309 


3405 


3502 


3598 


3695 


3791 


3888 


3984 


4080 


96 


451 


4177 


4273 


4369 


4465 


4562 


4658 


4754 


4850 


4946 


5042 


96 


452 


5138 


5235 


5331 


5427 


5523 


5619 


5715 


5810 


5906 


6002 


96 


453 


6098 


6194 


6290 


6386 


6482 


6577 


6673 


6769 


6864 


6960 


96 


454 


7056 


7152 


7247 


7343 


7438 


7534 


7629 


7725 


7820 


7916 


96 


455 


8011 


8107 


8202 


8298 


8393 


8488 


8584 


8679 


8774 


8870 


95 


456 


8965 


9060 


9155 


9250 


9346 


9441 


9536 


9631 


9726 


9821 


95 


457 


* 9916 


♦Oil 


0106 


0201 


0296 


0391 


0486 


0581 


0676 


0771 


95 


458 


66 0865 


0960 


1055 


1150 


1245 


1339 


1434 


1529 


1623 


1718 


95 


459 


1813 


1907 


2002 


2096 


2191 


2286 


2380 


2475 


2569 


2663 


95 


]V. 


« 


1 


2 


3 


4. 


5 


6 


T 


8 


9 


r>. 



APPENDIX. 



851 



LOGARITHMS OP NUMBERS. 



IV. 


o 


1 


3 


3 


4. 


5 


G 


7 


8 


O 


I>. 


460 


66 2758 


2852 


2947 


3041 


3135 


3230 


3324 


3418 


3512 


3607 


94 


461 


3701 


3795 


3889 


3983 


4078 


4172 


4266 


4360 


4454 


4548 


94 


462 


4642 


4736 


4830 


4924 


5018 


5112 


5206 


5299 


5393 


5487 


94 


463 


5581 


5675 


5769 


5862 


5956 


6050 


6143 


6237 


6331 


6424 


94 


464 


6518 


6612 


6705 


6799 


6892 


6986 


7079 


7173 


7266 


7360 


94 


465 


7453 


7546 


7640 


7733 


7826 


7920 


8013 


8106 


8199 


8293 


93 


466 


8386 


8479 


8572 


8665 


8759 


8852 


8945 


9038 


9131 


9224 


93 


467 


* 9317 


9410 


9503 


9596 


9689 


9782 


9875 


9967 


♦060 


0153 


93 


468 


67 0246 


0339 


0431 


0524 


0617 


0710 


0802 


0895 


0988 


1080 


93 


469 


1173 


1265 


1358 


1451 


1543 


1636 


1728 


1821 


1913 


2005 


93 


470 


2098 


2190 


2283 


2375 


2467 


2560 


2652 


2744 


2836 


2929 


92 


471 


3021 


3113 


3205 


3297 


3390 


3482 


3574 


3666 


3758 


3850 


92 


472 


3942 


4034 


4126 


4218 


4310 


4402 


4494 


4586 


4677 


4769 


92 


473 


4861 


4953 


5045 


5137 


5228 


5320 


5412 


5503 


5595 


5687 


92 


474 


5778 


5870 


5962 


6053 


6145 


6236 


6328 


6419 


6511 


6602 


92 


475 


6694 


6785 


6876 


6968 


7059 


7151 


7242 


7333 


7424 


7516 


91 


476 


7607 


7698 


7789 


7881 


7972 


8063 


8154 


8245 


8336 


8427 


91 


477 


8518 


8609 


8700 


8791 


8882 


8973 


9064 


9155 


9246 


9337 


91 


478 


*9428 


9519 


9610 


9700 


9791 


9882 


9973 


♦063 


0154 


0245 


91 


479 


68 0336 


0426 


0517 


0607 


0698 


0789 


0879 


0970 


1060 


1151 


91 


480 


1241 


1332 


1422 


1513 


1603 


1693 


1784 


1874 


1964 


2055 


90 


481 


2145 


2235 


2326 


2416 


2506 


2596 


2686 


2777 


2867 


2957 


90 


482 


3047 


3137 


3227 


3317 


3407 


3497 


3587 


3677 


3767 


3857 


90 


483 


3947 


4037 


4127 


4217 


4307 


4396 


4486 


4576 


4666 


4756 


90 


484 


4845 


4935 


5025 


5114 


5204 


5294 


5383 


5473 


5563 


5652 


90 


485 


5742 


5831 


5921 


6010 


6100 


6189 


6279 


6368 


6458 


■ 6547 


89 


486 


6636 


5726 


6815 


6904 


6994 


7083 


7172 


7261 


7351 


7440 


89 


487 


7529 


7618 


7707 


7796 


7886 


7975 


8064 


8153 


8242 


8331 


89 


488 


8420 


8509 


8598 


8687 


8776 


8865 


8953 


9042 


9131 


9220 


89 


489 


*9309 


9398 


9486 


9575 


9664 


9753 


9841 


9930 


♦019 


0107 


89 


490 


69 0196 


0285 


0373 


0462 


0550 


0639 


0728 


0816 


0905 


0993 


89 


491 


1081 


1170 


1258 


1347 


1435 


1524 


1612 


1700 


1789 


1877 


88 


492 


1965 


2053 


2142 


2230 


2318 


2406 


2494 


2583 


2671 


2759 


88 


493 


2847 


2935 


3023 


3111 


3199 


3287 


3375 


3463 


3551 


3639 


88 


494 


3727 


3815 


3903 


3991 


4078 


4166 


4254 


4342 


4430 


4517 


88 


495 


4605 


4693 


4781 


4868 


4956 


5044 


5131 


5219 


5307 


5394 


88 


496 


5482 


5569 


5657 


5744 


5832 


5919 


6007 


6094 


6182 


6269 


87 


497 


6356 


6444 


6531 


6618 


6706 


6793 


6880 


6968 


7055 


7142 


87 


498 


7229 


7317 


7404 


7491 


7578 


7665 


7752 


7839 


7926 


8014 


87 


499 


8101 


8188 


8275 


8362 


8449 


8535 


8622 


8709 


8796 


8883 


87 


500 


8970 


9057 


9144 


9231 


9317 


9404 


9491 


9578 


9664 


9751 


87 


501 


*9838 


9924 


♦Oil 


0098 


0184 


0271 


0358 


0444 


0531 


0617 


87 


502 


70 0704 


0790 


0877 


0963 


1050 


1136 


1222 


1309 


1395 


1482 


86 


503 


1568 


1654 


1741 


1827 


1913 


1999 


2086 


2172 


2258 


2344 


86 


504 


2431 


2517 


2603 


2689 


2775 


2861 


2947 


3033 


3119 


3205 


86 


505 


3291 


3377 


3463 


3549 


3635 


3721 


3807 


3895 


3979 


4065 


86 


506 


4151 


4236 


4322 


4408 


4494 


4579 


4665 


4751 


4837 


4922 


86 


507 


5008 


5094 


5179 


5265 


5350 


5436 


5522 


5607 


5693 


5778 


86 


508 


5864 


5949 


6035 


6120 


6206 


6291 


6376 


6462 


6547 


6632 


85 


509 


6718 


6803 


6888 


6974 


7059 


7144 


7229 


7315 


7400 


7485 


85 


510 


7570 


7655 


7740 


7826 


7911 


7996 


8081 


8166 


8251 


8336 


85 


511 


8421 


8506 


8591 


8676 


8761 


8846 


8931 


9015 


9100 


9185 


85 


512 


*9270 


9355 


9440 


9524 


9609 


9694 


9779 


9863 


9948 


♦033 


85 


513 


71 0117 


0202 


0287 


0371 


0456 


0540 


0625 


0710 


0794 


0879 


85 


514 


0963 


1048 


1132 


1217 


1301* 


1385 


1470 


1554 


1639 


1723 


84 


515 


1807 


1892 


1976 


2060 


2144 


2229 


2313 


2397 


2481 


2566 


84 


516 


2650 


2734 


2818 


2902 


2986 


3070 


3154 


3238 


3323 


3407 


84 


517 


3491 


3575 


3650 


3742 


3826 


3910 


3994 


4078 


4162 


4246 


84 


518 


4330 


4414 


4497 


4581 


4665 


4749 


4833 


4916 


5000 


5084 


84 


519 


5167 


5251 


5335 


5418 


5502 


5586 


5669 


5753 


5836 


5920 


84 


IV. 


O 


! 1 


^ 


3 


4: 


5 


« 


T 


S 


9 


I>. 



852 



APPENDIX. 



liOGARITHWIS OF NUMBERS. 



IV. 


o 


1 


3 


3 


4. 


5 


6 


7- 


8 


9 


I>. 


520 


71 6003 


6087 


6170 


6254 


6337 


6421 


6504 


6588 


6671 


6754 


83 


521 


6838 


6921 


7004 


7088 


7171 


7254 


7338 


7421 


7504 


7587 


83 


622 


7671 


7754 


7837 


7920 


8003 


8086 


8169 


8253 


8336 


8419 


83 


523 


8502 


8585 


8668 


8751 


8834 


8917 


9000 


9083 


9165 


9248 


83 


524 


*9331 


9414 


9497 


9580 


9663 


9745 


9828 


9911 


9994 


♦077 


83 


525 


72 0159 


0242 


0325 


0407 


0490 


0573 


0655 


0738 


0821 


0903 


83 


526 


0986 


1068 


1151 


1233 


1316 


1398 


1481 


1563 


1646 


1728 


82 


527 


1811 


1893 


1975 


2058 


2140 


2222 


2305 


2387 


2469 


2552 


82 


528 


2634 


2716 


2798 


2881 


2963 


3045 


3127 


3209 


3291 


3374 


82 


529 


3456 


3538 


3620 


3702 


3784 


3866 


3948 


4030 


4112 


4194 


82 


530 


4276 


4358 


4440 


4522 


4604 


4685 


4767 


4849 


4931 


5013 


82 


531 


5095 


5176 


5258 


5340 


5422 


5503 


5585 


5667 


5748 


5830 


82 


532 


5912 


5993 


6075 


6156 


6238 


6320 


6401 


6483 


6564 


6646 


82 


533 


6727 


6809 


6890 


6972 


7053 


7134 


7216 


7297 


7379 


7460 


81 


534 


7541 


7623 


7704 


7785 


7866 


7948 


8029 


8110 


8191 


8273 


81 


535 


8354 


8435 


8516 


8597 


8678 


8759 


8841 


8922 


9003 


9084 


81 


536 


9165 


9246 


9327 


9408 


9489 


9570 


9651 


9732 


9813 


9893 


81 


537 


*9974 


♦055 


0136 


0217 


0298 


0378 


0459 


0540 


0621 


0702 


81 


538 


73 0782 


0863 


0944 


1024 


1105 


1186 


1266 


1347 


1428 


1508 


81 


539 


1589 


1669 


1750 


1830 


1911 


1991 


2072 


2152 


2233 


2313 


81 


540 


2394 


2474 


2555 


2635 


2715 


2796 


2876 


2956 


3037 


3117 


80 


541 


3197 


3278 


3358 


3438 


3518 


3598 


3679 


3759 


3839 


3919 


80 


542 


3999 


4079 


4160 


4240 


4320 


4400 


4480 


4560 


4640 


4720 


80 


543 


4800 


4880 


4960 


5040 


5120 


5200 


5279 


5359 


5439 


5519 


80 


544 


5599 


5679 


5759 


5838 


5918 


5998 


.6078 


6157 


6237 


6317 - 


80 


545 


6397 


6476 


6556 


6635 


6715 


6795 


6874 


6954 


7034 


7113 


80 


546 


7193 


7272 


7352 


7431 


7511 


7590 


7670 


7749 


7829 


7908 


79 


547 


7987 


8067 


8146 


8225 


8305 


8384 


8463 


8543 


8622 


8701 


79 


548 


8781 


8860 


8939 


9018 


9097 


9177 


9256 


9335 


9414 


9493 


79 


549 


*9572 


9651 


9731 


9810 


9889 


9968 


♦047 


0126 


0205 


0284 


79 


550 


74 0363 


0442 


0521 


0600 


0678 


0757 


0836 


0915 


0994 


1073 


79 


551 


1152 


1230 


1309 


1388 


1467 


1546 


1624 


1703 


1782 


1860 


79 


552 


1939 


2018 


2096 


2175 


2254 


2332 


2411 


2489 


2568 


2646 


79 


553 


2725 


2804 


2882 


2961 


3039 


3118 


3196 


3275 


3353 


3431 


78 


554 


3510 


3588 


3667 


3745 


3823 


3902 


3980 


4058 


4136 


4215 


78 


555 


4293 


4371 


4449 


4528 


4606 


4684 


4762 


4840 


4919 


4997 


78 


556 


5075 


5153 


5231 


5309 


5387 


5465 


5543 


5621 


5699 


5777 


78 


557 


5855 


5933 


6011 


6089 


6167 


6245 


6323 


6401 


6479 


6556 


78 


558 


6634 


6712 


6790 


6868 


6945 


7023 


7101 


7179 


7256 


7334 


78 


559 


7412 


7489 


7567 


7645 


7722 


7800 


7878 


7955 


8033 


8110 


78 


560 


8188 


8266 


8343 


8421 


8498 


8576 


8653 


8731 


8808 


8885 


77 


561 


8963 


9040 


9118 


9195 


9272 


9350 


9427 


9504 


9582 


9659 


77 


562 


*9736 


9814 


9891 


9968 


♦045 


0123 


0200 


0277 


0354 


0431 


77 


563 


75 0508 


0586 


0663 


0740 


0817 


0894 


0971 


1048 


1125 


1202 


77 


564 


1279 


1356 


1433 


1510 


1587 


1664 


1741 


1818 


1895 


1972 


77 


565 


2048 


2125 


2202 


2279 


2356 


2433 


2509 


2586 


2663 


2740 


77 


566 


2816 


2893 


2970 


3047 


3123 


3200 


3277 


•3353 


3430 


3506 


77 


567 


3583 


3660 


3736 


3813 


3889 


3966 


4042 


4119 


4195 


4272 


77 


568 


4348 


4425 


4501 


4578 


4654 


4730. 


4807 


4883 


4960 


5036 


76 


569 


5112 


5189 


5265 


5341 


5417 


5494 


5570 


5646 


5722 


5799 


76 


570 


5875 


5951 


6027 


6103 


6180 


6256 


6332 


6408 


6484 


6560 


76 


571 


6636 


6712 


6788 


6864 


6940 


7016 


7092 


7168 


7244 


7320 


76 


572 


7396 


7472 


7548 


7624 


7700 


7775 


7851 


7927 


8003 


8079 


76 


573 


8155 


8230 


8306 


8382 


8458 


8533 


8609 


8685 


8761 


8836 


76 


574 


8912 


8988 


9063 


9139 


9214 


9290 


9366 


9441 


9517 


9592 


76 


575 


*9668 


9743 


9819 


9894 


9970 


♦045 


0121 


0196 


0272 


0347 


75 


576 


76 0422 


0498 


0573 


0649 


0724 


0799 


0875 


0950 


1025 


1101 


75 


577 


1176 


1251 


1326 


1402 


1477 


1552 


1627 


1702 


1778 


1853 


75 


.578 


1928 


2003 


2078 


2153 


2228 


2303 


2378 


2453 


2529 


2604 


75 


579 


2679 


2754 


2829 


2904 


2978 


3053 


3128 


3203 


3278 


3353 


75 


N. 


O 


1 


3 


3 


4= 


5 


6 


T 


S 


9 


I>. 



APPENDIX. 



853 



LOGARITHMS OP NUMBERS. 



N. 


o 


1 


3 


3 


4= 


5 


6 


7- 


8 


9 


I>. 


580 


76 3428 


3503 


3578 


3653 


3727 


3802 


3877 


3952 


4027 


4101 


75 


581 


4176 


4251 


4326 


4400 


4475 


4550 


4624 


4699 


4774 


4848 


75 


582 


4923 


4998 


5072 


5147 


5221 


5296 


5370 


5445 


5520 


5594 


75 


583 


5669 


5743 


5818 


5892 


5966 


6041 


6115 


6190 


6264 


6338 


74 


584 


6413 


6487 


6562 


6636 


6710 


6785 


6859 


6933 


7007 


7082 


74 


585 


7156 


7230 


7304 


7379 


7453 


7527 


7601 


7675 


7749 


7823 


74 


586 


7898 


7972 


8046 


8120 


8194 


8268 


8342 


8416 


8490 


8564 


74 


587 


8638 


8712 


8786 


8860 


8934 


9008 


9082 


9156 


9230 


9303 


74 


588 


*9377 


9451 


9525 


9599 


9673 


9746 


9820 


9894 


9968 


♦042 


74 


589 


77 0115 


0189 


0263 


0336 


0410 


0484 


0557 


0631 


0705 


0778 


74 


590 


0852 


0926 


0999 


1073 


1146 


1220 


1293 


1367 


1440 


1514 


74 


591 


1587 


1661 


1734 


1808 


1881 


1955 


2028 


2102 


2175 


2248 


73 


592 


2322 


2395 


2468 


2542 


2615 


2688 


2762 


2835 


2908 


2981 


73 


593 


3055 


3128 


3201 


3274 


3348 


3421 


3494 


3567 


3640 


3713 


73 


594 


3786 


3860 


3933 


4006 


4079 


4152 


4225 


4298 


4371 


4444 


73 


595 


4517 


4590 


4663 


4736 


4809 


4882 


4955 


5028 


5100 


5173 


73 


596 


5246 


5319 


5392 


5465 


5538 


5610 


5683 


5756 


5829 


5902 


73 


597 


5974 


6047 


6120 


6193 


6265 


6338 


6411 


6483 


6556 


6629 


73 


598 


6701 


6774 


6846 


6919 


6992 


7064 


7137 


7209 


7282 


7354 


73 


599 


7427 


7499 


7572 


7644 


7717 


7789 


7862 


7934 


8006 


8079 


72 


600 


8151 


8224 


8296 


8368 


8441 


8513 


8585 


8658 


8730 


8802 


72 


601 


8874 


8947 


9019 


9091 


9163 


9236 


9308 


9380 


9452 


9524 


72 


602 


* 9596 


9669 


9741 


9813 


9885 


9957 


♦029 


0101 


0173 


0245 


72 


603 


78 0317 


0389 


0461 


0533 


0605 


0677 


0749 


0821 


0893 


0965 


72 


604 


1037 


1109 


1181 


1253 


1324 


1396 


1468 


1540 


1612 


1684 


72 


605 


1755 


1827 


1899 


1971 


2042 


2114 


2186 


2258 


2329 


2401 


72 


606 


2473 


2544 


2616 


2688 


2759 


2831 


2902 


2974 


3046 


3117 


72 


607 


3189 


3260 


3332 


3403 


3475 


3546 


3618 


3689 


3761 


3832 


71 


608 


3904 


3975 


4046 


4118 


4189 


4261 


4332 


4403 


4475 


4546 


71 


609 


4617 


4689 


4760 


4831 


4902 


4974 


5045 


5116 


5187 


5259 


71 


610 


5330 


5401 


5472 


5543 


5615 


5686 


5757 


5828 


5899 


5970 


71 


611 


6041 


6112 


6183 


6254 


6325 


6396 


6467 


6538 


6609 


6680 


71 


612 


6751 


6822 


6893 


6964 


7035 


7106 


7177 


7248 


7319 


7390 


71 


613 


7460 


7531 


7602 


7673 


7744 


7815 


7885 


7956 


8027 


8098 


71 


614 


8168 


8239 


8310 


8381 


8451 


8522 


8593 


8663 


8734 


8804 


71 


615 


8875 


8946 


9016 


9087 


9157 


9228 


9299 


9369 


9440 


9510 


71 


616 


*9581 


9651 


9722 


9792 


9863 


9933 


♦004 


0074 


0144 


0215 


70 


617 


79 0285 


0356 


0426 


0496 


0567 


0637 


0707 


0778 


0848 


0918 


70 


618 


0988 


1059 


1129 


1199 


1269 


1340 


1410 


1480 


1550 


1620 


70, 


619 


1691 


1761 


1831 


1901 


1971 


2041 


2111 


2181 


2252 


2322 


70 


620 


2392 


2462 


2532 


2602 


2672 


2742 


2812 


2882 


2952 


3022 


70 


621 


3092 


3162 


3231 


3301 


3371 


3441 


3511 


3581 


3651 


3721 


70 


622 


3790 


3860 


3930 


4000 


4070 


4139 


4209 


4279 


4349 


4418 


70 


623 


4488 


4558 


4627 


4697 


4767 


4836 


4906 


4976 


5045 


5115 


70 


624 


5185 


5254 


5324 


5393 


5463 


5532 


5602 


5672 


5741 


5811 


70 


625 


5880 


5949 


6019 


6088 


6158 


6227 


6297 


6366 


6436 


6505 


69 


626 


6574 


6644 


6713 


6782 


6852 


6921 


6990 


7060 


7129 


7198 


69 


627 


7268 


7337 


7406 


7475 


7545 


7614 


7683 


7752 


7821 


7890 


69 


628 


7960 


8029 


8098 


8167 


8236 


8305 


8374 


8443 


8513 


8582 


69 


629 


8651 


8720 


8789 


8858 


8927 


8996 


9065 


9134 


9203 


9272 


69 


630 


9341 


9409 


9478 


9547 


9616 


9685 


9754 


9823 


9892 


9961 


69 


631 


80 0029 


0098 


0167 


0236 


0305 


0373 


0442 


0511 


0580 


0648 


69 


632 


0717 


0786 


0854 


0923 


0992 


1061 


1129 


1198 


1266 


1335 


69 


633 


1404 


1472 


1541 


1609 


1678 


1747 


1815 


1884 


1952 


2021 


69 


634 


2089 


2158 


2226 


2295 


236.5 


2432 


2500 


2568 


2637 


2705 


69 


635 


2774 


2842 


2910 


2979 


\ 3047 


3116 


3184 


3252 


3321 


3389 


68 


636 


3457 


3525 


3594 


3662 


3730 


3798 


3867 


3935 


4003 


4071 


68 


637 


4139 


< 4208 


4276 


4344 


' 4412 


! 4480 


4548 


4616 


4685 


4753 


68 


638 


4821 


; 4889 


4957 


I 5025 


: 5093 


5161 


5229 


5297 


5365 


5433 


68 


639 


5501 


5569 


5637 


' 5705 


5773 


5841 


5908 


5976 


6044 


6112 


68 


TV. 


O 


1 


2 


3 


4. 


3 


6 


7 


H 


9 


r>. 



854: 



APPENDIX. 



LOGARITHMS OP NUMBERS. 



IV. 


o 


X 


3 


3 


4. 


5 


O 


7 


^ 


9 


I>. 


640 


80 6180 


6248 


6316 


6384 


6451 


6519 


6587 


6655 


6723 


6790 


68 


641 


6858 


6926 


6994 


7061 


7129 


7197 


7264 


7332 


7400 


7467 


68 


642 


7535 


7603 


7670 


7738 


7806 


7873 


7941 


8008 


8076 


8143 


68 


643 


8211 


8279 


8346 


8414 


8481 


8549 


8616 


8684 


8751 


8818 


67 


644 


8886 


8953 


9021 


9088 


9156 


9223 


9290 


9358 


9425 


9492 


67 


645 


*9560 


9627 


9694 


9762 


9829 


9896 


9964 


♦031 


0098 


0165 


67 


646 


81 0233 


0300 


0367 


0434 


0501 


0569 


0636 


0703 


0770 


0837 


67 


647 


0904 


0971 


1039 


1106 


1173 


1240 


1307 


1374 


1441 


1508 


67 


648 


1575 


1642 


1709 


1776 


1843 


1910 


1977 


2044 


2111 


2178 


67 


649 


2245 


2312 


2379 


2445 


2512 


2579 


2646 


2713 


2780 


2847 


67 


650 


2913 


2980 


3047 


3114 


3181 


3247 


3314 


3381 


3448 


3514 


67 


651 


3581 


3648 


3714 


3781 


3848 


3914 


3981 


4048 


4114 


4181 


67 


652 


4248 


4314 


4381 


4447 


4514 


4581 


4647 


4714 


4780 


4847 


Q7 


653 


4913 


4980 


5046 


5113 


5179 


5246 


5312 


5378 


5445 


5511 


66 


654 


5578 


5644 


5711 


5777 


5843 


5910 


5976 


6042 


6109 


6175 


66 


655 


6241 


6308 


6374 


6440 


6506 


6573 


6639 


6705 


6771 


6838 


66 


656 


6904 


6970 


7036 


7102 


7169 


7235 


7301 


7367 


7433 


7499 


66 


657 


7565 


7631 


7698 


7764 


7830 


7896 


7962 


8028 


8094 


8160 


66 


658 


8226 


8292 


8358 


8424 


8490 


8556 


8622 


8688 


8754 


8820 


66 


659 


8885 


8951 


9017 


9083 


9149 


9215 


9281 


9346 


9412 


9478 


66 


660 


*9544 


9610 


9676 


9741 


9807 


9873 


9939 


♦004 


0070 


0136 


66 


661 


82 0201 


0267 


0333 


0399 


0464 


0530 


0595 


0661 


0727 


0792 


66 


662 


0858 


0924 


0989 


1055 


1120 


1186 


1251 


1317 


1382 


1448 


66 


663 


1514 


1579 


1645 


1710 


1775 


1841 


1906 


1972 


2037 


2103 


65 


664 


2168 


2233 


2299 


2364 


2430 


2495 


.5560 


2626 


2691 


2756 


65 


665 


2822 


2887 


2952 


3018 


3083 


3148 


3213 


3279 


3344 


3409 


65 


666 


3474 


3539 


3605 


3670 


3735 


3800 


3865 


3930 


3996 


4061 


65 


667 


4126 


4191 


4256 


4321 


4386 


4451 


4516 


4581 


4646 


4711 


65 


668 


4776 


4841 


4906 


4971 


5036 


5101 


5166 


5231 


5296 


5361 


65 


669 


. 5426 


5491 


5556 


5621 


5686 


5751 


5815 


5880 


5945 


6010 


65 


670 


6075 


6140 


6204 


6269 


6334 


6399 


6464 


6528 


6593 


6658 


65 


671 


6723 


6787 


6852 


6917 


6981 


7046 


7111 


7175 


7240 


7305 


65 


672 


7369 


7434 


7499 


7563 


7628 


7692 


7757 


7821 


7886 


7951 


65 


673 


8015 


8080 


8144 


8209 


8273 


8338 


8402 


8467 


8531 


8595 


64 


674 


8660 


8724 


8789 


8853 


8918 


8982 


9046 


9111 


9175 


9239 


64 


675 


9304 


9368 


9432 


9497 


9561 


9625 


9690 


9754 


9818 


9882 


64 


676 


* 9947 


♦Oil 


0075 


0139 


0204 


0268 


0332 


0396 


0460 


0525 


64 


677 


83 0589 


0653 


0717 


0781 


0845 


0909 


0973 


1037 


1102 


1166 


64 


678 


1230 


1294 


1358 


1422 


1486 


1550 


1614 


1678 


1742 


1806 


64 


679 


1870 


1934 


1998 


2062 


2126 


2189 


2253 


2317 


2381 


2445 


64 


680 


2509 


2573 


2637 


2700 


2764 


2828 


2892 


2956 


3020 


3083 


64 


681 


3147 


3211 


3275 


3338 


3402 


3466 


3530 


3593 


3657 


3721 


64 


682 


3784 


3848 


3912 


3975 


4039 


4103 


4166 


4230 


4294 


4357 


64 


683 


4421 


4484 


4548 


4611 


4675 


4739 


4802 


4866 


4929 


4993 


64 


684 


5056 


5120 


5183 


5247 


5310 


5373 


5437 


5500 


5564 


5627 


63 


685 


5691 


5754 


5817 


5881 


5944 


6007 


6071 


6134 


6197 


6261 


63 


686 


6324 


6387 


6451 


6514 


6577 


6641 


6704 


6767 


6830 


6894 


63 


687 


6957 


7020 


7083 


7146 


7210 


7273 


7336 


7399 


7462 


7525 


63 


688 


7588 


7652 


7715 


7778 


7841 


7904- 


7967 


8030 


8093 


8156 


63 


689 


8219 


8282 


8345 


8408 


8471 


8534 


8597 


8660 


8723 


8786 


63 


690 


8849 


8912 


8975 


9038 


9101 


9164 


9227 


9289 


9352 


9415 


63 


691 


*9478 


9541 


9604 


9667 


9729 


9792 


9855 


9918 


9981 


♦043 


63 


692 


84 0106. 


0169 


0232 


0294 


0357 


0420 


0482 


0545 


0608 


0671 


63 


693 


0733 


0796 


0859 


0921 


0984 


1046 


1109 


1172 


1234 


1297 


63 


694 


1359 


1422 


1485 


1547 


1610 


1672 


1735 


1797 


1860 


1922 


63 


695 


1985 


2047 


2110 


2] 72 


2235 


2297 


2360 


2422 


2484 


2547 


62 


696 


2609 


2672 


2734 


2796 


2859 


2921 


2983 


3046 


3108 


3170 


62 


697 


3233 


3295 


3357 


3420 


3482 


3544 


3606 


3669 


3731 


3793 


62 


698 


3855 


3918 


3980 


4042 


4104 


4166 


4229 


4291 


4353 


4415 


62 


699 


4477 


4539 


4601 


4664 


4726 


4788 


4850 


4912 


4974 


5036 


62 


IV, 


O 


1 


i 3 


3 


^ 


' 5 


^ 


7 


H 


o 


I>. 



APPENDIX. 



855 



LOGARITHMS OP NUMBERS. 



IV. 


o 


1 


3 


3 


4. 


5 


« 


7 


8 


9 


r>. 


700 


84 5098 


5160 


5222 


5284 


5346 


5408 


5470 


5532 


5594 


5656 


62 


701 


5718 


5780 


5842 


5904 


5966 


6028 


6090 


6151 


6213 


6275 


62 


702 


6337 


6399 


6461 


6523 


6585 


6646 


6708 


6770 


6832 


6894 


62 


703 


6955 


7017 


7079 


7141 


7202 


7264 


7326 


7388 


7449 


7511 


62 


704 


7573 


7634 


7696 


7758 


7819 


7881 


7943 


8004 


8066 


8128 


62 


705 


8189 


8251 


8312 


8374 


8435 


8497 


8559 


8620 


8682 


8743 


62 


706 


8805 


8866 


8928 


8989 


9051 


9112 


9174 


9235 


9297 


9358 


61 


707 


9419 


9481 


9542 


9604 


9665 


9726 


9788 


9849 


9911 


9972 


61 


708 


85 0033 


0095 


0156 


0217 


0279 


0340 


0401 


0462 


0524 


0585 


61 


709 


0646 


0707 


0769 


0830 


0891 


0952 


1014 


1075 


1136 


1197 


61 


710 


1258 


1320 


1381 


1442 


1503 


1564 


1625 


1686 


1747 


1809 


61 


711 


1870 


1931 


1992 


2053 


2114 


2175 


2236 


2297 


2358 


2419 


61 


712 


2480 


2541 


2602 


2663 


2724 


2785 


2846 


2907 


2968 


3029 


61 


713 


3090 


3150 


3211 


3272 


3333 


3394 


3455 


3516 


3577 


3637 


61 


714 


3698 


3759 


3820 


3881 


3941 


4002 


4063 


4124 


4185 


4245 


61 


715 


4306 


4367 


4428 


4488 


4549 


4610 


4670 


4731 


4792 


4852 


61 


716 


4913 


4974 


5034 


5095 


5156 


5216 


5277 


5337 


5398 


5459 


61 


717 


5519 


5580 


5640 


5701 


5761 


5822 


5882 


5943 


6003 


6064 


61 


718 


6124 


6185 


6245 


6306 


6366 


6427 


6487 


6548 


6608 


6668 


60 


719 


6729 


6789 


6850 


6910 


6970 


7031 


7091 


7152 


7212 


7272 


60 


720 


7332 


7393 


7453 


7513 


7574 


7634 


7694 


7755 


7815 


7875 


60 


721 


7935 


7995 


8056 


8116 


8176 


8236 


8297 


8357 


8417 


8477 


60 


722 


8537 


8597 


8657 


8718 


8778 


8838 


8898 


8958 


9018 


9078 


60 


723 


9138 


9198 


9258 


9318 


9379 


9439 


9499 


9559 


9619 


9679 


60 


724 


*9739 


9799 


9859 


9918 


9978 


♦038 


0098 


0158 


0218 


0278 


60 


725 


86 0338 


0398 


0458 


0518 


0578 


0637 


0697 


0757 


0817 


0877 


60 


726 


0937 


0996 


1056 


1116 


1176 


1236 


1295 


1355 


1415 


1475 


60 


727 


1534 


1594 


1654 


1714 


1773 


1833 


1893 


1952 


2012 


2072 


60 


728 


2131 


2191 


2251 


2310 


2370 


2430 


2489 


2549 


2608 


2668 


60 


729 


2728 


2787 


2847 


2906 


2966 


3025 


3085 


3144 


3204 


3263 


60 


730 


3823 


3382 


3442 


3501 


3561 


3620 


3680 


3739 


3799 


3858 


59 


731 


3917 


3977 


4036 


4096 


4155 


4214 


4274 


4333 


4392 


4452 


59 


732 


4511 


4570 


4630 


4689 


4748 


4808 


4867 


4926 


4985 


5045 


59 


733 


5104 


5163 


5222 


5282 


5341 


5400 


5459 


5519 


5578 


5637 


59 


734 


5696 


5755 


5814 


5874 


5933 


5992 


6051 


6110 


6169 


6228 


59 


735 


6287 


6346 


6405 


6465 


6524 


6583 


6642 


6701 


6760 


6819 


59 


736 


6878 


6937 


6996 


7055 


7114 


7173 


7232 


7291 


7350 


7409 


59 


737 


7467 


7526 


7585 


7644 


7703 


7762 


7821 


7880 


7939 


7998 


59 


738 


8056 


8115 


8174 


8233 


8292 


8350 


8409 


8468 


8527 


8586 


59 - 


739 


8644 


8703 


8762 


8821 


8879 


8938 


8997 


9056 


9114 


9173 


59 


740 


9232 


9290 


9349 


9408 


9466 


9525 


9584 


9642 


9701 


9760 


59 


741 


*9818 


9877 


9935 


9994 


♦053 


0111 


0170 


0228 


0287 


0345 


59 


742 


87 0404 


0462 


0521 


0579 


0638 


0696 


0755 


0813 


0872 


0930 


58 


743 


0989 


1047 


1106 


1164 


1223 


1281 


1339 


1398 


1456 


1515 


58 


744 


1573 


1631 


1690 


1748 


1806 


1865 


1923 


1981 


2040 


2098 


58 


745 


2156 


2215 


2273 


2331 


2389 


2448 


2506 


2564 


2622 


2681 


58 


746 


2739 


2797 


2855 


2913 


2972 


3030 


3088 


3146 


3204 


3262 


58 


747 


3321 


3379 


3437 


3495 


3553 


3611 


3669 


3727 


3785 


3844 


58 


748 


3902 


3960 


4018 


4076 


4134 


4192 


4250 


4308 ■ 


4366 


4424 


58 


749 


4482 


4540 


4598 


4656 


4714 


4772 


4830 


4888 


4945 


5003 


58 


750 


5061 


5119 


5177 


5235 


5293 


5351 


5409 


5466 


5524 


5582 


58 


751 


5640 


5698 


5756 


5813 


5871 


5929 


5987 


6045 


6102 


6160 


58 


752 


6218 


6276 


6333 


6391 


6449 


6507 


6564 


6622 


6680 


6737 


58 


753 


6795 


6853 


6910 


6968 


7026, 


7083 


7141 


7199 


7256 


7314 


58 


754 


7371 


7429 


7487 


7544 


7602 


7659 


7717 


7774 


7832 


7889 


58 


755 


7947 


8004 


8062 


8119 


8177 


8234 


8292 


8349 


8407 


8464 


57 


756 


8522 


8579 


8637 


8694 


8752 


8809 


8866 


8924 


8981 


9039 


57 


757 


9096 


9153 


9211 


9268 


9325 


9383 


9440 


9497 


9555 


9612 


57 


758 


* 9669 


9726 


9784 


9841 


9898 


9956 


♦013 


0070 


0127 


0185 


57 


759 


88 0242 


0299 


0356 


0413 


0471 


0528 


0585 


0642 


0699 


0756 


57 


IV. 


O 


1 


3 


3 


4. 


5 


G 


7 


8 


O 


O. 



856 



APPENDIX. 



LOGARITHMS OP NUMBERS. 



jV. 


o 


1 


2 


3 


4. 


5 


6 


7 


8 





I>. 


760 


88 0814 


0871 


0928 


0985 


1042 


1099 


1156 


1213 


1271 


1328 


57 


761 


1385 


1442 


1499 


1556 


1613 


1670 


1727 


1784 


1841 


1898 


57 


762 


1955 


2012 


2069 


2126 


2183 


2240 


2297 


2354 


2411 


2468 


57 


763 


2525 


2581 


2638 


2695 


2752 


2809 


2866 


2923 


2980 


3037 


57 


764 


3093 


3150 


3207 


3264 


3321 


3377 


3434 


3491 


3548 


3605 


57 


765 


3661 


3718 


3775 


3832 


3888 


3945 


4002 


4059 


4115 


4172 


57 


766 


4229 


4285 


4342 


4399 


4455 


4512 


4569 


4625 


4682 


4739 


57 


767 


4795 


4852 


4909 


4965 


5022 


5078 


5135 


5192 


5248 


5305 


57 


768 


5361 


5418 


5474 


5531 


5587 


5644 


5700 


5757 


5813 


5870 


57 


769 


5926 


5983 


6039 


6096 


6152 


6209 


6265 


6321 


6378 


6434 


56 


770 


6491 


6547 


6604 


6660 


6716 


6773. 


6829 


6885 


6942 


6998 


56 


771 


7054 


7111 


7167 


7223 


7280 


7336 


7392 


7449 


7505 


7561 


56 


772 


7617 


7674 


7730 


7786 


7842 


7898 


7955 


8011 


8067 


8123 


56 


773 


8179 


8236 


8292 


8348 


8404 


8460 


8516 


8573 


8629 


8685 


56 


774 


8741 


8797 


8853 


8909 


8965 


9021 


9077 


9134 


9190 


9246 


56 


775 


9302 


9358 


9414 


9470 


9526 


9582 


9638 


9694 


9750 


9806 


56 


776 


*9862 


9918 


9974 


♦030 


0086 


0141 


0197 


0253 


0309 


0365 


56 


777 


89 0421 


0477 


0533 


0589 


0645 


0700 


0756 


0812 


0868 


0924 


56 


778 


0980 


1035 


1091 


1147 


1203 


1259 


1314 


1370 


1426 


1482 


56 


779 


1537 


1593 


1649 


1705 


1760 


1816 


1872 


1928 


1983 


2039 


56 


780 


2095 


2150 


2206 


2262 


2317 


2373 


2429 


2484 


2540 


2595 


56 


781 


2651 


2707 


2762 


2818 


2873 


2929 


2985 


3040 


3096 


3151 


56 


782 


3207 


3262 


3318 


3373 


3429 


3484 


3540 


3595 


3651 


3706 


56 


783 


3762 


3817 


3873 


3928 


3984 


4039 


4094 


4150 


4205 


4261 


55 


784 


4316 


4371 


4427 


4482 


4538 


4593 


^4648 


4704 


4759 


4814 


55 


785 


4870 


4925 


4980 


5036 


5091 


5146 


5201 


5257 


5312 


5367 


55 


786 


5423 


5478 


5533 


5588 


5644 


5699 


5754 


5809 


5864 


5920 


55 


787 


5975 


6030 


6085 


6140 


6195 


6251 


6306 


6361 


6416 


6471 


55 


788 


6526 


6581 


6636 


6692 


6747 


6802 


6857 


6912 


6967 


7022 


55- 


789 


7077 


7132 


7187 


7242 


7297 


7352 


7407 


7462 


7517 


7572 


55 


790 


7627 


7682 


7737 


7792 


7847 


7902 


7957 


8012 


8067 


8122 


55 


791 


8176 


8231 


8286 


8341 


8396 


8451 


8506 


8561 


8615 


8670 


55 


792 


8725 


8780 


8835 


8890 


8944 


8999 


9054 


9109 


9164 


9218 


55 


793 


9273 


9328 


9383 


9437 


9492 


9547 


9602 


9656 


9711 


9766 


55 


794 


*9821 


9875 


9930 


9985 


♦039 


0094 


0149 


0203 


0258 


0312 


55 


795 


90 0367 


0422 


0476 


0531 


0586 


0640 


0695 


0749 


0804 


0859 


55 


796 


0913 


0968 


1022 


1077 


1131 


1186 


1240 


1295 


1349 


1404 


55 


797 


1458 


1513 


1567 


1622 


1676 


1731 


1785 


1840 


1894 


1948 


54 


798 


2003 


2057 


2112 


2166 


2221 


2275 


2329 


2384 


2438 


2492 


54 


799 


2547 


2601 


2655 


2710 


2764 


2818 


2873 


2927 


2981 


3036 


54 


800 


3090 


3144 


3199 


3253 


3307 


3361 


3416 


3470 


3524 


3578 


54 


801 


3633 


3687 


3741 


3795 


3849 


3904 


3958 


4012 


4066 


4120 


54 


802 


4174 


4229 


4283 


4337 


4391 


4445 


4499 


4553 


4607 


4661 


54 


803 


4716 


4770 


4824 


4878 


4932 


4986 


5040 


5094 


5148 


5202 


54 


804 


5256 


5310 


5364 


5418 


5472 


5526 


5580 


5634 


5688 


5742 


54 


805 


5796 


5850 


5904 


5958 


6012 


6066 


6119 


6173 


6227 


6281 


54 


806 


6335 


6389 


6443 


6497 


6551 


6604 


6658 


•6712 


6766 


6820 


54 


807 


6874 


6927 


6981 


7035 


7089 


7143 


7196 


7250 


7304 


7358 


54 


808 


7411 


7465 


7519 


7573 


7626 


7680 


7734 


7787 


7841 


7895 


54 


809 


7949 


8002 


8056 


8110 


8163 


8217 


8270 


8324 


8378 


8431 


54 


810 


8485 


8539 


8592 


8646 


8699 


8753 


8807 


8860 


8914 


8967 


54 


811 


9021 


9074 


9128 


9181 


9235 


9289 


9342 


9396 


9449 


9503 


54 


812 


* 9556 


9610 


9663 


9716 


9770 


9823 


9877 


9930 


9984 


♦037 


53 


813 


91 0091 


0144 


0197 


0251 


0304 


0358 


0411 


0464 


0518 


0571 


53 


814 


0624 


0678 


0731 


0784 


0838 


0891 


0944 


0998 


1051 


1104 


53 


815 


1158 


1211 


1264 


1317 


1371 


1424 


1477 


1530 


1584 


1637 


53 


816 


1690 


1743 


1797 


1850 


1903 


1956 


2009 


2063 


2116 


2169 . 


53 


817 


2222 


2275 


2328 


2381 


2435 


2488 


2541 


2594 


2647 


2700 


53 


818 


2753 


2806 


2859 


2913 


2966 


3019 


3072 


3125 


3178 


3231 


53 


819 


3284 


3337 


3390 


3443 


3496 


3549 


3602 


3655 


3708 


3761 


53 


IV. 


O 


1 


3 


3 


4= 


5 


6 


7- 


8 


9 


r>. 



APPENDIX. 



857 



L.OGARITHBIS OF NU3IBERS, 



]V. 


O 


1 


2 


3 


4. 


5 


6 


7 


8 


9 


I>. 


820 


91 3814 


3867 


3920 


3973 


4026 


4079 


4132 


4184 


4237 


4290 


53 


821 


4343 


4396 


4449 


4502 


4555 


4608 


4660 


4713 


4766 


4819 


53 


822 


4872 


4925 


4977 


5030 


5083 


5136 


5189 


5241 


5294 


5347 


53 


823 


5400 


5453 


5505 


5558 


5611 


5664 


5716 


5769 


5822 


5875 


53 


824 


5927 


5980 


6033 


6085 


6138 


6191 


6243 


6296 


6349 


6401 


53 


825 


6454 


6507 


6559 


6612 


6664 


6717 


6770 


6822 


6875 


6927 


53 


826 


6980 


7033 


7085 


7138 


7190 


7243 


7295 


7348 


7400 


7453 


53 


827 


7506 


7558 


7611 


7663 


7716 


7768 


7820 


7873 


7925 


7978 


52 


828 


8030 


8083 


8135 


8188 


8240 


8293 


8345 


8397 


8450 


8502 


52 


829 


8555 


8607 


8659 


8712 


8764 


8816 


8869 


8921 


8973 


9026 


52 


830 


9078 


9130 


9183 


9235 


9287 


9340 


9392 


9444 


9496 


9549 


52 


831 


* 9601 


9653 


9706 


9758 


9810 


9862 


9914 


9967 


♦019 


0071 


52 


832 


92 0123 


0176 


0228 


0280 


0332 


0384 


0436 


0489 


0541 


0593 


52 


833 


0645 


0697 


0749 


0801 


0853 


0906 


0958 


1010 


1062 


1114 


52 


834 


1166 


1218 


1270 


1322 


1374 


1426 


1478 


1530 


1582 


1634 


52 


835 


1686 


1738 


1790 


1842 


1894 


1946 


1998 


2050 


2102 


2154 


52 


836 


2206 


2258 


2310 


2362 


2414 


2466 


2518 


2570 


2622 


2674 


52 


837 


2725 


2777 


2829 


2881 


2933 


2985 


3037 


3089 


3140 


3192 


52 


838 


3244 


3296 


3348 


3399 


3451 


3503 


3555 


3607 


3658 


3710 


52 


839 


3762 


3814 


3865 


3917 


3969 


4021 


4072 


4124 


4176 


4228 


52 


840 


4279 


4331 


4383 


4434 


4486 


4538 


4589 


4641 


4693 


4744 


52 


841 


4796 


4848 


4899 


4951 


5003 


5054 


5106 


5157 


5209 


5261 


52 


842 


5312 


5364 


5415 


5467 


5518 


6570 


5621 


5673 


5725 


5776 


52 


843 


5828 


5879 


5931 


5982 


6034 


6085 


6137 


6188 


6240 


6291 


51 


844 


6342 


6394 


6445 


6497 


6548 


6600 


6651 


6702 


6754 


6805 


51 


845 


6857 


6908 


6959 


7011 


7062 


7114 


7165 


7216 


7268 


7319 


51 


846 


7370 


7422 


7473 


7524 


7576 


7627 


7678 


7730 


7781 


7832 


51 


847 


7883 


7935 


7986 


8037 


8088 


8140 


8191 


8242 


8293 


8345 


61 


848 


8396 


8447 


8498 


8549 


8601 


8652 


8703 


8754 


8805 


8857 


61 


849 


8908 


8959 


9010 


9061 


9112 


9163 


9215 


9266 


9317 


9368 


51 


850 


9419 


9470 


9521 


9572 


9623 


9674 


9725 


9776 


9827 


9879 


51 


851 


*9930 


9981 


♦032 


0083 


0134 


0185 


0236 


0287 


0338 


0389 


51 


852 


93 0440 


0491 


0542 


0592 


0643 


0694 


0745 


0796 


0847 


0898 


51 


853 


0949 


1000 


1051 


1102 


1153 


1204 


1254 


1305 


1356 


1407 


51 


854 


1458 


1509 


1560 


1610 


1661 


1712 


1763 


1814 


1865 


1915 


51 


855 


1966 


2017 


2068 


2118 


2169 


2220 


2271 


2322 


2372 


2423 


51 


856 


2474 


2524 


2575 


2626 


2677 


2727 


2778 


2829 


2879 


2930 


61 


857 


2981 


3031 


3082 


3133 


3183 


3234 


3285 


3335 


3386 


3437 


61 


858 


3487 


3538 


3589 


3639 


3690 


3740 


3791 


3841 


3892 


3943 


51' 


859 


3993 


4044 


4094 


4145 


4195 


4246 


4296 


4347 


4397 


4448 


51 


860 


4498 


4549 


4599 


4650 


4700 


4751 


4801 


4852 


4902 


4953 


50 


861 


5003 


5054 


5104 


5154 


5205 


5255 


5306 


5356 


5406 


5457 


50 


862 


5507 


5558 


5608 


5658 


5709 


5759 


5809 


5860 


5910 


5960 


50 


863 


6011 


6061 


6111 


6162 


6212 


6262 


6313 


6363 


6413 


6463 


50 


864 


6514 


6564 


6614 


6665 


6715 


6765 


6815 


6865 


6916 


6966 


50 


865 


7016 


7066 


7117 


7167 


7217 


7267 


7317 


7367 


7418 


7468 


50 


866 


7518 


7568 


7618 


7668 


7718 


7769 


7819 


7869 


7919 


7969 


50 


867 


8019 


8069 


8119 


8169 


8219 


8269 


8320 


8370 


8420 


8470 


50 


868 


8520 


8570 


8620 


8670 


8720 


8770 


8820 


8870 


8920 


8970 


50 


869 


9020 


9070 


9120 


9170 


9220 


9270 


9320 


9369 


9419 


9469 


50 


870 


9519 


9569 


9619 


9669 


9719 


9769 


9819 


9869 


9918 


9968 


50 


871 


94 0018 


0068 


0118 


0168 


0218 


0267 


0317 


0367 


0417 


0467 


50 


872 


0516 


0566 


0616 


0666 


0716 


0765 


0815 


0865 


0915 


0964 


50 


873 


1014 


1064 


1114 


1163 


1213. 


1263 


1313 


1362 


1412 


1462 


50 


874 


1511 


1561 


1611 


1660 


1710 


1760 


1809 


1859 


1909 


1958 


50 


875 


2008 


2058 


2107 


2157 


2207 


2256 


2306 


2355 


2405 


2455 


50 


876 


2504 


2554 


2603 


2653 


2702 


2752 


2801 


2851 


2901 


2950 


60 


877 


3000 


3049 


3099 


3148 


3198 


3247 


3297 


3346 


3396 


3445 


49 


878 


3495 


3544 


3593 


3643 


3692 


3742 


3791 


3841 


3890 


3939 


49 


879 


3989 


4038 


4088 


4137 


4186 


4236 


4285 


4335 


4384 


4433 


49 


IV. 


o 


1 


3 


3 


4. 


5 


6 


7 


8 


9 


o. 



858 



APPENDIX. 



liOGARITHMS OP NUMBERS. 



jV. 


o 


1 


3 


3 


4. 


5 


e 


7 


8 


O 


I>. 


880 


94 4483 


4532 


4581 


4631 


4680 


4729 


4779 


4828 


4877 


4927 


49 


881 


4976 


5025 


5074 


5124 


5173 


5222 


5272 


5321 


5370 


5419 


49 


882 


5469 


5518 


5567 


5616 


5665 


5715 


5764 


5813 


5862 


5912 


49 


883 


5961 


6010 


6059 


6108 


6157 


6207 


6256 


6305 


6354 


6403 


49 


884 


6452 


6501 


6551 


6600 


6649 


6698 


6747 


6796 


6845 


6894 


49 


885 


6943 


6992 


7041 


7090 


7140 


7189 


7238 


7287 


7336 


7385 


49 


886 


7434 


7483 


7532 


7581 


7630 


7679 


7728 


7777 


7826 


7875 


49 


887 


7924 


7973 


8022 


8070 


8119 


8168 


8217 


8266 


8315 


8364 


49 


888 


8413 


8462 


8511 


8560 


8609 


8657 


8706 


8755 


8804 


8853 


49 


889 


8902 


8951 


8999 


9048 


9097 


9146 


9195 


9244 


9292 


9341 


49 


890 


9390 


9439 


9488 


9536 


9585 


9634 


9683 


9731 


9780 


9829 


49 


891 


*9878 


9926 


9975 


♦024 


0073 


0121 


0170 


0219 


0267 


0316 


49 


892 


95 0365 


0414 


0462 


0511 


0560 


0608 


0657 


0706 


0754 


0803 


49 


893 


0851 


0900 


0949 


0997 


1046 


1095 


1143 


1192 


1240 


1289 


49 


894 


1338 


1386 


1435 


1483 


1532 


1580 


1629 


1677 


1726 


1775 


49 


895 


1823 


1872 


1920 


1969 


2017 


2066 


2114 


2163 


2211 


2260 


48 


896 


2308 


2356 


2405 


2453 


2502 


2550 


2599 


2647 


2696 


2744 


48 


897 


2792 


2841 


2889 


2938 


2986 


3034 


3083 


3131 


3180 


3228 


48 


898 


3276 


3325 


3373 


3421 


3470 


3518 


3566 


3615 


3663 


3711 


48 


899 


3760 


3808 


3856 


3905 


3953 


4001 


4049 


4098 


4146 


4194 


48' 


900 


4243 


4291 


4339 


4387 


4435 


4484 


4532 


4580 


4628 


4677 


48 


901 


4725 


4773 


4821 


4869 


4918 


4966 


5014 


5062 


5110 


5158 


48 


902 


5207 


5255 


5303 


5351 


5399 


5447 


5495 


5543 


5592 


5640 


48 


903 


5688 


5736 


5784 


5832 


5880 


5928 


5976 


6024 


6072 


6120 


48 


904 


6168 


6216 


6265 


6313 


6361 


6409 


J6457 


6505 


6553 


6601 


48 


905 


6649 


6697 


6745 


6793 


6840 


6888 


6936 


6984 


7032 


7080 


48 


906 


7128 


7176 


7224 


7272 


7320 


7368 


7416 


7464 


7512 


7559 


48 


907 


7607 


7655 


7703 


7751 


7799 


7847 


7894 


7942 


7990 


8038 


48 


908 


8086 


8134 


8181 


8229 


8277 


8325 


8373 


8421 


8468 


8516 


48" 


909 


8564 


8612 


8659 


8707 


8755 


8803 


8850 


8898 


8946 


8994 


48 


910 


9041 


9089 


9137 


9185 


9232 


9280 


9328 


9375 


9423 


9471 


48 


911 


9518 


9566 


9614 


9661 


9709 


9757 


9804 


9852 


9900 


9947 


48 


912 


'' 9995 


♦042 


0090 


0138 


0185 


0233 


0280 


0328 


0376 


0423 


48 


913 


96 0471 


0518 


0566 


0613 


0661 


0709 


0756 


0804 


0851 


0899 


48 


914 


0946 


0994 


1041 


1089 


1136 


1184 


1231 


1279 


1326 


1374 


47 


915 


1421 


1469 


1516 


1563 


1611 


1658 


1706 


1753 


1801 


1848 


47 


916 


1895 


1943 


1990 


2038 


2085 


2132 


2180 


2227 


2275 


2322 


47 


917 


2369 


2417 


2464 


2511 


2559 


2606 


2653 


2701 


2748 


2795 


47 


918 


2843 


2890 


2937 


2985 


3032 


3079 


3126 


3174 


3221 


3268 


47 


919 


3316 


3363 


3410 


3457 


3504 


3552 


3599 


3646 


3693 


3741 


47 


920 


3788 


3835 


3882 


3929 


3977 


4024 


4071 


4118 


4165 


4212 


47 


921 


4260 


4307 


4354 


4401 


4448 


4495 


4542 


4590 


4637 


4684 


47 


922 


4731 


4778 


4825 


4872 


4919' 


4966 


5013 


5061 


5108 


5155 


47 


923 


5202 


5249 


5296 


5343 


5390 


5437 


5484 


5531 


5578 


5625 


47 


924 


5672 


5719 


5766 


5813 


5860 


5907 


5954 


6001 


6048 


6095 


47 


925 


6142 


6189 


6236 


6283 


6329 


6376 


6423 


6470 


6517 


6564 


47 


926 


6611 


6658 


6705 


6752 


6799 


6845 


6892 


•6939 


6986 


7033 


47 


927 


7080 


7127 


7173 


7220 


7267 


7314 


7361 


7408 


7454 


7501 


47 


928 


7548 


7595 


7642 


7688 


7735 


7782. 


7829 


7875 


7922 


7969 


47 


929 


8016 


8062 


8109 


8156 


8203 


8249 


8296 


8343 


8390 


8436 


47 


930 


8483 


8530 


8576 


8623 


8670 


8716 


8763 


8810 


8856 


8903 


47 


931 


8950 


8996 


9043 


9090 


9136 


9183 


9229 


9276 


9323 


9369 


47 


932 


9416 


9463 


9509 


9556 


9602 


9649 


9695 


9742 


9789 


9835 


47 


933 


* 9882 


9928 


9975 


♦021 


0068 


0114 


0161 


0207 


0254 


0300 


47 


934 


97 0347 


0393 


0440 


0486 


0533 


0579 


0626 


0672 


0719 


0765 


46 


935 


0812 


0858 


0904 


0951 


0997 


1044 


1090 


1137 


1183 


1229 


46 


936 


1276 


1322 


1369 


1415 


1461 


1508 


1554 


1601 


1647 


1693 


46 


937 


1740 


1786 


1832 


1879 


1925 


1971 


2018 


2064 


2110 


2157 


46 


938 


2203 


2249 


2295 


2342 


2388 


2434 


2481 


2527 


2573 


2619 


46 


939 


2666 


2712 


2758 


2804 


2851 


2897 


2943 


2989 


3035 


3082 


46 


IV. 


O 


1 


3 


3 


4 


5 


e 


T 


S 


9 


I>. 



APPENDIX. 



859 



LOGARITHMS OF NUMBERS. 



N. 


O 


1 


3 


3 


4. 


3 


G 


7 


8 


9 


I>. 


940 


97 3128 


3174 


3220 


3266 


3313 


3359 


3405 


3451 


3497 


3543 


46 


941 


3590 


3636 


3682 


3728 


3774 


3820 


3866 


3913 


3959 


4005 


46 


942 


4051 


4097 


4143 


4189 


4235 


4281 


4327 


4374 


4420 


4466 


46 


943 


4512 


4558 


4604 


4650 


4696 


4742 


4788 


.4834 


4880 


4926 


46 


944 


4972 


5018 


5064 


5110 


5156 


5202 


5248 


5294 


5340 


5386 


46 


945 


5432 


5478 


5524 


5570 


5616 


5662 


5707 


5753 


5799 


5845 


46 


946 


5891 


5937 


5983 


6029 


6075 


6121 


6167 


6212 


6258 


6304 


46 


947 


6350 


6396 


6442 


6488 


6533 


6579 


6625 


6671 


6717 


6763 


46 


948 


6808 


6854 


6900 


6946 


6992 


7037 


7083 


7129 


7175 


7220 


46 


949 


7266 


7312 


7358 


7403 


7449 


7495 


7541 


7586 


7632 


7678 


46 


950 


7724 


7769 


7815 


7861 


7906 


7952 


7998 


8043 


8089 


8135 


46 


951 


8181 


8226 


8272 


8317 


8363 


8409 


8454 


8500 


8546 


8591 


46 


952 


8637 


8683 


8728 


8774 


8819 


8865 


8911 


8956 


9002 


9047 


46 


953 


9093 


9138 


9184 


9230 


9275 


9321 


9366 


9412 


9457 


9503 


46 


954 


9548 


9594 


9639 


9685 


9730 


9776 


9821 


9867 


9912 


9958 


46 


955 


98 0003 


0049 


0094 


0140 


0185 


0231 


0276 


0322 


0367 


0412 


45 


956 


0458 


0503 


0549 


0594 


0640 


0685 


0730 


0776 


0821 


0867 


45 


957 


0912 


0957 


1003 


1048 


1093 


1139 


1184 


1229 


1275 


1320 


45 


958 


1366 


1411 


1456 


1501 


1547 


1592 


1637 


1683 


1728 


1773 


45 


959 


1819 


1864 


1909 


1954 


2000 


2045 


2090 


2135 


2181 


2226 


45 


960 


2271 


2316 


2362 


2407 


2452 


2497 


2543 


2588 


2633 


2678 


45 


961 


2723 


2769 


2814 


2859 


2904 


2949 


2994 


3040 


3085 


3130 


45 


962 


3175 


3220 


3265 


3310 


3356 


3401 


3446 


3491 


3536 


3581 


45 


963 


3626 


3671 


3716 


3762 


3807 


3852 


3897 


3942 


3987 


4032 


45 


964 


4077 


4122 


4167 


4212 


4257 


4302 


4347 


4392 


4437 


4482 


45 


965 


4527 


4572 


4617 


4662 


4707 


4752 


4797 


4842 


4887 


4932 


45 


966 


4977 


5022 


5067 


5112 


5157 


5202 


5247 


5292 


5337 


5382 


45 


967 


5426 


5471 


5516 


5561 


5606 


5651 


5696 


5741 


5786 


5830 


45 


968 


5875 


5920 


5965 


6010 


6055 


6100 


6144 


6189 


6234 


6279 


45 


969 


6324 


6369 


6413 


6458 


6503 


6548 


6593 


6637 


6682 


6727 


45 


970 


6772 


6817 


6861 


6906 


6951 


6996 


7040 


7085 


7130 


7175 


45 


971 


7219 


7264 


7309 


7353 


7398 


7443 


7488 


7532 


7577 


7622 


45 


972 


7666 


7711 


7756 


7800 


7845 


7890 


7934 


7979 


8024 


8068 


45 


973 


8113 


8157 


8202 


8247 


8291 


8336 


8381 


8425 


8470 


8514 


45 


974 


8559 


8604 


8648 


8693 


8737 


8782 


8826 


8871 


8916 


8960 


45 


975 


9005 


9049 


9094 


9138 


9183 


9227 


9272 


9316 


9361 


9405 


45 


976 


9450 


9494 


9539 


9583 


9628 


9672 


9717 


9761 


9806 


9850 


44 


977 


*9895 


9939 


9983 


♦028 


0072 


0117 


0161 


0206 


0250 


0294 


44 


978 


99 0339 


0383 


0428 


0472 


0516 


0561 


0605 


0650 


0694 


0738 


44' 


979 


0783 


0827 


0871 


0916 


0960 


1004 


1049 


1093 


1137 


1182 


44 


980 


1226 


1270 


1315 


1359 


1403 


1448 


1492 


1536 


1580 


1625 


44 


981 


1669 


1713 


1758 


1802 


1846 


1890 


1935 


1979 


2023 


2067 


44 


982 


2111 


2156 


2200 


2244 


2288 


2333 


2377 


2421 


2465 


2509 


44 


983 


2554 


2598 


2642 


2686 


2730 


2774 


2819 


2863 


2907 


2951 


44 


984 


2995 


3039 


3083 


3127 


3172 


3216 


3260 


3304 


3348 


3392 


44 


985 


3436 


3480 


3524 


3568 


3613 


3657 


3701 


3745 


3789 


3833 


44 


986 


3877 


3921 


3965 


4009 


4053 


4097 


4141 


4185 


4229 


4273 


44 


987 


4317 


4361 


4405 


4449 


4493 


4537 


4581 


4625 


4669 


4713 


44 


988 


4757 


4801 


4845 


4889 


4933 


4977 


5021 


5065 


5108 


5152 


44 


989 


5196 


5240 


5284 


5328 


5372 


5416 


5460 


5504 


5547 


5591 


44 


990 


5635 


5679 


5723 


5767 


5811 


5854 


5898 


5942 


5986 


6030 


44 


991 


6074 


6117 


6161 


6205 


6249 


6293 


6337 


6380 


6424 


6468 


44 


992 


6512 


6555 


6599 


6643 


6687 


6731 


6774 


6818 


6862 


6906 


44 


993 


6949 


6993 


7037 


7080 


7124* 


7168 


7212 


7255 


7299 


7343 


44 


994 


7386 


7430 


7474 


7517 


7561 


7605 


7648 


7692 


7736 


7779 


44 


995 


7823 


7867 


7910 


7954 


7998 


8041 


8085 


8129 


8172 


8216 


44 


996 


8259 


8303 


8347 


8390 


8434 


8477 


8521 


8564 


8608 


8652 


44 


997 


8695 


8739 


8782 


8826 


8869 


8913 


8956 


9000 


9043 


9087 


44 


998 


9131 


9174 


9218 


9261 


9305 


9348 


9392 


9435 


9479 


9522 


44 


999 


9565 


9609 


9652 


9696 


9739 


9783 


9826 


9870 


9913 


9957 


43 


W. 


« 


1 


3 


3 


4= 


3 


6 


^ 


8 


9 


£>. 



860 



APPENDIX. 



The Application of Logarithms. — The logarithm of a number is set down as a decimal, 
and addition of ciphers to numbers does not change the logarithm ; it is the same for 11, 
110, 1100, but the value of the number is established by figures to the left of the decimal 
point ; thus, if the number is among the units, the characteristic is ; if in the tens, 1 ; 
in the hundreds, 2 ; thousands, 3 ; tens of thousands, 4, and so on ; if the number is a 
decimal fraction and the first figure a tenth, the characteristic is 1, if hundredths 2, thou- 
sandths 3. 

Multiplication of two numbers is performed by the addition of their logarithms and 

characteristics, and finding the number corresponding to their sum ; thus, to multiply 119 

by 2760. 

Characteristic of 119 2, logarithm. 

" 2760 3, 



3284 



2-075547 
3-440909 
5-516456 
403 



401 



328440-1 



D = 132)53(401 
528 
200 
132 
~68 
As the characteristic is 5, the result is 6 figures of whole numbers. 
Division is performed by subtracting the logarithm of the divisor from that of the divi- 
dend, and finding the logarithm of the remainder for the quotient. But if the divisor is 
the larger, then the characteristic of the remainder is,r— . 
Thus, to divide 500 by 63008. 

Logarithm of 500 
Logarithm of 63000 = 4-799341 
8 X 69 



2-698970 



D = 



10 



55-2 



Logarithm of 63008 
Corresponding number -007935 = 



4.799396 



8-899574 

Numbers are raised to any power by multiplying their logarithm by the exponents, and 
roots are extracted by dividing the logarithm. Thus, to get the square of any number, its 
logarithm is multiplied by 2, for the cube by 3, for the 4th power by 4 ; in like manner, to 
obtain the square root of the number, divide the logarithm by 2 ; by 3 for ^ ; by 4 
fory. 

The roots of numbers are better expressed by fractional exponents, thus: Va by a!''^-, 
\^a by a s. 

The raising of numbers to different powers is extremely simple, by logarithms, when 
the numbers are whole numbers, but becomes somewhat more complicated when the num- 
bers are decimals. 



Thus, to find the 4th power of -07. 
Logarithm 



-07 



Number -00002401 
To extract the 4th root of -07 — 

Logarithm -07 
Add 2 to the characteristic to make it 
divisible by 4, and a positive 2 to the 
logarithm to balance it. 

Number -5143 



2-845098 


4 


8 3-380392 


5-380392 


2-845098 


2-2-845098 


4)4-2-845098 



1- 711274 



APPENDIX. 861 

The exponent of a root is often a decimal ; thus the ^'07 may be expressed by *07*"^ 



ogarithm -07 


2-845098 




•25 




4225490 




1690196 




•5-21127450 




•5-5 


umber -5143 


i-71127450 



Note. — In this example, '5 Is added to the resultant characteristic to bring it to an integer, and 
an equal positive amount to the logarithm to balance it. 

The same logarithm as by dividing by 4* and corresponding to the number -5143. The 
rule is to consider the logarithm as a plus quantity, and multiply by the exponent and the 
characteristic as minus, and, after similar multiplication, subtract it from the first product. 
When a characteristic has a minus sign (3), and it is to be subtracted, the sign is changed 
and added. 

Thus, to divide lO* by yV 

Logarithm 10* 1-00000 

rV 1 



Logarithm of 100- 2-000 

To divide yV Logarithm 1-00000 

Logarithm of 10' 1-0000 

To divide y^Vo Logarithm 3-00000 

by 100 2 

Logarithm of -00001 5 

Table of Reciprocals, pages 828 and 829. 

Use of Reciprocals. — Reciprocals may be conveniently used to facilitate computations 
in long divisions. Instead of dividing as usual, multiply the dividend by the reciprocal 
of the divisor. The method is especially useful when many different dividends are re-, 
quired to be divided by the same divisor. In this case find the reciprocal of the divisor, 
make a small table of its multiples up to nine times, and use this as a multiplication 
table, instead of actually performing the multiplication in each case. 



SCRAPS. 

It is good practice to collect, from the circulars of manufacturers, and from 
illustrated newspapers and magazines, varied illustrations of tools and machines, 
engineering structures, buildings, etc., and arrange them under their appropri- 
ate heads in scrap-books. They will be found very useful in designing, not 
only enabling one the more readily to make drawings, but to convey to the 
draughtsman the character and proportions of the design which is to be made. 
And those parts which are of common use and purchasable in the market can 
be readily arranged in position and executed more economically than from a 
new design. There is a saving in the matter of drawing, and also in the cost 
of construction. 

A proper combination and arrangement of parts which have served a pur- 
pose will afford material for a more practical and satisfactory design than can 
usually be made from attempts at originality. Knowledge of what has been 
done is economy in all labour. If the construction or machine can not be seen, 
its picture can supply its place, and its details can be studied at leisure ; and 
as the education of the eye is of essential importance to the draughtsman, let 
him see as much as he can practically, and at the same time acquire a good 
collection of scraps from which to design. There are few constructions from 
which something of education can not be drawn, parts if not a whole. 

In this view a small collection of scraps has been made pertinent to the 
book. Its page does not admit of the sizes which will be found in the illus- 
trated papers and magazines — the quarto will be found much more generally 
useful — and a library of such scrap-books will furnish material for a draughts- 
man which can not be found in any encyclopasdia. 



SCRAPS. 



863 




Compound Steam Cylinders. H. M. S. Spartan, 





Wrought-Iron Plates and Covers. 




Compressed- Air Locomotive, St. Gothard Tunnel. 



864 



SCRAPS. 




Three- Throw Crank. 




Weight, 25 tons 10 cwt 



SCRAPS. 



86.' 




Screw Propeller. 
Vessel, U<:iO gross tons. Engines, 130 nominal English horse-power 



866 



SCRAPS. 




Spherical Bearing. 




tO(S)a^iooo 



I. 



15 '^ 




Conventional Signs of Riveting. 







In the WilTcinson stoker the coal is fed mechanically through an inclined pipe on to 
the dead plate P and slides down upon the bars, which are hollow^ and set at an angle. 
The top of the bars is stepped, and ^w?/6re-shaped openings about J x 3 inches are pro- 
vided in each riser. The bars are carried at their ends on hollow boxes, and are 4-inch 
centres. For the feeding, adjacent bars move in opposite directions by a system of tog- 
gles driven by the stoker engine. 



SCRAPS. 



867 




The Coxe stoTcer consists of a travelling grate Avitli fire on its upper surface. The 
coal is fed by the motion of the grate at the front. There are four blast compartments, 
A, B, C, D, under the fire connected by dampers. The sides of the furnace are pro- 
tected by wrought-iron water backs, through which the water circulates under slight 
pressure. 




The Stirling Boiler consists of three upper steam-drums and a lower mud-drum. All 
the steam-drums are connected at the top, but the front and middle drums only are con- 
nected in the water space. Tubes, 3^" diameter; movement of flame shown by arrows 
around baffle plates. 



868 



SCRAPS. 




The Adendroth and Root Boiler was the earliest of its type on the market, and has 
been modified in its details since its introduction to meet necessities which were devel- 
oped by use. The section gives the latest form. The angles of the tubes, with the hori- 
zontal and the bafl^le plates beneath and around the tubes making a positive circulation 
of the flame, are of the original design, but longitudinal drums extend lengthwise over 
the tubes with a water circulation in the lower half toward the rear and downward 
by vertical "pipes to the lower ends of the tubes. On these vertical pipes there are 
two cross-drums — the intermediate one to receive the feedwater, the lower for a mud- 
drum. The long drums connect with the steam-drum ^^laced above and crosswise of 
them. 



SCRAPS. 



869 




870 



SCRAPS. 




Andover, Mass., Steam Pumping Plant, hy the Deane Steam Pump Co., HolyoTce, Mass. 
Diameter H. P. cylinder, 17''; L. P., 30". Pump plunger, 8f". Stroke, 30". Ca- 
pacity at 205' plunger speed, 1,205 gals, per minute. Average observed steam pressure, 
90-3; water, 139-79 ; in test trial, pump exceeded contract duty of 125,000,000. 




Reidler Valve, from LeavitVs Thames- Ditton Pump. (See page 365.) 



SCRAPS. 



871 




^ 



872 



SCRAPS. 




SCRAPS. 



878 



ss«Q 




k-3'95><--5?-->K-5'9"->K- 5'2"-^ ll'5l" --k-- 6'0"-->Ki-- e'0"--->k-4'/0'>i<3'o'W:3'o\?'sk 4'e'->* 

I K- ■ •! } SO 4i ••---} I- ! -^ I 

X--] 1 1 f- , eo/o"\ r ] ■ ^ 

§ ' ^ § s & & ^ 



^ 



;s^ 



Claso R. 



?3 /' 




^ 



k-7 2 --» 



/25i 



kfi^^-3'9|->|2/j5-5^'> 



O QfO 



f) Q^jin}^('^iM^^)W [^M>\ Si 




u-|; 



\<-5'5"-->k--5'/0'-)i<- 5'5'X e'6=:"----->^-4'ff"-^-4'S"--)K- 4'//"-:M- 4'/0"-->K^- 6's" --■A24k- 4'e"-> 



«^-f-«#-': 



27'i" 



k- v's'-^i 



->1 K-— /O 3 — ^ 



^" ^ 



N^ to 



Class "6" 



From the ''Engineering News.'''* 




Elliptic Spring apjplied to Car Truck. 



Bolster Spring. 



874 



SCRAPS. 




Third Avenue Elevated Railroad. 




Cable-car Orip. 
The accompanying figures rep- 
resent a side elevation and an end 
view respectively of a cable-car 



The gripping apparatus is 
shown in its open position, and 
the cable is therefore running in- 
operatively through it. When it 
is required to grip the cable it is 
merely necessary to pull over the 
lever A, whereupon the lever, its 
quadrant frame and shank attach- 
ments C, are raised up bodily 
about the fixed fulcrum of the 
link c, and the pair of rollers E, 
carried at the lower extremities 
of C, forces the jaws G close to- 
gether, and tightly grasps the 
cable between the concave dies or 
packing jiieces A. 



SCRAPS. 



875 




Derrick. 



876 



SCRAPS. 




^/ w- \^ >y 




4 "--• / -—' 

/ 

Canvas Bams. (From Trans. A. S. C. E.) 




Earth Portion of the Neio Croton Dam, showing RubUe Masonnj Core. 




Sweetwater Arched Masonry Dam, Southern California. 

The dimensions of this dam are : Thickness at base, 46 ft. ; thickness at top, 12 ft. ; 
height, 90 ft. ; radius of arch at top, 222 ft. The upper face batter is 1 to 6 to within 
6 ft. of the top, thence vertical ; on the lower face it is 1 to 3 for 28 ft. ; 1 to 4 for 32 
ft. ; thence 1 to 6 to the coping. In January, 1895, a freshet discharge flooded the waste 
weir and rose 32 inches over the parapet wall. The dam was subjected to this cataract 
action for a period of forty hours without injury. 








Bear Valley Arched Masonry Bam, California. 

This receives a sufficient support from the arch-action, and has stood since 1884. Its 
length at top is 270 ft., and its radius of curvature is 355 ft. At the centre the deviation 
of the dam from a straight line is about 27 ft., this being the versed sine of the sub- 
tended angle. It is 38 inches in thickness at top and 102 inches at a point 48 ft. 
below\ 



878 



SCRAPS. 



A-^'-&^'.. 







SCRAPS. 
BUILDERS' HARDWARE. 



879 




Mortise-Lock, cover off. 



Boxed Strike, Front. 




Front 

Sliding-door 

Lock. 






TTiumh- Piece, 



Knob and Rose. 



Escutcheons. 



880 



SCRAPS. 




Sash-Lifts 



Hook and Eye. 



Shutter- 
Knob. 



SCRAPS. 



881 



Examples of Ancie^it Hinges and Doors. 






\T/ron 



—^...-^^^^m !^, 




Safe Construction. 



v^ --^ x-- N^' >>- N^ >^ N/S>^JVXi^^V^N?x^^ 

V- >^ V^ N^ >,^- >^ >y^ N<i^ N>^V^rSl^>^^?>Jp?></^^^ 






^ 



Cast-iron Tread. 



57 



882 



SCRAPS. 




J Feet 



Plan, Section, and Elevation of a Wooden Mantel and Fire-Place. 



SCRAPS. 



883 




^'- ■ " ' " ' 




f/>///ff/f'Ul. 



Sectional Plan' of Grate and Flue. 
Details of Fireplace. 



884 



SCRAPS. 




Plan. 



Vestibule Doors. 



SCRAPS. 



885 





Examples of Inlaid Floors or Marquetry. 



886 



SCRAPS. 





Mailing. 



SCRAPS. 



887 




'^''^^r^''\;a' 



888 



SCRAPS. 






WM- 




f 






I MmI\ . 




r -Jfe^ii^ 







Enameled Tile. 





Terra Coita. 



SCRAPS. 



889 




^MM n P 



890 



SCRAPS. 




SCRAPS. 



891 




892 



SCRAPS. 




SCRAPS. 



893 




.#' ■ y^^M 




894 



SCRAPS. 




SCRAPS. 



895 




896 



SCRAPS. 




SCRAPS. 



897 




898 



SCRAPS. 




SCRAPS. 



899 




900 



SCRAPS. 




fc.^ 



SCRAPS. 



901 




902 



SCRAPS. 




SCRAPS. 



903 




904 



SCRAPS. 




■i>, R^-CATHEPRAL OF NEW-YORK 



SCRAPS. 



905 







:^ jL' -•^rw3zrt:i :*iiiiffli 



906 



SCRAPS. 





_:^Poi/7f of Sighf 



Perspectwe Diagram. (See page 714.) 



SCRAPS. 



907 




f^ 



908 



SCRAPS. 




SCRAPS. 



909 




/ 



910 



SCRAPS. 




SCRAPS. 



911 




Coney Island. 



912 



SCRAPS. 




"^ A'L \-?.ioW ^X^'^v 



Coney Island. Q^^ 



INDEX. 



Abendroth & Root water tube boiler, 868. 

Acanthus leaf or scroll, 863. 

Accumulator for water pressure, 412. 

Acoustics, general principles of, 630. 

Adiabatic curve, 206. 

Aerial perspective, 751. 

Air-chambers of pumps, 365, 411, 412. 

Air ducts to furnaces, area of, 640. 

Air, flow of, diagrams, 791. 

Air-lock, use of, 431 ; Barr-Moran, 435. 

Air taken into and expired from the lungs of a 

person, 636. 
Alloys and compositions, table of, 810. 

brass, Muntz metal. Babbit-metal, copper with 
various metals and proportions, 180. 

chart of strength. Prof Thurston, 180. 
Aluminum, properties of, 180. 
Anchor bolts, kinds and strength of, 253. 
Anchors for beams and walls, 559. 
Angle blocks in truss bridges, 499. 

irons, equal and unequal legs, dimensions of, 246. 
Angles, definition of, 4; sum of, in figures, 16. 
Angular perspective, example of, 714. 
Anthemion or honeysuckle, architecture, 683. 
Antimony, properties and use of, 179. 
Apartment houses, 609, 610. 
Apron, for protection of dam, 443. 
Apse, circular end of a church, 673 ; of basilicas, 

624. 
Arch and architrave mouldings, 679. 

bridges, parts and proportions of, 518. 

Melan concrete, Stockbridge, Mass., 522. 
Arched bridge in angular perspective, 716. 
Arches, complex, ogee, Tudor, trefoil, triangular, 
roundheaded, and pointed, 667. 

of the Minneapolis Viaduct, 520, 

table of dimensions of, 521. 
Artificial building material, 174. 
Ashti reservoir, for irrigation, India, 438. 
Asphalt lining for reservoirs, pavement with con- 
crete foundation, 476. , 
Axle and rolling friction, 199. 
Axles, car, 261. 

Babbit-metal for journal-boxes, 180. 
Babcock and Wilcox water tube boiler, 796. 
Ball-and-socket joint for flexible pipe, 405. 
59 



Ball valves, varieties of, 374. 

Baltimore Academy of Music, ventilation of, 623. 

heater, 641. 
Baluster and newel post, 579, 
Base and base mouldings, 680. 
Batter and offsets to retaining walls, 436. 
Beams, loading of, transverse stress, 235. 
Bear Valley arched masonry dam, 877. 
Beetaloo dam, concrete. South Australia, 444. 
Bell-cots, designs for, 673. 
Bell-trap for sink, 655. 

Belts, tight and loose, 287 ; transmission of power 

by diagram, 292 ; speed of, 292 ; width and 

thickness of, 293 ; leather, canvas, rubber, 293. 

Bevel gears, relative sizes of, 310 ; mortise, 316 ; 

projection of, 321 ; skew, 323. 

wheel, isometrical projection of, 699. 
Bismuth, properties of, in fusible alloys, 179. 
Blocks for running rigging, 333 ; dimensions of, 

table, 334. 
Blowers to improve chimney draft, 368. 
Blue print paper for reproduction, 731. 
Board and timber measure, 768. 
Body plans of vessels, wave lines, 546. 
Boiler, locomotive, details of, 394-396. 

setting, horizontal and tubular, 523. 

stays, forms of, 391. 

tubes, 775. 

corrugated fire-boxes, 395-397. 

Shapley upright, 396. 
Boilers, horizontal, tubular, proportions of, number 
of tubes, 389, 390. 

water tube, 395; Babcock and "Wilcox, 706; 
Heine, 797; Clonbrock, 804; Stirling, 867; 
Abendroth and Boot, 868. 
Bolts and nuts, forms of threads, 250. 
Bolts, strength of, 255. 
Boston Water Works conduit, 458. 
Boulevard, wide avenues, 474. 
Boundary lines on topographical drawings, 119. 
Bowtel moulding, simple fillet and rule joint, 681. 
Box car, elevation and plan of, 539. 

end of a locomotive rod, 351. 

girders, strength and thickness of steel, 245, 246. 
Braces and counter braces, 484. 
Bracing truss of wrought iron between wooden 
beams, 249. 



913 



914 



INDEX. 



Bracket for baluster, 583 ; ornamental, 886. 

Brass, composition of, 180. 

Brick arches, architectural, 557. 
pavements, laying of, 478. 
walls, bond of, 557. 
walls for foundations, 428. 

Bricks and brickwork, dimensions and varieties 
of, 174. 

Bridges, general principles of bracing, 483 ; Howe 
and Pratt trusses, 499 ; Howe truss highway 
bridge, 499-501 ; combination truss. Northern 
Pacific E. E., 502, 503 ; iron bridge, N. Y. & 
N. H. E. E., 503-505 ; Phoenix Bridge Company, 
505-507 ; Pratt truss from the Lima and Oroya 
E. E., 509, 510; highway bridge. King Bridge 
Company, 508-510 ; ferry landing bridge, 
512; Ei Vermont bridge, Lynchburg, 514; ele- 
vation of a pier and bridge over the Eio Galis- 
teo, N. M. and S. P. E. E., 515; arch bridges, 
518 ; viaduct at Minneapolis, 520 ; Cabin John 
Bridge, 521 ; dimensions of arch bridges, 521 ; 
Melan concrete arch bridge, 522; suspension 
bridge, 523. 
spaces between the ports of steam cylinders, 217. 

Bridge trusses, rules for, 498. 

Bridging of floor beams, 558. 

Bristol board, 54. 

Broad Street station, Philadelphia, Pa., 899. 

Brooklyn Water Works conduit, 458. 

Brushes for tints, 162. 

Builders' hardware, 879, 880. 

Building heated by steam, plan of, 649. 
in angular perspective, 713. 
materials, 168. 

Built columns, sections of, 232. 

Bulkhead wall. New York city, 419. 

Butler's pantry, water connections, 651. 

Butterfly valves, 375. 

Buttress, Norman, English, flying, 669. 

By-pass pipe to valves, 376. 

Byzantine and Saracenic doorways, 677. 
ornaments, 685. 

Cabin John Bridge, Washington conduit, 521. 
Cable-car grip, 874. 

Caisson, steel, 428 ; framing of wooden, 432. 
Caissons for piers, of the Poughkeepsie, of the 

Susquehanna bridge, 429. 
Cam punch and shear, 414. 
Cams, eccentrics, wipers, 343-346. 
Canal, representation of earth bank, 167. 
Canals, Erie, Delaware and Earitan, Chesapeake, 

and Canadian, 452. 
Cantilever beams for foundations, 416. 
Canvas dams, 876.* 
Cape Cod Bay, map of, 105. 

Capitals, Byzantine, Norman, Gothic, 667 ; dis- 
tinct parts, 680. 
Car-axles, M. C. B. A., 260. 
Caryatides, Atlantes, Hermes pillars, 664. 
Casement of French window, 578. 
Castings, crystallization in cooling, 178. 



Cast-iron balls, volume and weight of, 772 ; beams, 
forms of, 241 ; shafts, 258 ; connecting rods, 
354 ; girders, 492 ; pintle and joint details, 
566 ; pipes, standard weights of, 772 ; posts 
protected from fire, 564 ; stairs and carriages, 
584 ; treads and platforms, 881. 

Cast- and wrought-iron piles, 427. 

Catch basins for sewers, 471-473. 

Cathedral of Bourges, piers of, 667. 

Cedar-block pavement, 479. 

Ceilings, furring strips for, 560, 587. 

Cement-faced walks, 475. 

Ceinent, Portland, natural, sand, 176. 

Centennial Exhibition 1876, buildings of, 907. 

Central Park roads. New York city, 473. 

Centre plates of railway truck, 539. 

Centrolinead, 9. 

Chains, cables, couplings, 336. 

Chains, power transmission by, 299, 

Chain wheels with pockets, 335. 

Chamfer plane, moulded, 677. 

Channel beams, section and dimensions of, 245. 

Chimneys, drawing and description of, wrought- 
iron, 526-530. 

Chimney tops or cowls, 637. 

Chinese anchors, 429 ; capstan, 194. 

Chords, definition of, 3 ; scale of, 25. 

Churches, 900-906. 

Churches, theatres, lecture rooms, music and legis- 
lative halls, 620-631. 

Circles, 2; radius, diameter, chord, segment, sec- 
tor, quadrant, 3 ; tangent, 10 ; circles inscribed 
in polygons, 17 ; circle in a profile plane, per- 
spective of, 712. 

Circumference of a circle, diameter, arc, 766. 

Circumferences and areas of circles, tables of, 811- 
819. 

Cisterns and tanks of wood and wrought iron, 
461. 

Clearances of steam cylinder, 209, 369. 

Clevis, standard, 510. 

Clonbrock water tube boiler, 804. 

Clutch, cylinder-friction, 280. 

Coal, fire, and steam, representation of, 185. 

Coaling bins for locomotives, 497. 

Coff"er-dam, 417. 

Cohoes dam, 442. 

Coils, spiral, flat, of wrought-iron pipe, 403. 

Cold rolled wrought-ivon shafts, 178. 

Columns, cast-iron, wrought-iron. Phoenix, Key- 
stone,^ strength of, 230-232. 

Combination bridge truss, 503. 

Compacting sands for foundations, 417-419. 

Compasses, 44 ; portable, beam, 45 ; use of, 88. 

Composite beams, wood, iron-trussed, 249. 

Composition and design of figures, Dictionnaire 
Eaisonne de I'Architecture, 731. 

Compound steam engines, 209. 
steam cylinders, 863. 

Concrete base blocks, Department of Docks, New 
York city, 421. 

Concrete, lime, and bituminous cements, 176 ; 



INDEX. 



915 



floors, 566; sewer in situ, 468; walls for 
houses, 558. 

Conduit for electric and cable lines, 482. 

Conduits for water supplies, of wood, cast and 
wrought iron, of masonry for Brooklyn, Bos- 
ton, and New York city, 457-461, 

Cone pulleys, 286. 

Conic sections, orthographic projection of, 127. 

Connecting and coupling rods, 347-354. 

Connections of angles for 1-beains and Z-bars, 
566-568. 

Contours, representation of topography, 99 ; head 
of Franklin, 100. 

Co-ordinates of curvature for maps, table of, 115. 

Copper and brass rods, table of weights, 776. 

Copper in alloys, 179. 

Corbels and brackets, 681. 

Corliss steam engine, 219, 869 ; valve gear, 220. 

Cornice from the temple of Jupiter Stator at Kome, 
683. 

Cornices in plaster, 587. 

Corrugated boiler flues and furnaces, 392, 864. 

Cottage, rural style, 606, 902. ' 

Cottered joints, 347. 

Cotton spindles, friction in driving, 199. 

Country house, plan and elevation of, 599. 

Coupled I-beams, 242. 

Coupling and pulley combined, 283. 

Coupling rod, stub end of, 354. 

Couplings, of shafts, face, 273 ; sleeve, screw, cone, 
274; clamp, box, horn, 275; pipe, Oldham's, 
Hooke's universal, 277; clutch, 278; friction 
cone, Weston double friction cone, 279 ; elas- 
tic, Weston disk, 280; cylinder friction 
clutches, 281 ; magnetic coupling, spring hub, 
282. 

Cow houses, 633. 

Crank, path of, 211. 

Cranks and crank axles, proportions of, hand, 340, 
864. 

Crib dam in Colorado, 439. 

Crib dock, 422. 

Cross-head and guides of horizontal engine, 357. 

Crossing stones in streets, 475. 

Cross-section paper, 104. 

Croton conduits, old and new, reservoirs, 458. 459. 

Croton dam, earth portion of new, 876. 

Crowfoot to rafter, 488. 

Culvert, isometrical projection of, 702. 

Curbstones, 476. 

Curves, variable, adjustable, 40; elliptic, etc., 41. 

Curvilineal figures, area of, 767. 

Cycloid, 303; epicycloid, hvpocycloid, 304; area 
of, 766. 

Cylindrical surfaces, representation of, 58. 

Cylindrical valves, 372. 

Damper valve, 380. 

Damp stretchino^ of drawing papers, 54. 

Dams, Lake McMillan dam across the Pecos River, 
Colorado, 437; Ashti tank, India, 438; crib 
dam, Colorado, 439 ; Holyoke crib across the 



Connecticut River, 440; across the Croton 
River, 441 ; across the Merrimac at Lowell, 
442 ; across the Mohawk at Cohoes, 442 ; 
Beetaloo dam. South Australia, 443 ; canvas 
dams, 876; Sweetwater dam. Bear Valley 
dam, 877 ; movable dam. Great Kanawha, 878 ; 
section of the new Croton dam, 876. 
Dash-pot of a Corliss engine, 220. 
Dead points in crank motion, 212. 
Deafening of floors, 560. 
Deane steam pump at Holyoke, 870. 
Deck beams, 242. 

Density of gases and vapours, table of, 808. 
Derrick, drawings and details of, 875. 
Designing of a house, 591. 

Designs, enlarging and reduction of, cloth and 
wall ornatuentation, 60 ; ornamental, in line 
and tracery, 77-82. 
Diagram of comparison of United States and met- 
ric units, 71. 
velocity and path of water in a flume, 72. 
ditference between the charge per ton of transit 

on canal and i-ailroad, 73. 
annual product of pig iron in the (J. S., 74. 
railway time-table, 75. 
mortality record with range of temperature and 

humidity, 76. 
velocity of falling bodies, 196. 
expansions under pressures, 208. 
link movement, 223. 
strength of wrought -iron columns, 234. 
strength of wrought-iron beams, 248. 
strength of shafts, 260. 
horse power transmitted by shafts, 262. 
pressures on thrust collars, areas to resist, 273. 
horse power transmitted by belts, 292. 
horse power transmitted by ropes, 297. 
distance between pulleys in rope driving, 297. 
pitches and faces of gears and stress, 311. 
elbows, tees, crosses, and branches for wrought- 
iron pipes, 402. 
flow of water through pipes, 785-790. 
proportions of the human flgure, 729. 
flow of gas through pipes, 792, 793. 
wiring computer, 806. 
Diapering, architectural, 687. 
Dike breakwater, 426. 
Dikes of earth across salt marshes, 438. 
Dimensions of suspension bridges, table of, 523. 

walls. New York city building laws, 569. 
Diminishing glass, use of, 751. 
Discharge of weirs, table of, 782, 
Dining rooms, kitchens, and parlours, sizes of. 

591, 
Disengagement of large pulley from main shaft, 

277. 
Dished head for wrought-iron cylinders, 412, 
Distribution of water mains, 462, 
Dividers, hair, 44 ; three-legged, proportional, 45, 
Docks, bulkhead of New York Dock Department, 
420 ; crib dock west bank, New York harbour, 
423 ; Thames embankment, London, England, 



916 



INDEX. 



424 ; iron pier Coney Island, quay at Calais, 

427. 
Domes and vaults, 667. 
Doors, dimensions of, parts of, stiles, bottom rail, 

lock, parting, top panels, muntin, architrave, 

studs, jambs; sliding and folding; side and 

transom lights, 571-574. 
Doorways, circular-headed, 676 ; pointed, 677. 
Dormer windows, 678. 

Double-beat valves for steam and water, 372. 
Drawing-board, 36. 
Drawing pen, exercises with, 57. 
Drawing-table, 37. 
Drip or cap stones, 681. 

Driver or leader, and driven or follower, 302. 
Drums or wooden pulleys, 284. 
Dry rot, 169. 
Dynamic table, 770. 

Earth, shrinkage in refill, clay, glacier till, hard- 
pan, quicksand, 167. 

Eccentrics, 342 ; curve, drawing of, 344 ; strap with 
metallic disks, 349. 

Egg and dart, architecture, 683. 

Egg-shaped sewers, equivalent circular areas, table 
of, 468. 

Electrical units, 771. 

Electric conduit, 481. 

Electric lighting, wiring for, series, multiple, three- 
wire systems, 656. 

Electric switch, lamp socket, 806. 

Elevated Kailroad, Third Avenue, New York, 874. 

Elizabethan style, 689. 

Ellipse, construction of, 30 ; circumference of, 767. 

Elliptic spring applied to car truck, 873. 

Enamelled brick, 176 ; tile, 888. 

English basement house, 599. 

Entasis on columns, 658. 

Equilibrium, stable and unstable, 187. 

Erie Canal, locks of, 453. 

Evaporation, factors of, 800. 

Expansion bolts, 254 : expansion coupling, 271. 

Expansion, law of, for gases, Mariotte, 206. 

Expansive working of steam, table of, 800. 

Factor of safety, 229. 

Fan flush to water-closet, 664. 

Fang nut, 254. 

Fan in connection with radiators, 648. 

Fan-tracery vaulting, 668. 

Fifth powers, table of, 772. 

Fire brick, 175. 

Fireplaces and mantel, 584. 

Fireproof buildings, 563. 

Fireproof of old builders, 561. 

Fire-retarding constructions, 569-571. 

Flange connections for steam and water pipes, 

398. 
Flash boards on dams, 444. 
Flashings for roofs, 587. 

Flexible joints for submerged water mains, 405. 
Float trap for condensed water, 645. 



Flooring frame, headers, trimmers, tail beams, 558. 

Floor plan of steel girders and beams, 566. 

Floors, load on, 559, 560. 

Flows of air, 791 ; of gas, diagram, 792, 793. 
of water and air, comparison of, 794 ; of water in 
pipes and conduits, 784-790. 

Flues, stacks for house, 585 ; for every room, 636. 

Flumes, discharge of, 783 ; penstock to water 
wheel, 457. 

Fly-wheels, 408-411. 

Foliage, sculptured, 688. 

Foot-pan and bidet-pan, 652. 

Free-hand drawing, illustrations : proportions of 
the human frame, 729 ; half-tone of ecorche 
figures, 730 ; pen drawing of ecorche, 732 ; of 
Sandow, 733, 734 ; drawing of figures geomet- 
rically, 735-737 ; figures in skeleton lines and 
manikins, 738 ; pen drawing of Venus de Milo, 
739 ; pen drawings of male hands, 739 ; of legs 
and feet, of female hands and arms, 740 ; of 
children's hands and arms, of human head and 
face, 741 ; of Electioneer, 742 ; of cow, horse, 
donkey, 743; of hoofs and paws of animals, 
noses, 744 ; pen drawing of Southern sketch, 
745; pumping station, drawn with toothpick 
and splatter, 746 ; Salvini, Venetian fete on 
the Seine on stipple paper, 747, 748 ; pen draw- 
ings of Alexandre Dumas, Erik Werenskiold, 
749 ; wash drawings of flowers, 750 ; design in 
pen and ink by Fortuny, 752 ; and woodcuts 
of various sketches and paintings, 753-764. 

Foot-walks in cities, 474. 

Force, definition of, 186. 

Formula for the strength of wrought-iron beams, 
247. 

Foundations for structures, 415. 

Four-centred arch, proportions of, architecture, 669. 

Framing for stairs, headway, 581. 
of a caisson, 433. 

Freezing process for foundations, 435. 

Freight shed, of wood, for railroad, 494. 

Fret, guilloche, architectural ornaments, 683. 

Frictional gear, 331-333. 

Friction, coefficient of, Morin's tables, 197; of rail- 
way trains. Chanute, 200. 

Friction- wheels and friction-rollers, 199. 

Furring strips, 560, 587. 

Fusible alloys, 179, 810. 

Gases and vapours, density of, 808. 

Gas fitting's, service mains, 656. 

Gas, flow of, 792, 793. 

Gates, guard and canal, Cohoes, 444; Lowell, 447 t 

Holyoke, 449 ; Cheney, tubular gates at 

Windsor Locks, 449 ; Sudbury Kiver Conduit, 

451 ; lock gates, 453. 
Gate valves, Peet, Coffin, Pratt and Cady, 380. 
Gauging of streams, 784. 
Gearing, spur, bevel, and screw, 301. 
Geological map of the United States, 108 ; sections 

of the earth's crust, 109. 
Geometrical and flowing traceries, 675. 



INDEX. 



917 



Girders, cast-iron, table of strength of, 242 ; plate 

and lattice, 502 ; beams, iioor plan, 565. 
Glacier till, 167. 
Glass, representation and varieties of, transparency 

of, 183. 
Globe valves, dimensions of, 377-378. 
Glue, mouth, 54. 
Gold, properties of, 182. 
Gothic architecture, characteristics of, 665 ; roofs 

of churches, technical names, 627 ; towers, 

spires, 671. 
Governors, balls, shifting cams, 407. 
Grades of roads and highways, 474. 

of steel, 779. 
Granite block pavement, 475. 
Gravity, centre of, 186 ; velocity due to, 196. 
Green economizer in chimneys, 796. 
Greenhouses, designs for, 634. 
Greenwood Cemetery, contoured map of, 101. 
Grid, flexible, for indicator cards, 207. 
Groined arches in concrete, 563. 
Grooved pulley, shadow on, 157. 
Groove packing, test of, 365. 
Guides, cross-head, 357. 
Guide pulleys for belts, 289. 
Gutters of buildings, 586. 

Hard-pan, 167. 

Handrails of stairs, 582. 

Hangers, 265-268 ; hanger bolts, 255. 

Hearth and supports, 585. 

Heating by hot water, 645 ; direct and indirect 
radiation, 642-645. 

Heat and electrical unit, 771. 

Heavy bearings, friction of, 200. 

Height of stories of dwelling houses, 593. 

Heine water tube boiler, 797. 

Helix, orthographic projection of, 139. 

High-stoop city house, 599. 

Highway bridge, Pratt truss, 510. 

Hills, representation of, by verticals, 98 ; by con- 
tours, 99. 

Hinges and doors, ancient, 881. 

Hodgkinson, experiments of, on columns and 
beams, 98. 

Hoisting apparatus for small water gates, 447. 

Hollow brick, 563. 

Hood moulding, architecture, 681. 

Hooks, proportions of, 337. 

Hoosac Tunnel, construction and completion of, 
537. 

Horizontal thrust of arch, 519. 

Hospitals, 630. 

Hot-air furnaces, 638. 

House, designing of, 591. 

Housing for journals, 414. ♦ 

Howe truss, 499 ; highway bridge, 500. 

Hydrants, 382. 

Hydraulic press, 195; riveting machine, 412; tees 
and crosses, 404. 

Hydrometrical and marine survey, plots of, 105. 

Hyperbola, construction of, 34. 



I-beams, 241 ; table of dimensions and strengtli of 

iron and steel, 243, 244, 779. 
Idlers, or binders for belts, 291. 
Inches and sixteenths in decimals of a foot, table 

of, 770. 
Inclined forces, resultant of, 192 ; plane, principle 

of, 190. 
India ink, grinding, 56 ; slabs for, 57. 
Indicator cards of a steam engine, 206-210. 
Injector for boiler feed, 336. 

Inked thumb, for representing a background, 751. 
Inking in of topographical drawings, 118. 
Instruments, drawing, management of, 55. 
Internal gearing, 308 ; wheel driven by a pinion 

and driving a pinion, 325. 
Involute, construction of, 305 ; teeth, rack, and 

pinion, 308. 
Iron and plank pipes for the conveyance of water, 

457. 
Iron roofs, corrugated and framed, 490. 
Iron shoes and plates for braces and rafters of 

roofs, 488. 
Iron tank with inverted-dome bottom, 461. 
Isle of Wight, chart of, 106. 
Isometrical drawing, illustrations : Principles of 

cubic projections, curved lines, 698; practical 

application to projection of gear wheels, 699 ; 

pillow-block, water-closet cistern, culvert, 701 ; 

roof frame, plan and elevation of a school- 
house, ship construction, 704 ; elevation of a 

seaside resort, 705. 
Italian campaniles, 670; schools of architecture, 

677. 

Jack-rafters, dimensions of, 490. 

Jack-screw, 414. 

Janney car coupler, 215. 

Joinings for beams, 490. 

Joints, pipe, under heavy pressure, 399 ; steam 

pipe, 400. 
Journal bearings of box, M. C. B. A., 272. . 
Joy's valve gear, 226. 

Kentucky, geological survey of, 106. 
Keys, metal strips to secure hubs to shafts, 259. 
Kinzua Viaduct, 514. 
Kitchen range, boiler, and sink, 650. 
Knuckle joint, 347. 

Korting blower to increase draft in flues, 368. 
Kutter's formula for flow of water in pipes, graph- 
ically, 784-790. 

Landing bridge for ferry, 513. 
Lap and lead, slide valve, 217. 
Latitudes and departures, table of, 830-835. 
Lattice bars, spacing of, 232. 

deck bridge, bill of material, 505. 
Lead, properties of, 181. 

pipe, weights of, 780. 
Leather link belting, 301. 

packing for pumps and cylinders of hydraulic 
presses, 363. 



918 



INDEX. 



Legislative halls, requirements of, 630. 

Lettering, varieties of, triangles for, 62. 

Lever, principle of, 188 : hand and foot, 338 ; under 
inclined forces, 195. 

Lewis, for raising stones, 254. 

Lineal measure, table of, 768. 

Line, geometrical, 2 ; horizontal, vertical, parallel, 
5; irregular, plotted, 91; orthographic projec- 
tion of, 122. 

Lines of shafting, laying out of, 262. 
position and division, guide lines, 727. 

Link belting, 300. 
motion, 222. 

Lintels, 557. 

Liverpool water-works, Norton Tower, 461. 

Load, dead, live, 229. 

Lock nut, 251 ; washers, 256. 

Locks of canals, 453. 

Locomotive, driving-wheel of, 341 ; boiler for, 395 ; 
plan and elevation of frame of, 545 ; No. 999, 
N. Y. C. & H. E. E. E., 871 ; N. Y., O. & W., 
872 ; distribution of load, 873. 

Logarithms of numbers, table of, 845-859 ; applica- 
tion of, 860. 

Longitude, table of length of a degree of, 
116. 

Loop system of piping, 802. 

Louis Quatorze style, Lotiis Quinze style, 690. 

Lundell electric motor, 807. 

Machine and blacksmith shop, city, 614. 

foundations, 535. 
Machines, location of, 530. 
Malleable cast-iron, 178. 
Man-hole, 390; hand-hole covers, 863. 
Man-holes, for sewer, 470. 
Mansard roof, 585-586. 
Mantel and fireplace, plan, section, and elevation 

of, 882, 883. 
Mantels, flues, jambs, 584. 
Map projections, orthographic, stereograph ic, 

globular, Mercator's, conic, Bonne's, polyconic, 

110-115. 
Marine boiler of steamer Minneapolis, 395. 
Mariotte, law of, 206. 
Marquetry, examples, 885. 
Masonry, conventional signs of, technical terms 

for, representations of, 171. 
Masonry curbs sunk by water jets, 427. 

terms of, 171. 
Materials, earth and wood, characteristics and rep- 
resentation of, 167-171. 
Measures of surface, 768 ; of capacity, 769 ; cubic 

or solid, 770. 
Mechanical stokers, Wilkinson, Coxe, 866. 

work or effect, 201. 
Mensuration, 766. 
Mercator's projection, 112. 
Meridians, topographical drawing, 119. 
Metals, antimony, bismuth, copper, lead, tin, and 

zinc, properties of, 179 ; conventional signs to 

represent, 177 ; table of properties of, 809. 



Metres and United States units, graphic compari- 
son of, 71. 

Mill constructions, fire-retarding, 569. 

Miner's inch, 784. 

Morin, experiments of, on friction, and table of 
sliding and rolling, 197. 

Mortality and disease by graphics, 76, 77. 

Mortars, lime, cement, sand cement, 175, 176. 

Mortise wheels, proportions of, 316. 

Motion, 211, 228. 

Moulded timbers, 682. 

Mouldings, classical, Eoraanesque, Gothic, Nor- 
man, 679. 
Greek and Eoman, 588 ; stuck in wood, 589 ; 
perpendicular style of, 682. 

Mounting paper and drawings, varnishing, 55, 

Movable dam. Great Kanawha Eiver, 878. 

Muntz metal, 180. 

Mutules and guttse, 683. 

Nails and spikes, weight, table of, 777-778. 

Natural sines and cosines, table of, 836-844. 

Neutral surface under transverse stress, 240. 

New Haven, map of the harbour and city of, 101. 

New York city schoolhouse, a, 619. 

New York State canals, lock specification, 455. 

Nipple, close and shoulder, 403. 

Northern Canal'at Lowell, Mass., section of, 452. 

Nuts, various forms of, 251. 

Open fire in a tavern, 638. 

Orders of architecture, Tuscan, 659. 
Doric, 660. 
Ionic, 662. 
Corinthian and Composite, 664. 

Organs of churches, 627. 

Ornamental mouldings, chevron, billet, star, fir 
cone, cable, embattled, nail head, dog tooth, 
ball flower, serpentine, vine scroll, 686. 

Ornament, architectural, 682. 

Orthographic projection, 121 ; of a point, of a line, 
of a solid, of simple bodies, 123; conic sec- 
tions, 127; intersection of solids, 130; the 
helix, 139. 

Ox gall for drawing on the ordinary photograph, 
731. 

Packing for water-pumps, 362 ; of stuffing-boxes, 

370. 
Paints, 184. 

Palace of Diocletian, 665, 
Pan-closet, 653. 
Panels, ceilings in Italy, 562. 
Pantagraph, 51. 

Paper, drawing, tracing, transfer, parchment, he- 
liographic, 52. 

pencils, chalks, pens, ink, 727-728. 

profile and cross-section, 71. 
Parabola, construction of, 33 ; area of, 766. 
Parallel motions, 215, 
Parallelogram, rhombus, rhomboid, 16. 

of forces, 193. 



INDEX. 



919 



Parallels, 22; parallel ruler, drawing of, 39. 

Parapets, architectural, 6S7. 

Paris boulevard, 475. 

Partitions, framing of, 556. 

Passenger ear, elevations and sections of, 539. 

Patent Office requirements, drawings, registration, 

765. 
Pavements, granite- block, with and without con- 
crete foundation, 476 ; asphalt, 477 ; Salt Lake 
City, 478 ; brick, cedar block, 479. 
Pediments, brackets, railing, 886. 
Pelton water-wheel, 204. 
Pen-and-ink drawings, to clean, 751. 
Pencils, marks of, 1. 
Pen, drawing or right-line, 42; railroad, border, 

curve, 42 ; dotting, 43. 
Perspective drawing, planes of, 706 ; points of, par- 
allel and angular, 707 ; of squares, cubes, 
scales for, prisms, pavement, horizontal circle, 
in profile, cylinder, octagonal prism, building, 
interior of room, arch bridge, schoolhouse, 
cottage, stairs, reflection of objects in water 
projection of shadows ; capstan and winch, 725. 
Pews, length of, 627. 

Pier, iron curb of, with piles driven inside, 431. 
Piers of the Third Avenue Bridge, 431. 
Piers, Poughkeepsie Bridge, 430 ; pile, 497 ; trestle 
bent, 498; Kinzua Viaduct, 513; over Eio 
Galisteo, .N. M. and S. P. E. K., 513 ; Third 
Avenue Elevated Suburban, 515, 516 : stone 
pier of railroad bridge over Susquehanna at 
Havre de Grace, 516; of bridge across the 
Missouri at Bismarck, 517. 
Pile-pier, 497. 

Piles for foundations, 417 ; splicing of, 419. 
Pillow-block, isometrical projection of, 699. 
Pillow or plumber-block, standard and hangers, 

263. 
Pin-nut. standard, 510. 
Pinion driving a rack, 324. 
Pipe coupling, lead, 404. 
for driven wells, table of, 776. 
air-chamber, 650. 
Pistons of steam engines, and of pumps, 360. 
Piston-ring and packing, 362. 
Pitch of roof, 486. 
Plan and elevations of a small house, drawings of, 

548-553. 
Plane table, 84. 

Plan of church, transept, nave, and chancel, 625. 
Plastering, 176: furring of walls, 587. 
Plate girder, bill of material for, 503. 
Plates and covers, wrought-iron, 863. 
and wire, weights of ^vrought iron and brass, 
table of, 774. 
Platforms for foundations, grillages, 415. ♦ 
Plots, transferring of, 110. 

Plotting, scales used in, 83 ; traverse table used in, 

87 ; meridian assumed in, 89 ; irregular lines, 

91. 

Plough for electric conduit, 482. 

Plugs and caps for pipes, 403. 



Plumbing, 649. 

Pneumatic piles, 431. 

Point, geometrical, 2 ; pricking, 43 ; tracing, 44. 

Polygons, 14; irregular, 17; inscribed, 18; con- 
struction of, 19 ; similar, 26 ; regular, areas of, 
766. 

Pondage, rule of, for permanent mill powers, 436. 

Pop safety valve, 382. 

Porous brick tiles, 564. 

Ports of steam cylinders, 217 ; exhaust, 217 ; di- 
mensions of, 371. 

Principles of architectural design, 691. 

Printing frame for heliographic paper, 53. 

Proportions of the members of a roof, 489. 

Protractor, 21, 25, 50. 

Privies, water-closets, and outhouses, 593. 

Pulley, principle of, 190. 

Pulleys, 282 ; cast-iron, 283 ; plate, wrought-iron 
rim, split, pulley and coupling combined, 
wooden-plate pulley, drums, cone, fast and 
loose, 286 ; guide, 289; idlers or binders, 291. 

Pumping engine at St. Louis, 345 ; Leavitt pump, 
365 ; Worthington, 366 ; Deane pump, Hol- 
yoke, 870 ; Eeidler valves, to Leavitt's pump, 
870. 

Quicksand, 167. 

Quoin and pintal for heelpost of lock, 455. 

Eack gear and pinion, 301 ; involute teeth of, 309 ; 

rack driving a pinion, 325; pinion driving 

rack, 324. 
Eadiating surface for heating, 643. 
Eadiators, wall coil, box coil, wrought-iron tube, 

cast-iron loop, cast-iron pin, 647. 
Eail joints of the West Shore Eailroad, 480. 
Eailroads, standard sections of permanent way, 

480. 
Eails, standard, drawing and dimensions of, 481. 
Eailway rolling stock, 539-543. 

surveys, plots of, 103. 
Eanges, United States survey, 93. 
Eeciprocals, table of, 828 ; use of, 861. 
Eegister valve for steam, 381. 
Eeidler water valve, 870. 
Eenaissance style, 677 ; ornaments of. 688 ; Tii- 

cento and the Quatrecento, Cinquecento, 689. 
Eeservoirs for water-works, 459. 
Eetaining walls, 435. 

Eiver wall, Thames embankment, 422—426. 
Eiveted joints, lap, single, double, treble riveted, 

butt and angular connections, 383-386. 
Eiveting, conventional signs of, 866. 
Eivets for plate girders, 247 ; forms and dimen- 
sions of, 383 ; pitch of, 777. 
Eoads and highways, dirt, gravel, oyster shells, 

Macadam, Telford, 472, 473. 
Eolled I-beams, section of, 242. 
iron, table of weight of, 773. 
Eolling friction on roads, 200-201. 
Eomanesque and Byzantine architecture, 665. 
church or basilicon, 624 ; pillars, 667. 



920 



INDEX. 



Eoman order, characteristics of, 665 ; vaulting, 

668 ; school of architecture, 678. 
Eoofs, plans and sections of, 585. 
Koof truss, isometrical projection of, 702. 

parts of, 485 ; varieties of, 490. 
Eooms, proportions and distribution of, 589, 594. 
Kopes, transmission of power by, 293, 299. 
Eubber, properties and use of, 184. 

ring joint, 405. 

valves, 374. 
Eudder post and screw frame, 864. 
Eulers and triangles, 36-38. 
Eussian towers, architecture, 674. 

Safety valve, 381. 

Safe-vault construction, 881. 

Sag of rope in driving, 298. 

Salted paper, recipe for, 731. 

Sand cement, 176. 

Saracenic diapers, architecture, 685. 

Saturated steam, table of, 798. 

Scales, 25 ; application of, 27 ; forms of, plotting, 
46 ; diagonal, 47 ; vernier, 48 ; off-set, 92 ; on 
drawings for photography, 119 ; for lines in 
perspective, 709. 

School-houses, 616-622; isometrical view of, 702. 

Screw pile, 427. 

Screw, principle of, 191 ; the differential, 194. 

Screw propeller, 865. 

Screws, shades and shadows on, 157 ; wood and 
metal, 252 ; drawing of triangular and square 
threaded, 327. 

Scroll moulding, 681. 

Seasoning of timber, 168. 

Seats, desks, school furniture, 616 ; space occupied 
by, 624. 

Sector, drawing instrument, 49 ; area of, 766. 

Sewers, 466 ; of vitrified ware or cement, 467 ; 
Washington, Brooklyn, 466. 

Shade lines, 144. 

Shading and shadows, manipulation of, and meth- 
ods of tinting, 159-166. 

Shadows, perspective projection of, 721. 

Shafting, diagram of strength and length between 
bearings, 260. 

Shafts, cold-rolled, 178 ; wooden, iron, and steel 
257 ; cast-iron, plan and sections, 259. 

Sheds for wood or coal, 594. 

Sheet-iron arches for concrete floors, 563. 

Sheet-piling, 417. 

Ship construction, wave-line, isometrical projec- 
tion of, 704. 

Shipping measure, 770. 

Shoe for wooden curb of well, 428. 

Silver, properties of, 182. 

Sine, cosine, versed sine, secant, tangent, 21. 

Sink, cast-iron, 650. 

Skeleton construction of iron and steel, 565, 693, 
898. 

Skeleton frame of working beam, 354. 

Sketching from Nature, 745. 

Skew bevels, plan of, 323. 



Skew bridges, 520. 

Smith's process for coating pipes, 465. 

Sockets for wire ropes, 336. 

Soil or house-sewer pipe, 650 ; extension to roof, 
652. 

Soldering union, nipple, 403. 

Solders, composition and use of, 810. 

Solids, orthographic projection of, 122; intersec- 
tions, 130. 

Spaces occupied by check valves, table of, 376 ; 
globe valves, 378. 

Specials for water mains, 463. 

Specifications of pipe mains, Brooklyn, N. Y., 465. 

Specific gravity of liquids, earths, 808; woods, 
metals, and gases, 809. 

Speed of belts, 291, 292. 

Sphere, development of the surface of, 144 ; shade 
on, 155. 

Spberical bearing, 866. 

Spike frames, 555. 

Spiral, construction of, 35. 
riveted pipes, 776. 

Spire finials, 673. 

Spires, 900, 901 ; of English churches, 671. 

Splatter work in drawing, 751. 

Split pulleys, 283. 

Sponge, means of correcting errors in drawings, 
166. 

Springs, driving, equalizing bar, elliptic, bolster, 
873. 

Sprocket wheels, 300. 

Spur wheel, drawing of, 317; oblique projection 
of, 319. 

Spur wheels, parts of, 302, 306. 

Square, multiples of, 27 ; on the hypothenuse, 29 ; 
reduction of areas of, 30. 

Squares, cubes, and roots of numbers, table of, 820- 
827. 
divisions into triangles and octagons, 59. 

Stables, barn, carriage house, stable proper, floor 
of, 631. 

Stairs, 578; treads and risers, fliers and wind- 
ers, landing, headway, nosing, strings, car- 
riages, newel post, and baluster, 579 ; laying 
out, framing for, 581 ; hand rail, 582 ; wrought- 
iron strings and rails, cast-iron treads and 
risers, 584. 

Stalls, pitch of bottom and breadth of, 631. 

Stamp mill, 347. 

Standard for the support of shafting, 265. 

Standard I-beams, channels, A. A. S. M., 779. 

Standard rails, dimensions of, 481. 

Stanhope levers, 212. 

Stationary boilers, Philadelphia Water- Works, 392. 

Stay bolts, proportions of, 392. 

Steam and hot-water circulation as a means of 
heating, 641. 

Steam cylinders, 359. 

Steam engine, horizontal frame, 356; Corliss, 219, 
220, 869. 

Steam heating, arrangement of mains and returns 
for, 642. 



INDEX. 



921 



steam, its application, 205. 

Steam jacket, 346. 

Steam piston packing, 347. 

Steam valve, plan and section of, 379. 

Steel, homogeneous metal, 178 ; from pure wrought- 
iron, 179. 

Steelyard and platform scales, 194. 

Step for an upright shaft, 269. 

Steps for stairs, breadth of, treads of, and height 
of I'isers, 579. 

Stiffeners for the webs of plate girders, 247. 

Stipple paper or clay board, 751. 

Stirling boiler, 867. 

Stirrup irons for wooden beams, 559. 

Stokers, mechanical, Wilkinson and Coxe, 866. 

Stones and masonry, conventional signs of, 171. 

Stones, granitic, argillaceous, sand, lime, charac- 
teristics of, 173. 

Stop chamfering, 682. 

Stores and warehouses, 612, 614. 

Stoves, open and close, 638. 

Straight edges, 37. 

Strength of men and animals, 202. 

Stress, tensile, compressive, shearing, transverse, 
tortional, 230, 234. 

String courses, 680. 

St. Sophia, roof of, 667. 

Studs for house framing, 556. 

Stuffing boxes and glands, packings for, 369. 

Stylus, tracing point, 44. 

Suspension bearings, 270. 

Suspension bridges, table of dimensions, 523. 

Sulphur, characteristics of, 182. 

Summer house, 887. 

Surfaces, development of, cylinders and cones, 141. 
in shade, tinting, 160. 

Sweetwater arched masonry dam, 877. 

Table of railway curves, 1C3. 
co-ordinates of curvature for maps, 115. 
length of degree of longitude, 116. 
sliding and rolling friction, Morin, 198. 
safe loads of cast-iron columns, 231. 
safe loads of Phoenix columns, 232. 
safe central load of yellow-pine beams, 239. 
strength of wrought-iron I-beams, 243. 
strength of steel beams, 244. 
strength of steel box girders, 245. 
dimensions and weights of Z-bars, 247. 
dimensions of bolts and nuts, United States 

standard, 256. 
proportions of sunk keys, 260. 
distances between bearings of shafts, 261. 
horse power transmitted by shafts. 262. 
horse power transmitted by wire ropes, 298. 
pitch, diameters, and teeth of gears, 312. 
relation of diametral to circular pitch, 313. 
radius of arcs of circles for gear teeth, Adcock, 

313-315. 
sizes of sheaves and blocks, 334. 
capacities and sizes of hooks, 337. 
dimensions of eyes and cranks, 339. 



Table of space occupied by check valves, 376. 

dimensions of globe valves, 378. 

dimensions of single-riveted lap joints, 384. 

dimensions of double-riveted lap joints, 385. 

dimensions of treble-riveted lap joints, 386. 

number of tubes in horizontal and tubular boil- 
ers, 390. 

proportions of stay bolts for flat surfaces, 392. 

dimensions of pipe flanges and cast-iron pipes, 
399. 

dimensions of WTOught-iron tubes and coup- 
lings, 401. 

diameters and thicknesses of cast-iron pipes, 
with lead for joints, 463. 

size of egg-shaped sewer and circular equiva- 
lents, 468. 

dimensions of standard rails, 481. 

dimensions of parts of roofs, 489, 490. 

dimensions of a wrought-iron roof, 492. 

material for plate-girder bridges, 503. 

material for lattice-girder bridges, 505. 

arch bridges, dimensions of, 521. 

suspension bridges, dimensions of, 523. 

loads for floors, 559. 

theatres and their dimensions, 630. 

polygons, chords, verticals, and areas, 766. 

lineal measures and of surfaces, 768. 

capacity, liquid and dry measui-e, 769. 

weights, apothecaries', Troy, avoirdupois, dy- 
namic, 770. 

cubic or solid measure, 770. 

inches and sixteenths in decimals of a foot, 770. 

fifth powers, 772. 

weight of cast-iron balls, of cast-iron pipes, 772. 

weight of rolled iron, 773. 

weight of wrought-iron and brass plates, 774. 

wrought-iron welded tubes, of boiler tubes, 775. 

weight of pipes for driven wells, spiral pipe, 
light pipe for leaders, and air pipes, 776. 

weight of copper and brass rods, 776. 

weight of rivets, spikes, 777 ; of cut nails, ot 
iron nails, of telegraph wire, 778. 

weight of beams and channels of the A. ot 
A. S.M.,779. 

weights of lead pipe, of a cubic foot of water, 780. 

discharges of water over weirs, 782, 783. 

equalizing the diameter of pipes, 791. 

volume and weight of dry air, 794. 

saturated steam, 798, 799. 

expansive working of steam, factors of evapora- 
tion, 800. 

mils and ohms, 807. 

specific gravities of gases, of liquids, of earths, 
etc., 808. 

woods and metals and properties of, 809. 

circumferences, diameters, and areas of circles, 
811-819. 

squares, cubes, and roots of numbers, 820-827. 

reciprocals, 828, 829. 

latitudes and departures, 830-835. 

natural sines and cosines, 836-844. 

logarithms of numbers, 845-859. 



922 



INDEX. 



Tanks, lead-lined, coated with asphalt varnish, 
650. 

Taps for city mains, sizes of, 649. 

Telegraph and telephone lines, table of sizes of 
wire, 778. 

Teredo and Limnoria, 169. 

Terra cotta, 175, 888. 

Thames-Ditton pump, 365. 

Theatres, dimensions and plans of, 6S0. 

Thrust bearings for screw-propeller shafts, 272. 

Thumb-nut, 338. 

Timber frames, forms and dimensions of parts, 
555. 

Timber, sections, conventional signs, seasoning, 168. 

Tin, properties of, 182. 

Tinting and shading, manipulation of, 159; pre- 
paring colours for, 164. 

Tires of wagons, 201. 

Titles of maps and charts, 69. 

Toggle-joint, 195. 

Topographical drawing, conventional signs of, 95 

Topography, coloured, 116; conventional colours 
of, 117. 

Torsional stress, 234. 

Tower for water tank in New York city, 674. 

Towers, Eomanesque, 670. 

Traceries, perpendicular, leaf, flamboyant, Sara- 
cenic, and Moorish, 676. 

Tracing cloth, 52. 

Trains, time-table of, 74. 

Trammel, ellipsograph, 31. 

Transverse stress of beams, 235. 

Traps, antisiphoning, 653 ; for sewer pipes, 655. 

Trestle bent of elevated railroad, 498. 

Trestles for drawing-table, 37. 

Triangles for drawing, 37. 

Triangle and square, use of, 22. 

Triangles, isosceles, equilateral, right-angled, simi- 
lar, 26. 

Triple compound steam engine, 210. 

Trundle pins or wheels, 301. 

Truss bridges, effect of unequal loading, 484; 
wooden, Howe, Pratt, 499. 

Trusses for roof and floor of a gymnasium, 493. 

Trussing of a beam by struts and tension rods, 250. 

T-square, 38. 

Tubes, weight of wrought-iron welded, table of 
775. 

Tubs set for washing, 651. 

Tudor arched doorway with hood mouldings, 677. 

Tunnels and principles of timbering, 535. 
Turbine, Fourneyron, Boyden, and Jonval, 204. 
Turn-buckle or swivels, 255. 
Turn-table, 510. 
Tusk tenons, 558. 

United Electric Light and Power Station, 801. 

United States Survey, ranges of, 93. 

Unit of force and space, 201. 

Upright boiler, Shapley's, 396. 

Upset of bolts, 255. 

Urinals, 656. 



Valve diagrams, steam, 218. 
gear, Corliss, link, Joy's, Walschaert, 219-228. 
motion of St. Louis pumping engine, 345. 
motion, slide valves, 216. 

Valves, automatic, double-beat, 372 ; poppet, disk, 
rubber, flap, ball, air, pump, loaded flap, but- 
terfly, check, 377 ; safety, 381 ; controlled by 
hand, 376 ; cocks, bibs, plain, hose, compres- 
sion, air, stop and plug cocks, globe, straight, 
angle and cross, damper, 380; regulator, 
steam-hammer, hydrant, 383. 

Variable speed gear, 333. 

Vaulting, fan-tracery, 668. 

Vaults and domes, 667. 

Venetian school of architecture, 678, 

Ventilation and warming, 634. 
by compressed air in French exhibition, 368. 

Vessels in launching, friction of, 198. 

Vestibule doors, 884. 

Villa, Italian, 607. 

Wagon tires, 473. 
Wall girders, position of, 568. 
Walls, dimensions of, New York city laws, 569. 
Walls in masonry, 556 ; concrete, 555. 
Walschaert valve gear, 226. 
Wash-basins, sizes of, 651. 
Wash drawings,''749. 
Washers, table of, 256. 
Water-back, 650. 

Water-closets, appliances of, 652; basins, 655; cis- 
tern, isometrical projection of, 700. 

washout, hopper, pan, flap, siphon-jet, 652-654. 
Water, diagram of path and velocity in flume, 72. 

flow of, 781. 

jet for the sinking of piles, 426. 

lines of a ship, 546. 

mains, dimensions, and weight of, 462, 463. 

pipe of sheet iron, 460. 

power and its applications, 203. 

weight of a cubic foot of, at different tempera- 
tures, table of, 780. 

wheels, tub, flutter, breast, overshot, undershot, 
Scotch, turbines, Pelton, 203, 204. 
Wave-line principle of ship construction, 545. 
Waves of sound in halls of audience, 623. 
Weather-cocks, 673. 
Weaving-room, location of looms, 531. 
Wedge gearing, 332. 
Weight of gas mains, 472. 
Weights, apothecaries', Troy, avoirdupois, 769. 

of material, 177. 
Weirs, table of discharge of, 782. 
Westinghouse engines, steepled compound, 804. 
Weston-Capen double-friction clutch, 279. 
Wheel and axle, principle of, 189. 
Whitworth's quick return motion, 213. 
Winch, centrreboai'd, 724. 
Windlass, 724. 

Window frames, sashes, blinds, 573-578 ; dimen- 
sions of, 577. 
Windows and doors, examples of, 889-897. 



INDEX. 



923 



Windows and doors, Byzantine, Romanesque, Nor- 
man, Lancet, traceried, 674. 
Wire nails, weight of, 778. 

ropes, sockets for, 336. 
Wiring computer, Carl Hering, 806. 
Wooden plate pulley, 285, 
shaft in plan and section, 258. 
steps for sliafts, 271. 
packing for pump pistons, 363. 
Woods, characteristics and use of, 169 ; white pine, 
Southern pine, Canadian red, Norway, and 
silver pines, spruce, hemlock, ash, chestnut, 
black walnut, butternut, hickory, beech, live 
oak, Avhite oak, bass, poplar, white wood, 
cedar, locust, elm, maples, 170. 
Working beam, 354. 
Working strain of one-inch rope, 296. 



World's Fair buildings, 908-910. 
Worm and worm wheel, 330 ; the Albro, 328. 
Worthington steam pump, 366. 
Wrought-iron columns, strength of, 233. 

diagram of, 234. 

rim pulleys, 283. 

crank connections of river-boat engines, 354. 

pipe connections, 400. 

tubes and couplings, dimensions of, 401. 

curb pier with inside piles, 431. 

trestles for bridges, 514. 

chimney stack, 530. 

string and rail for stairs, 583. 

spikes, table of weight of, 777. • 



Zinc, properties and uses of, 182. 



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Cong^ress. 
Hon. J. R. SOLEY, formerly Assistant Secretary of the Navy. 
EDWARD ATKINSON, LL. D., Ph. D. 
Col. T. a. DODGE, U. S. A. 
Col. GEORGE E. WARING, Jr. 

J. B. Mc MASTER, Professor of History in the University of Pennsylvania. 
CHARLES DUDLEY WARNER, LL. D. 
Major J. W. POWELL, Director of the United States Geological Survey and the Bureau 

of Ethnology. 
WILLIAM T. HARRIS, LL. D., United States Commissioner of Education. 
LYMAN ABBOTT, D. D. 

H. H. BANCROFT, author of " Native Races of the Pacific Coast." 
HARRY PRATT JUDSON, Head Dean of the Colleges, University of Chicago. 
Judge THOMAS M. COOLEY, formerly Chairman of the Interstate Commerce Com-" 

mission. 
CHARLES FRANCIS ADAMS. 

D. A. SARGENT, M. D., Director of the Hemenway Gymnasium, Harvard University. 
CHARLES HORTON COOLEY. 
A. E. KENNELLY, Assistant to Thomas A. Edison. 
D. C. OILMAN, LL. D., President of Johns Hopkins University. 
H. G. PROUT, Editor of the Railroad Gazette. 

F. D. MILLET, formerly Vice-President of the National Academy of Design. 
F. W. TAUSSIG, Professor of Political Economy in Harvard University. 
HENRY VAN BRUNT. 
H. P. FAIRFIELD. 

SAMUEL W. ABBOTT, M. D., Secretary of the State Board of Health, Massachusetts. 
N. S. SHALER. 

Sold only by subscription. Prospectus, giving detailed chapter titles and specimen 
illustrations, mailed free on request. 



New York: D. APPLETON & CO., 72 Fifth Avenue. 



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The Warfare of Science with Theology. 

A History of the Warfare of Science with Theology in Christendom. 
By ANDREW D. WHITE, LL. D., 

Late President and Professor of History at Cornel] University, 
In two volumes. 8vo. Cloth, $5.00. 

" The story of the struggle of searchers after truth with the organized forces of ignorance, 
bigotry, and superstition is the most inspiring chapter in the whole history of mankind. 
That story has never been better told than by the ex- President of Cornell University in these 
two volumes. ... A wonderful story it is that he tells." — London Daily Chronicle. 

" The two noble volumes, packed with rare historical data and printed and clothed in the 
best style of modern typographical art, more than realize the promise of the earlier essays. 
The book is an invaluable record of the difficulties that biblical superstition has interposed to 
the advance of physical knowledge; a treasury of information concerning the progress of 
modern science, gathered with the most assiduous and patient research during a quarter of 
a century in the libraries not only of this country, but of Europe also. The painstaking in- 
vestigations and rare erudition it embodies, the broad field it has so diligently delved and 
gleaned, and the reverent Christian spirit it manifests, make it a monumental work, destined 
to become a classic authority on the subjects it has made its own henceforth. The previous 
works in this field, such as Dr. Draper's ' Conflict of Religion and Science,' and Professor 
Shields's ' Final Philosophy,' must yield pre-eminence to President White's admirable history. 
The new book is far fuller and more accurate in its narrative, clearer in its treatment, and 
more judicious in its judgments." — The New World, London. 

" It is a complete survey of the whole field of battle. . . . The chapters are full of striking 
interest. The author of these volumes shows that the warfare of science has never been with 
religion but only with old errors that were confounded with-it, and that the Eternal Verities 
become the more clear and sure as the ancient guesses which have been confounded with 
them are cleared finally away." — London Daily News. 

" Such an honest and thorough treatment of the subject in all its bearings that it will carry 
weight and be accepted as an authority in tracing the process by which the scientific method 
has come to be supreme in modern thought and life." — Boston Herald. 

" It is graphic, lucid, even-tempered — never bitter nor vindictive. No student of human 
progress should fail to read these volumes. While they have about them the fascination of a 
well-told tale, they are also crowded with the facts of history that have had a tremendous 
bearing upon the development of the race. " — Brooklyn Eagle. 

" A conscientious summary of the body of learning to which it relates, accumulated during 
long years of research. . . . A monument of industry." — New York Evening Post. 

" So interesting as to enchain the attention at once and keep it enchained. Concise as a 
history of the universe could be made, tabulated so that instant reference to a particular bit 
of history, theory, or biography may be had, it will be valuable as a lexicon relating to 
religious controversy." — Chicago Times- Herald. ' 

" Dr. White knows much of science and he knows much of theology. But his point of 
view is that of a historian. It is this fact which gives the greatest value to his book. We 
have whole libraries of controversial works dealing with the relations between science and 
theology, but they have been written either by scientists or theologians. President White 
occupies the impartial position of the historic scholar, who has no prejudices against the 
truth of science and no hostility toward the truth of rehgion." — N. Y. Review of Reviews. 

"The work is a masterpiece of a mind as devoid of wanton iconoclasm as of moral 
cowardice. It is a definite statement of where the best thinkers of the world now stand in 
the religio-scientific conflict. It is clear, honest, brave, and must be given a place among the 
great books of the year." — Chicago Tj'ibune. 

" This is and will continue to be one of the great books of the world, like Thucydides's 
' History of the Peloponnesian War.' So long as Science and Theology retain their place in 
human interest, this history of the conflict of ages between them will exert its attraction and 
read its lesson. It is a great book." — The Outlook. 



New York: D. APPLETON & CO., 72 Fifth Avenue. 



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